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In today's episode of The Quiz, we're testing your knowledge on everything from the depths of our planet's oceans to the mathematical constants that shape our understanding of science. Can you answer these? Deep Blue: Which ocean is the largest in the world? Science Class: What is the boiling point of water at sea level in degrees Celsius? Advanced Algebra: What is the name of the mathematical constant that represents the base of natural logarithms? Play. Share. Listen, with Actor and Comedian, Jeff Foxworthy. Learn more about your ad choices. Visit podcastchoices.com/adchoices

[powerpresss] My co-host Ken Suzan and I are welcoming you to episode 175 of our podcast IP Fridays! Today's interview guest is Bruce Dearling, patent attorney and partner at Hepworth Browne in the UK, and we talk about how non-technical features must be considered when assessing inventive step of patents at least according to recent decisions of the UK supreme court and the Unified Patent Court. Profile of Bruce Dearling UK Supreme Court Emotional Perception AI Limited UPC Abbot vs Sinocare But before we jump into this interesting interview, I have news for you: On May 20, 2026, the Swiss Federal Council adopted the fully revised Patent Ordinance, which will enter into force on January 1, 2027, together with the revised Patent Act. In the future, the Swiss Federal Institute of Intellectual Property will prepare a mandatory search report for each application; applicants can choose between a partially examined version and a full examination that assesses novelty and inventive step. The full examination costs an additional 300 Swiss francs, and renewal fees will increase by a total of eight percent over the 20-year term. On May 19, 2026, Asus entered into a licensing agreement with the Wi-Fi multimode patent pool managed by Sisvel, thereby ending all ongoing infringement proceedings. Sisvel bundles standard-essential patents in the pool from, among others, Atlantia, ETRI, and Mitsubishi Electric. On May 18, 2026, the UPC Local Chamber in Düsseldorf rejected Align Technology's application for a preliminary injunction against its Chinese competitor Angelalign. Angelalign may continue to sell its clear aligners within the UPC jurisdiction. Our partners Dirk Schulz, Ulrich Storz, and Wanze Zhang, together with Arnold Ruess, successfully represented Angelalign. The U.S. Patent and Trademark Office (USPTO) announced midweek that, since October of last year, it has invalidated or is seeking to invalidate approximately 10,500 trademark applications and registrations in eleven administrative orders. Reasons include forged attorney signatures and the fabrication of non-existent filing requirements. This stems from ongoing abuse of the U.S. trademark system, primarily by non-U.S. applicants, which can lead to conflicts with validly registered trademarks for legitimate businesses. On May 12, 2026, the British Court of Appeal overturned a lower court decision that would have required Nokia to grant interim licenses for video coding patents. The court found that Nokia's license offer to the Taiwanese manufacturers Acer and Asus had already been made on RAND terms. In May, the U.S. Department of Justice (DOJ) filed a brief in the ongoing Corteva v. Inari litigation, expressing antitrust concerns regarding certain patent practices in the field of plant breeding. This marks the first time the agency has actively intervened in a biopharmaceutical patent dispute with implications for seed innovations. Episode 175 of the IP Fridays podcast was a conversation I will not forget quickly. My guest Bruce Dearling, partner at Hepworth Brown in the UK and a patent attorney for 36 years, took a case through every level of the British court system up to the Supreme Court and, in doing so, fundamentally changed patent law for AI inventions in the UK. The case is called Emotional Perception, and its effects reach well beyond British borders. Below I summarize the key points from our conversation. The full episode is available at IP Fridays. A. What Is the Emotional Perception Case About? The underlying invention concerns artificial neural networks. Specifically, it relates to a method of closing what is called the semantic gap at the output of a neural network. That sounds abstract, but the idea is straightforward: a neural network always produces an output that does not fully correspond to what a human would actually expect or feel. Closing that gap brings the system closer to human perception and human expectations. Bruce Dearling drafted this application himself and filed it at the UK Intellectual Property Office (UKIPO). The Office rejected it as excluded subject matter, characterizing it as essentially a computer program as such. The legal basis for that rejection was the Aerotel decision from 2006. The case then went to the High Court, which found in favor of the applicant. The Court of Appeal reversed that decision. Then the UK Supreme Court stepped in and changed everything. B. The Aerotel Test and Its Flaws Since 2006, the Aerotel test had been the standard British method for assessing whether an invention falls within the excluded categories under patent law. It was a four-step approach: construe the claim, identify the actual contribution the invention makes to human knowledge, ask whether that contribution falls solely within excluded subject matter, and finally check whether the contribution is technical in nature. The problem Dearling described in our conversation is that Aerotel reverses the logical order of the analysis. You start with the contribution and only then ask about the exclusions under Article 52 EPC. The UK Supreme Court described Aerotel in its judgment as “unsound law” and overturned it. The EPO’s Technical Boards of Appeal had previously called Aerotel “disingenuous,” which at the time led to a public dispute between the British courts and the Boards. With the Emotional Perception ruling, that conflict has now been resolved in favor of harmonization with the EPO. C. What the UK Supreme Court Decided The Supreme Court made two central findings. First, the exclusion of computer programs “as such” is overcome as soon as a claim includes any piece of hardware. It does not matter whether that is a processor, a memory module, or any other component. The threshold is deliberately low. Dearling described this as the “any hardware” approach, which aligns fully with the EPO’s position following G1/19. Second, and in Dearling’s assessment the more important finding: when assessing inventive step, the invention must be considered as a whole. The Court introduced what it called an “intermediate step,” an analytical stage in which the interactions between all features of a claim are examined before the question of inventive step is addressed. Non-technical features cannot simply be struck out if they contribute to the overall technical effect of the invention. D. Inventive Step: The Intermediate Step This is the heart of the judgment. In EPO practice, Dearling said, it happens regularly that examiners strike through features they consider non-technical and thereby fail to assess the invention’s inventive step correctly. A recent Technical Board of Appeal decision, T 1249/22, already criticized this approach: a claim directed at a technical solution to a problem can be patentable even if the underlying problem is non-technical in nature. Dearling recalled a remark made by a Board of Appeal member at a hearing he attended years ago: “We understand that examining divisions can operate with a degree of mental laziness and that it’s too easy to throw too many things out of the basket when considering the issues of inventive step.” That quote stayed with him because it names a structural problem that the intermediate step now addresses directly. The British method for assessing inventive step is the Pozzoli test, which differs from the EPO’s problem-solution approach. The Supreme Court explicitly retained Pozzoli because the problem-solution approach, in its view, is structurally infected with hindsight reasoning: you already know the invention, you work backwards to formulate an objective technical problem, and then you ask whether it would have been obvious for the skilled person to arrive at precisely that solution. Dearling sees this as a source of unfairness toward genuine inventions. E. Alignment with the Unified Patent Court In April 2025, the Court of Appeal of the Unified Patent Court issued a decision in Abbott v. Sinocare (APP_000000901/2025, judgment of 17 April 2025). Dearling pointed out that this decision uses language and reasoning strikingly similar to the UK Supreme Court’s Emotional Perception ruling of February 2025. That is significant because the UPC is bound neither by UK courts nor by the EPO. The overlap suggests voluntary convergence. Dearling reported a conversation with a person close to the EPO, whom he did not name, who used the word “permissive” to describe the UK Supreme Court’s approach and indicated that the EPO might move toward it. Whether and how quickly that happens remains to be seen. What is clear is that the UPC, as the new European patent court, is setting its own standards, and the question of how to handle non-technical features in inventive step assessment is now being asked at multiple levels simultaneously. F. Implications for the EPO and Practice The EPO is not directly bound by the ruling. It is an administrative body, not a court. Dearling is nonetheless optimistic that change is coming. On one hand, external pressure is building: when the UK Supreme Court and the UPC articulate similar principles, convergence becomes hard to resist. On the other hand, Article 27.1 TRIPS requires all contracting states to make patents available in all fields of technology. Examiners routinely striking non-technical features from AI claims and rejecting them on that basis sits uncomfortably with that obligation. For the underlying application in the Emotional Perception case, the ruling has a pointed consequence. The Supreme Court did not grant the patent itself; it referred the matter back to the UKIPO for reconsideration under the intermediate step. The Office’s subsequent response was, in Dearling’s words, unconvincing. He suspects the Office is attempting to reintroduce the Aerotel test through the back door. As a last resort, he has not excluded a judicial review, a procedure that does not simply challenge the substantive decision but holds the Comptroller General of Patents to account for whether the Office is deliberately circumventing the Supreme Court’s direction on the intermediate step. That is, as Dearling put it, “a nuclear option,” but one he would not rule out if the evidence in the file already suggests the Office is in contempt of court. There is also an international dimension. Singapore’s Intellectual Property Office launched a public consultation shortly after the ruling, asking whether Singapore should adopt the Emotional Perception approach into national law. That is British soft power operating in real time within the Commonwealth. G. Three Takeaways for Patent Practitioners At the end of our conversation I asked Bruce Dearling to distill the most important practical points. His first takeaway: make sure the claim contains hardware. This applies not only to UK and European applications but is simply good drafting hygiene. Without hardware in the claim, the application remains exposed. The second takeaway concerns the description. Anyone filing an AI invention needs to explain clearly which function is achieved by which piece of hardware, circuit, or software. Not as boilerplate, but as a complete technical account that describes the real-world effects. Dearling’s experience is that practitioners who write the claim first and fill in the description afterward run into trouble. The third takeaway emerged from the conversation itself: how the EPO assesses inventive step for AI inventions is not a settled question. It is worth following the development of UPC case law and any shifts in EPO practice closely. Anyone advising on AI patent applications today needs to know these arguments. H. Conclusion The UK Supreme Court’s Emotional Perception ruling is not a British footnote. It has declared the Aerotel test dead, introduced the intermediate step that brings non-technical features back into the inventive step analysis, and set off a convergence movement that is already visible at the UPC and still pending at the EPO. For everyone working in AI patent practice, whether in prosecution, examination, or counseling, this ruling is required reading. Rolf Claessen: Our interview guest on IP Fridays podcast is Bruce Dearling. He has been in the IP field and a patent attorney for 36 years and is partner at Hepworth Brown in the UK. Thank you very much for being on the podcast. Bruce Dearling: My pleasure, Rolf. Thank you for inviting me. Rolf Claessen: All right. We just met at the INTA annual meeting in London. And you talked about the UK Supreme Court case where you were involved. And the core questions were whether non-technical features would be considered when assessing inventive step of patents. Can you briefly summarize this case? Bruce Dearling: It’s a bit more than that. It started — I actually wrote the case. And I prosecuted it through the patent office. The patent office rejected the case for being excluded subject matter. So pretty much the excluded subject matter provisions in the UK are nearly identical. They’re as near as practical to the language of the EPC, so those of the European Patent Office — Article 52.2. But again, they apply as such. The actual technology relates to artificial neural networks. And the invention related to a very clever way of what is termed closing the semantic gap at the output of the neural network. So that means that in a neural network, there is always a discrepancy between the output of the neural network in terms of what it’s telling you you should be thinking essentially, and what reality is. So if you can close the semantic gap, then you align the neural network or the artificial intelligence system to better reflect human knowledge or human reactions and human expectations. So that’s really what the invention is about. There’s no point in going into too much detail with it — that’s the way it is. It’s very clever. So the UKIPO rejected this because they said it was essentially a computer program excluded from patentability as such. And they used a decision which is called Aerotel, which has been around since 2006. And that decision has caused considerable consternation and tension between the EPO Technical Boards of Appeal and the UK courts. Aerotel was described as being essentially disingenuous by the EPO Technical Board of Appeal. And the UK courts pushed back and said, you don’t know what you’re talking about. So that’s where it fell apart. So that’s where they rejected it for essentially being a computer program as such, possibly with a bit of business methods thrown in as well. But let’s leave that for the time being. So the case then went to the High Court and at the High Court, we won. The judge said, actually, it’s not a computer program. Neural networks aren’t computers. They’re not programs themselves. There’s more to them than that. And the invention as claimed is not excluded from patentability as such. The UKIPO obviously weren’t very happy about that because they liked their Aerotel case and so they appealed it. And they appealed it on several grounds, including a new one, which was that it was a mathematical method. The Court of Appeal decided that the UKIPO was right and that we were wrong, so we lost the case. So we then went to the Supreme Court. Well, actually, they denied us an ability to go to the Supreme Court. The court said no appeal. We went — actually, no, I think there is a bigger issue here — because we realized, or I realized at that point, that the work that we were doing was much broader than this. It requires real consideration of what an invention is at a fundamental level. So not only exclusions, but how inventive step is applied. And these issues were built into the case from the very beginning. And they sort of — I wouldn’t say crept up on the court as we went through — but they became more and more prominent to the extent that ultimately, when we made an application to the Supreme Court, the Supreme Court went, yeah, we’ve got some issues here. We want to hear the full arguments on why this is not excluded from patentability, why Aerotel is potentially bad and how we more or less try to align ourselves with the European Patent Office. So that’s essentially what happened. And the Supreme Court hearing was last July. It took them the thick end of eight months to come out with a decision, which was issued in early February, at which point the entire legal landscape in the UK changed because they said we were right. The Patent Office doesn’t know what they’re talking about. Aerotel is bad. It’s unsound. That’s what they described it as — unsound law. It needs to be removed and we’re going to harmonize with the European Patent Office. So before I — I’m just going on a bit of a rant here, standing on my soapbox telling you what you already know. But the Aerotel test essentially was — it was a four-step test, past tense. So you firstly had to construe the claim. That’s pretty straightforward. Then you actually had to identify the actual contribution. This is what they said — identify the contribution. Really in this aspect, you’re asking what, as a matter of substance rather than form, the inventor has added to human knowledge. So that’s what they said the contribution was. And then they said, the next step in Aerotel was to ask, well, does that contribution fall solely within the excluded subject matter field or realm? And then they said, well, if you get through that question, then you check the actual contribution or the alleged contribution to see whether it’s technical in nature. So that’s the Aerotel test as it was. And what the Supreme Court in their unanimous final decision said was that Aerotel at best jumbles up the order. It reverses the logical order of the analysis by starting with the contributions and then addressing the Article 52 exclusions. And then finally it goes back to what the technical nature of the invention is about. So they really went, no, we don’t like any of this stuff. It’s bad, it’s stupid, it puts the cart before the horse. So, in the intervening period between finding the case and actually seeing it progress all the way to the Supreme Court, we obviously had the G1/19 decision from the EPO Enlarged Board. And they basically said that they are going to validate any hardware as the approach. And that’s essentially what the UK also went with. The UK Supreme Court said we’re going to say that the threshold of patentability — or the exclusion to patentability — is simply overcome by the inclusion in a claim of any piece of hardware, whether it’s a processor or a piece of memory or whatever. It doesn’t matter. Any hardware makes the invention a technical invention. So it’s a really low threshold to consider. And they then went, well, actually, if we now align and harmonize with the European Patent Office sensibly, then we need to look at how we assess inventive step, which is the other thing that we raised with the Supreme Court. In fact, we probably raised it at other times and in all the other instances as well, but it came to a head at the Supreme Court. So the Supreme Court then also went a bit further and said, well, actually, whilst we do like the global approach to assessing inventive step for all fields of technology — whether it’s chemistry or biotech or electronics or software or AI — we use a test called Pozzoli. So that isn’t problem-solution. We don’t like problem-solution. We think it’s not codified in the European Patent Office. It’s just a mechanism that the EPO has come up with to try to objectively assess inventive step. We don’t particularly think that’s appropriate. We like our approach called Pozzoli. That’s it. So we’re going to say with Pozzoli, however, in order to actually understand — particularly in the context of mixed inventions having technical and non-technical features — it’s necessary for the examiner to undertake the so-called intermediate step, where you have to look at the interactions between features within a claim. The invention is defined by the claim. That’s what the act says. That’s what everyone understands. It’s the invention defined by the claim. So you look at the claim features and then you have to understand the interactions that take place. And even if they are between technical and non-technical features, if they bring about an overall technical effect when you consider the invention as a whole, then your claim should be good and you can assess it for classical inventive step. So that’s really where we’re at. There’s a lot to unpack there already. It’s probably a podcast in its own right, but that’s the positive history of where we’re at. And I can keep going if you wish me to for a second and talk about why I think this is — we’ll just contrast it quickly with the problem-solution approach at the EPO and COMVIK. So for inventions in the computer-implemented field, they use COMVIK and the problem-solution approach. The Supreme Court said, as I said, they don’t like problem-solution. I think the problem-solution issue is that it is also inherently pre-baked with hindsight because you have to look at the invention and then step back and exclude those features which are common. And then you formulate a problem based on the function that the claim achieves. And then you’re asking whether or not it would be obvious for a skilled person to arrive at the claimed invention, having been given that hindsight-developed problem. So COMVIK is not great by any means. And we know from a practical perspective that examiners are only too willing to look at a claim and simply line through features which they believe are non-technical, whereas they don’t actually look at the interaction of those features in the context of the claim as a whole. There is also a decision — very recent one actually, about a year ago — T 1249/22, where the Technical Board of Appeal told the examiners and the examining division, you cannot do this. It’s okay to have a claim directed towards an invention in a non-technical field, as long as the invention is directed to a technical solution of that problem. I think it’s paragraphs 11 and 12 or 10 of that decision that are worth looking at. But they’re saying that in all fields of technology, it doesn’t matter as long as the technical solution is about technology — therefore, you should be able to obtain a patent as long as there is a realistic and appropriate technical effect. Be careful actually, Bruce — I don’t mean technical contribution, I mean technical effect. There’s a reason for that distinction. Rolf Claessen: The non-technical features are nevertheless used to assess inventive step in the UK now after this decision, right? Bruce Dearling: Yes, that is the intermediate step. The decision says you must look at the invention as a whole. It’s the important thing. There are a couple of issues that arise out of this. The first one is that you have to provide context for the invention. The Supreme Court never provided any specific guidance about how we deal with the intermediate step or what the exact test is, which is in some respects fine. It seems to be fairly clear that you just have to engage your gray matter — your neurons — to work out what is going on in the real world. And once you work out what’s going on in the real world, what the benefits are, then you look at whether or not the actual implementation of the invention fundamentally has a technical flavor to it, which is not just coding, not just simple coding, but it does something smarter. There’s a real technical impetus. There’s a technical effect. Now that actually brings me onto something I’ve postulated or said. I think the intermediate step will follow something like what I’ve termed the holistic character test, which essentially is: work out what’s going on in the real world. Then once you’ve worked out what’s actually being achieved, what the benefits are, what the invention’s concerned with, then you ask the question, how am I achieving it technically? And how is there a technical effect? How does the technical effect arise? That brings out a couple of issues. The first one is that it’s actually about the word “contribution” because it depends on how the word is used. So if you look at head note one in COMVIK, it uses the word “contribute” — how the non-technical feature contributes to the invention. So that’s an additive inclusive concept. The UK IPO historically, and arguably at the moment today whilst they’re trying to retrain their 400 examiners — which this has caused them to have to do — their idea of contribution is this backward-looking concept. So technical contribution and technical effect, I think — although we mix them up and interchange them — are distinct. Technical contribution: you’re looking backwards. Technical effect is what you look at when you look forward into what’s going on. So this is subtle — it’s really subtle, but it’s important. And once you realize that you are actually looking for the technical effects, then you’re on much safer ground. It’s much more objective in terms of the assessment. This might be somewhat contentious, because it’s the way I’m looking at this, but I’ve been working on this a long, long time and thinking about it for probably decades, worryingly so. So technical contribution and technical effects are probably not the same, where they are interchangeably used to mean the same thing within existing decisions. Rolf Claessen: And in the beginning you said, now that Aerotel is dead basically, it’s more harmonized with the EPO’s approach. But what I take from the discussion now is that maybe — especially in view of the problem-solution approach — it’s not fully harmonized with the EPO’s approach at the moment, right? Or did the UK Supreme Court get something wrong, or was that a desired outcome from your point of view that this is not so completely harmonized with the EPO? Bruce Dearling: Well, the EPO — the any-hardware solution is fully harmonized, no doubt. So it’s now a question of inventive step under Article 56 or Section 3 of the Act. The EPC nowhere mandates the use of problem-solution. And we know that there are many different ways of actually assessing inventive step, including the concrete elaboration test from last year and problem-of-invention approaches. So there are numerous ways of assessing inventive step. So the UK says, “Pozzoli — we like Pozzoli.” Interestingly, I had a discussion with someone I probably can’t mention. They’re saying that the UK approach may actually be more permissive now. It might even influence how the EPO operates. So they may move away from COMVIK towards more of a Pozzoli approach, which basically says this: You identify the notion of the skilled person — step one. You identify the common general knowledge of that skilled person — step one B. You identify the inventive concept of the claim in question, where you construe it if you can’t work out what it is. You then identify what the differences are. And then you ask the question, is it obvious to the skilled person, given knowledge of the common general knowledge? This is entirely not artificial because, as I said beforehand, when you look at problem-solution, you are formulating a problem by backtracking from what the claimed invention is to a situation where you say, well, these are the common features and I’m going to project a problem to try and solve. Now that is already tainted with hindsight reasoning. It’s not safe, it’s not thoroughly objective. There is an inherent problem with this which sees good inventions cast by the wayside. Although it’s a preferred mechanism, it’s not fully baked. There are situations where examiners are inherently lazy, or they just simply use something like the requirements specification argument, which is just factual. It just demonstrates that they can’t be bothered to actually argue it properly or think about what the invention is. Sorry to any examiners listening to this, but this is just my personal view, that sometimes there are problems. I’m reminded of a quote from an EPI hearing I was at a long time ago, where the Legal Board of Appeal member said: “We understand that examining divisions can operate with a degree of mental laziness and that it’s too easy to throw too many things out of the basket when considering the issues of inventive step.” Now that one has stayed with me because you think — did someone just say that? And the answer is yes, they did. But it just goes to show that there is some tension between the TBA and the examining divisions, and they don’t always get it right. Rolf Claessen: So there might be a small difference now between the UKIPO’s future approach of assessing inventive step and the EPO? Bruce Dearling: Yeah, it might do. But the other interesting thing here — and thank you for pointing this out, I hadn’t entirely caught up with it, I’ve been traveling beforehand and I missed some of the UPC case law. So the UPC case law — in, was it — yeah, we talked about that. Rolf Claessen: Yeah. There was a decision in April, Abbott versus Sinocare. Bruce Dearling: Yeah, 901 of 2025. So a Court of Appeal decision from the UPC. It was APP_000000901, I believe, 2025. Decision 17th of April, hearing 27th of March. The UPC is not bound by — it’s a court. The European Patent Office is not a court, it’s an agency that administers and looks after the administrative rule of law. So the fact that this decision came out from the UK Supreme Court in February, and you see almost identical language used in the UPC decision, suggests that there is some alignment here, or some convergence in thought. Now, whilst the UPC decision also references G1/19 and uses problem-solution, there is enough — you’ve got to bear in mind that high-level courts do look at each other’s decisions. And this is really a question of influence and the desire to converge. So the fact that they’ve done this at this time is quite interesting. Again, I can’t quote someone directly from the EPO, although I would love to. They were saying — at a very high level — and they used the words “converge UPC practice towards UK Supreme Court practice on interpretation of the law.” So this may actually be happening in real time. Again, it would be wrong to actually refer to anyone by name, but it’s an observation that when I looked at the case, I can see why this is going ahead. And I can see why the judiciaries — they want to maintain independent judicial controls. They won’t reference the UK Supreme Court decision, not least because we’re not in the UPC. But if you look at the arguments in sections 106 and 107 of the UK Supreme Court’s Emotional Perception decision and head note one, you go — wow, this is very close. Rolf Claessen: Very close and nearly identical wording. Yeah. And the UPC also now uses non-technical features for assessing inventive step. Is that a problem for the EPO that has historically been aggressive in throwing out non-technical features for inventive step analysis? Bruce Dearling: Well, I think they really need to get to the situation — I don’t know — this holistic character test that I’m sort of proposing, where you really have to think about what the invention is achieving, and then look at how it’s technically being achieved. And then if you look at that again in the context of that other decision I mentioned — T 1249/22 — it says something like, in the case of an invention that amounts to a technical implementation of a non-technical method, provided the non-technical method does not contribute to the technical character of the invention. The board validated the approach of identifying the non-technical method and then goes through and says it’s patentable. There are decisions like this which suggest that examining divisions have to give it a bit more thought, because the Technical Board will realize that to satisfy the WTO requirements — which pretty much everyone is bound by — Article 27.1 TRIPS, which requires that you protect all fields of technology. And that means whether it’s data processing or business methods, because business methods can be patentable so long as they are implemented on a technical basis. That essentially seems to be what T 1249/22 is saying, although it doesn’t explicitly say “allowing business methods.” The exclusion is only “as such.” So does this decision, in combination with the Supreme Court case and the movement of the UPC, say: well, actually, let’s look at this properly? It requires objective assessments, not just superficial “let’s strike through that feature because I don’t like it, it looks non-technical.” Rolf Claessen: So are you hopeful that the EPO is adjusting and will reshape their case law in view of the UPC decision and the UK Supreme Court decision? Bruce Dearling: It’s a bit unfortunate that the corresponding UK case at the EPO was dropped by the applicants, because it was heading towards an examination hearing at the examining division. It would have gone to the TBA, and I’m sure it would then have gone from the TBA to the Enlarged Board. I’m pretty sure that’s the case. There is another case from the same client which will probably argue the same thing because the specs are almost identical. It’s just lagged in time. So is it going to change? I hope so, because I think the EPO have got it wrong — more often than not in this field. Well, maybe not more often than not — they get it wrong more times than they should do. Would I like to see it changed? Yes, I would, because I want the examiners to actually think about the technology as opposed to just — oh, it’s not — I don’t want to engage the gray matter. That serves no one. That doesn’t serve technology. That doesn’t serve industry. These patent rights are there for a reason. They are property rights. I’m referring to the award of the 2025 Nobel Prize for Economics — they are a core driver for society’s development. So the 2025 Nobel Prize was for something called creative destruction — the replacement of old technology with new — and it’s based on the patent paradigm. So all this stuff is coming to a head now. It’s just a question of how quickly the EPO actually catch up, and maybe they have something to catch up on. It’s just understanding that the examiners have to start to think. As I said, we’ve got the issues at the UKIPO where they’re going to have to retrain 400 examiners. Rolf Claessen: Yeah, right. Bruce Dearling: The Emotional Perception case wasn’t granted by the Supreme Court. They referred it back to the patent office for consideration under the intermediate step. So the patent office produced a response that I would describe as — I’d say arguably — not well reasoned, which I’ve filed the response to, which basically says you don’t really know what you’re talking about. What really worries me a bit is that I think they’re trying to introduce the Aerotel case through the back door. It’s backsliding. It’s a mechanism for trying to apply it in a different way or a different context, which would be wrong. I think they believe that the applicant will appeal this if they get a bad decision — they will appeal it back to the courts again via the High Court, Court of Appeal, Supreme Court route. I say maybe not. I say maybe the client will file what they call a judicial review, which is a nuclear option. That’s when you actually hold the Comptroller General of Patents to account and get full discovery of whether or not there’s internal documentation showing that they are deliberately circumventing the direction of the Supreme Court on the intermediate step. This is basically holding them to account and saying: if you’re not applying the intermediate step appropriately, you are in contempt of the law. So judicial review is a really serious thing to do, but it’s certainly something I would not exclude from consideration. We’ll see what happens. It’s not saying we’re just going to go through the courts and make them decide on this. We’re going to say you’re wrong. And there’s already enough evidence in the files to suggest that they are probably in contempt of court and they’re not applying the intermediate step appropriately. They may not know any better at the moment — they need to be guided — but the consequences for them are potentially severe. Rolf Claessen: I have another question for you. You were the instructing attorney — do you think the decision was perfect? What argument that you made was the most underappreciated by the court? And where do you think the judgment got it wrong, or was it all perfect? Bruce Dearling: No, it got 90% or 95% correct. The intermediate step is right. That’s the most important thing in the decision — it’s the intermediate step. The any-hardware thing — that’s logical, that makes some sense — but if people say “if the any-hardware rule is the important bit,” no it isn’t. It’s the intermediate step. That’s the important thing. Where do they go wrong? I think they went wrong because — and you’ve got to bear in mind that unlike German courts, I’ve got to be careful about how I express this — generally, as I understand it, and correct me if I’m wrong, but the judiciary in Germany on patent cases are generally more technically able. They’re normally technically qualified. I look at the Supreme Court justices and the Court of Appeal justices — we had one who was a humanities undergrad, one was a chemist. Good luck with trying to argue complex artificial neural network technologies, which are difficult even for me to understand. And I’ve been working in the field. They’re hard to understand. They require real understanding, real appreciation. They could say, well, actually we don’t need to look at the technology — but frankly, if you’re looking at the statutes and exclusions to patentability and asking what a computer program is, then you need to understand what these technical terms really are. And if you can’t, then the judgment is potentially flawed. Their finding that the neural network is a computer program is, I think, technically obtuse. You know that the Singaporean government — the Intellectual Property Office of Singapore — released about six weeks ago a consultation note to the Singaporean profession and population, asking: is the Emotional Perception case right, and do we need to adopt it into Singaporean national law? So this is direct soft power from the UK Supreme Court changing Commonwealth legislation and statutes. We’ll see what happens. But from what I’ve seen of a draft response from the attorneys, they’re saying essentially: we agree any hardware is right, the intermediate step is right. The assessment of the neural network as a computer program is wrong, or it just doesn’t make any sense. And I’ve made the same comments before in SIPA, in the relevant round in March. There’s a disconnect. I mean, it’s like they equate a computer program with being able to be run on an analog computer. Now, an analog computer has no central processing unit. An analog computer just has resistors and transistors and capacitors. So if they’re saying that an analog computer can run a program — that’s essentially what they’re saying in part of the judgment. Where is the program in an analog computer? And if they’re saying it’s in the values of the resistors and the capacitors, then that has implications for any circuit we’ve got — it’s potentially a computer program — which is just madness, because it doesn’t sit well with the legislation and decisions we’ve looked at over the last 50 years. This is a real problem. It may be a storm in a teacup because you can overcome the objections by having any hardware, but it’s an argument they shouldn’t have been making. It seems to be abstract legal argumentation which has little credibility in my personal view, although it’s now law. It may be that someone can take that, have an argument with the Supreme Court, get them to fix this. The other thing is the EPO looks at a neural network as a mathematical method, and the UK now says it’s a computer program. Neither is right. The EPO is wrong as well. If you look at the actual decision which they regularly quote — the Vicom case — if you actually read the claim and look at the case, you see that it doesn’t make a huge amount of sense. A neural network has applied mathematics in it. It can be based on a computer program because it’s required to set up the learning objectives and the loss function. Mathematical processes — it tweaks the weighting factors of neurons over the course of the training epochs. But at the end of the day, if the function performed by the neural network is new and it’s directed towards a technical implementation which is technically relevant, then it shouldn’t fail for being a mathematical method. And I think the EPO guidelines actually say that. Even recommendations — the UK court said that a recommendation is not technical. Well, actually it is, because it’s data processing, and you’ve got to work out how does the data processing work to provide an improved recommendation? Again, it goes back to the T 1249/22 decision. There’s a whole raft of these things which are left not entirely resolved. There’s enough here to keep someone busy for a few more years. Rolf Claessen: Right. So I have a question for you now that we’ve talked about the decision of the UK Supreme Court and the UPC — the Unified Patent Court — with very, very similar wording. What do you say are the three most important takeaways for patent practitioners in the US, in Europe, in the UK, before the EPO? Are there any things that you really want patent practitioners to take away from our discussion here? Bruce Dearling: Yeah, okay. So first: make sure the claim has some structure in it. You need to have any hardware. That’s number one — in terms of claim drafting. In terms of the description, you really have to understand what the invention is about. And you’ve got to make sure that you explain what function is achieved by what piece of hardware, kit or software. And if you do that — don’t nickel-and-dime this by writing the claim first — I would suggest that you run into problems. You need to understand what the invention is about. And you need to make sure that the description is complete and full to describe the functionality and the effects that are achieved in the real world. And if you can do that, then you’re on a much sounder basis — much, much stronger. There’s a much stronger foundation for this. So that’s two things. Is there a third one? That’s me being a bit cheeky, but I suppose I know what’s going on. Rolf Claessen: Yeah, but maybe the third takeaway is that maybe the EPO will rethink the way — at least how AI inventions are assessed for inventive step. Bruce Dearling: Well, as I said to you before, it could be that that’s the case. I don’t want to repeat myself again. The word “permissive” was used in a conversation I had with respect to the UK Supreme Court approach. COMVIK fundamentally still breaks with me and has done for years, because the way it’s set up and the way it’s applied distorts fundamentally what the invention is about. And until such time as that distortion is removed, there is a problem of objectivity versus subjectivity. And I think that’s really what the EPO has to grapple with. It’s not an easy thing to deal with, but maybe there are things going on. Bruce Dearling: It’s not an easy thing to deal with. I don’t know who’s going to argue it. It would have been useful for me to still have the original case up and running at the EPO because these arguments would have been fleshed out. I’m pretty sure they would have been referred to the Enlarged Board. We would have got it resolved. So it’s whether or not I can now work this into the existing case to try and get the examining division to — well, they will refuse, I suspect. And then it’ll go to the TBA. And then the TBA will have to look at this, hopefully with the referrals to the Enlarged Board. And then that fixes the problem on a national and international basis. Rolf Claessen: Yeah. Let’s see. [Laughs] Bruce Dearling: No, we don’t know. I mean, you might have a different view. What do you think? Do you think COMVIK is fundamentally right or fundamentally wrong? Rolf Claessen: Well, I’m not so much into AI inventions. I’m a chemist and I usually deal with chemistry inventions. But from the discussion that we had, I think that the EPO might rethink their position. I don’t know. Let’s see. Let’s hope so. Bruce Dearling: Well, they liked it. They liked problem-solution. It’s been with us for 25 years. It suggests that it’s a compromise. It’s not mandated by the European Patent Convention — that’s the point. It’s something they think works. And these things only work until such time as someone comes along and says, actually, you’re wrong, and this is the reason. Rolf Claessen: Let’s see if they choose a different route at least for AI inventions. So Bruce, thank you very much for your insight and for talking about the case that you were involved in with the UK Supreme Court. Where could people reach you if they have more questions about this field — basically patents, AI protection in the UK and Europe — and if they want to ask you more questions about this case? Bruce Dearling: Sure. Through the Hepworth Brown website or my LinkedIn profile, I suppose. The Hepworth Brown website has an email link. I’m trying to post things on it as well to try and provide a bit more context. But if people have fundamental questions on this stuff, then I’m happy to try and answer them. I suppose that I can be considered to be quite knowledgeable in the area. Rolf Claessen: Right. Certainly more than I am. [Laughing] Bruce Dearling: So I was fortunate. As a consequence of the work I’m doing, I was appointed last year to the WIPO Standing Committee on Patents and Privacy. That was discussed for the issues of where WIPO goes and what the direction of the problems are that we have in high-tech areas. So there seems to be some degree of understanding that I might know what I’m talking about. I think I probably do. Rolf Claessen: Thank you, Bruce. Thank you very much for being on IP Fridays. Bruce Dearling: My pleasure. Thank you very much, Rolf.

we investigate the functional limitations, environmental costs, and security vulnerabilities inherent in modern artificial intelligence and the Transformer architecture. Research from MIT and various technical papers highlights how AI faces "model collapse" when trained on synthetic data, as well as "catastrophic forgetting" where new information causes the system to lose prior knowledge. Mathematical analyses demonstrate that Transformers struggle with function composition and complex logic, often leading to factual hallucinations and reasoning errors. Furthermore, the texts identify prompt injection attacks as a significant security risk, where malicious instructions can bypass safety guardrails to leak data or spread misinformation. Collectively, the documents suggest that while AI is transformative, it remains constrained by technical bottlenecks, reliability issues, and high resource consumption. Efforts toward achieving Artificial General Intelligence must therefore overcome these fundamental obstacles through better data quality and enhanced architectural robustness.

Get your tickets for the⁠⁠⁠⁠⁠⁠⁠⁠ TDaPE Conference Online⁠⁠⁠⁠⁠⁠⁠For show notes, links, and a summary episode, sign up for the ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠Hey! What You Reading For ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠newsletter. Mondays at 7am BST - https://tdape.beehiiv.com/subscribe⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠AI For Teachers⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ newsletterFor maths curriculum questions contact us ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠here⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ or via support@alta-education.com Learn more about ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠The Story of Maths⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ - www.alta-education.com/tsom-overview and www.acel.proEpisode 289: In this episode of Thinking Deeply about Primary Education, I'm joined by Mark Bowen to explore mathematical journaling in action.Following on from a previous episode with Kirsten and Holly on mathematical journaling, Mark shares how he took the idea, adapted it for his own class, and developed a simple classroom structure built around three phases: download, investigate and communicate.We discuss how journaling can help students move beyond surface-level calculation, become more comfortable with struggle, draw on prior knowledge, experiment with different approaches, and explain their mathematical thinking with greater clarity.Mark also talks candidly about implementation: what worked, what did not, why he introduced a classroom character called Trev, how he used modelling and scaffolding to support students, and why he would slow the process down if he were starting again.This is a wonderfully practical episode about helping students become more active, reflective and confident mathematical thinkers.If you are interested in problem solving, reasoning, metacognition, mathematical journaling, curriculum design or simply making mathematics feel more purposeful in the classroom, this conversation is well worth your time.

Our moon is moving away from the earth at the rate of four centimeters per year. That might not seem like much. But that rate of movement away from the earth presents problems for those who believe the earth and moon have been around for 4.5 billion years.At the rate the moon is receding, it would have been so close to earth only 1.5 to 2 billion years ago that tidal friction would have melted earth's surface rocks. Mathematical fiddlings help a little, but not enough. By mathematically increasing the rate of earth's spin over supposed "billions" of years, and figuring in a factor for assumed different tidal rates, one can inch the earth moon relationship back to about 4 billion years.Evolutionary scientists believe the problem can be solved to keep their 4.5 billion years of evolutionary history intact. But, they admit that the assumptions being tried need investigation, since the matter is far from solved. In other words, evolutionists admit they have a problem making the earth moon relationship fit into their long age history.The mathematical models rule out the theory that the moon was formed billions of years ago from the same dust cloud that supposedly formed the earth. Also ruled out is the theory that the moon was captured by the earth's gravity. Only one explanation seems to satisfy the data--that the moon was formed relatively recently, orbiting the earth from the time of its creation.Psalm 148:3"Praise ye him, sun and moon: praise him, all ye stars of light.”Prayer: I thank You, dear Father in heaven, that Your Word to us in the Bible is true and can be trusted. With the creation I will bear witness to You as Creator, and with my mouth I will tell others of the salvation in Christ. In Jesus' Name. Amen.REF.: Dye, Brad. "The moon revisited." Creation Science Dialogue. Kerr, Richard A. "Where was the moon eons ago?" Science, v. 221. To support this ministry financially, visit: https://www.oneplace.com/donate/1232/29?v=20251111

Zak Mir talks to Dr Jim Millen, Non-Executive Chairman, Physiomics, regarding recent progress at the mathematical modelling, data science and biostatistics company, and issues regarding the forthcoming requisitioned meeting.What Physiomics actually doesPhysiomics is a specialised life sciences consultancy that works with companies developing new drugs. At its core, the business helps drug developers make better decisions about how they design and run studies.The company operates across two main areas. Mathematical modelling to support the design of preclinical and clinical trials, with a particular focus on oncology, though not limited to cancer treatment. Biostatistics, covering the statistical design of trials, reporting, planning, and regulatory interactions around trial outcomes. That combination matters. Drug development is expensive, time-consuming and high risk. The more rigorously a company can model likely outcomes and build trials correctly from a statistical standpoint, the better its chances of generating meaningful data and navigating the regulatory process successfully.In simple terms, Physiomics is there to help clients ask the right questions before they spend serious money answering them.Why mathematical modelling and biostatistics matter in drug developmentIt is worth pausing on this, because companies like Physiomics can easily be misunderstood as niche technical advisers operating in the background.In reality, their work sits close to the heart of pharmaceutical decision-making. A poorly designed trial can waste years. A weak statistical framework can undermine otherwise promising results. And if preclinical and clinical plans are not thought through properly, the cost of fixing mistakes later can be enormous.That is why the company's two-pronged offering is significant: Modelling helps shape trial design and strategy Biostatistics helps ensure studies are set up, analysed and reported in a way regulators and stakeholders can rely on For drug developers, especially in challenging therapeutic areas such as oncology, that expertise can be highly valuable.Signs the business is turning a cornerOne of the most important points to emerge recently is that Physiomics appears to be at a positive inflection point.The company has reported its highest-ever first-half income, up by around 50% on the comparable prior period. Market expectations are also for the business to deliver its highest-ever full-year income, and management has indicated that it believes the company remains on track to achieve that.That is not a trivial development. In a market where many life sciences businesses have struggled for funding and momentum, a services company tied to that ecosystem inevitably feels the pressure too.The logic is straightforward: Physiomics serves companies developing drugs If those companies are short of capital, they become more cautious about spending That pressure filters through to specialist service providers By that measure, the last few years have not been easy. Management has been candid in saying that the wider life sciences market, especially over the past five years, has created a difficult backdrop. So when stronger income figures start to come through, that is naturally seen as evidence that the business may be emerging from a tougher period.The phrase used was that the company feels like it is "turning a corner", and the recent numbers are being presented as proof of that shift.The wider market backdrop for life sciences consultanciesTo understand why recent progress matters, it helps to appreciate the commercial reality of a business like Physiomics.This is not a company that develops and sells its own blockbuster drug. It provides highly specialised consultancy services to clients who are themselves trying to advance drug programmes. That means demand for Physiomics' expertise is linked to confidence, budgets and capital availability across the biotech and pharma landscape.When funding conditions tighten, even capable drug developers may delay projects, reduce outsourced work or scale back trial activity. That can hit revenue visibility for service businesses, regardless of the quality of the service provided.Against that backdrop, a strong first-half performance and confidence in a record year carry added significance. They suggest not just resilience, but possible operational momentum.The share price has improved too, but that is not the whole storyAlongside the operational improvement, Physiomics' share price has also seen a notable rebound, rising by around 66% year to date at the time of discussion.In ordinary circumstances, that would probably be taken as a clear signal that sentiment around the company is improving. But the picture is complicated by corporate governance developments, namely a requisition notice from activist shareholder Mike Whitlow.That requisition has created a situation where improving business performance is happening at the same time as a challenge to the current board.So while there may be genuine momentum in the underlying business, there is also uncertainty about who should be steering it.What the requisition notice meansThe requisition notice would, if passed, replace the current board with a new board.Management's position is clear: it does not believe that outcome would be in the best interests of the company.The immediate practical consequence is that shareholders have been asked to vote at a general meeting. The chairman's strongest message on this point is simple and democratic: shareholders should vote.Whatever position an investor takes, the emphasis is on participation. This is being framed not as a routine procedural matter, but as a genuinely consequential decision about the company's future direction and governance.That is an important distinction. Boardroom disputes can sometimes appear remote or technical. Here, the argument is that the vote could materially affect how the company is run at a delicate stage in its development.Why management says this is the wrong time to “rock the boat”The timing is at the centre of the board's response.The current leadership's view is that this challenge is arriving just as the company is beginning to show evidence of a turnaround. In other words, if the business is finally moving towards stronger revenue and a better trajectory, this may be precisely the wrong moment to disrupt leadership and strategy.That argument rests on a few connected ideas: The company appears to be improving operationally Recent results suggest traction rather than stagnation Change at board level introduces uncertainty Uncertainty can be especially damaging when a business is at a sensitive inflection point The phrase “rock the boat” captures the concern neatly. A business that has spent years navigating a difficult market and is now seeing signs of recovery may not benefit from abrupt upheaval, particularly if the alternative leadership has not set out a clear and credible plan.The board's objections to the proposed replacement directorsManagement's opposition is not based only on timing. It has also raised several specific concerns about the individuals named in the requisition notice.1. Lack of clearly relevant life sciences services experienceOne criticism is that the proposed directors do not appear, from the current board's perspective, to have the right experience in life sciences services.That point matters because Physiomics operates in a specialist technical area. This is not a generic consultancy business. It works at the intersection of mathematical modelling, clinical development and biostatistics. Running such a company effectively may require sector-specific understanding, not just general boardroom experience.2. No clear plan has been presentedAnother issue is the lack of an articulated strategy.The current board says it has seen no evidence of a plan, not even at a high level, explaining what the replacement board would actually do with the company.That absence of detail is central to the concern. Replacing a board is one thing. Explaining the strategy that would follow is another. Without that second piece, shareholders are effectively being asked to back change without a roadmap.3. Concerns about independenceThe board has also highlighted governance concerns. Specifically, it says the proposed individuals are all connected parties in some way, either through previous or current working relationships.From a governance standpoint, that raises the question of board independence. Best practice generally favours having independent directors who can challenge each other, think autonomously and avoid groupthink.If all proposed appointees are closely connected, the argument is that this could weaken the balance and independence expected of a well-run board.The central problem: shareholders are being asked to choose without enough detailPerhaps the most striking concern is also the simplest one: nobody really knows what the incoming group would do if it took control.That uncertainty sits at the heart of management's case against the requisition. The issue is not merely whether change is good or bad in principle. It is whether shareholders should support a board replacement when the intended strategy has not been laid out.As framed by the current leadership, that creates an asymmetrical choice: Option one: keep the existing board in place while the business appears to be improving Option two: replace the board with a group that has not communicated a clear plan From that perspective, the proposed change looks less like a defined alternative and more like a leap into the unknown.That is really the essence of the argument.Could the new group still have good intentions?To be fair, the current board has not claimed that the requisitioning group intends to damage the company. In fact, the stated hope is that they are interested because they see real potential in Physiomics and want to continue building on the progress already made.But hope is not the same as certainty.Without a clearly stated strategy, the board's position is that shareholders are being asked to make a consequential decision based on assumptions rather than evidence. And in a listed company, particularly one operating in a specialist and commercially sensitive field, that may not be enough.What shareholders are being asked to doThe practical takeaway is very clear. Shareholders are being urged to participate in the vote at the general meeting.The board's formal recommendation is that the resolutions should be rejected. But beyond that recommendation, there is a broader appeal to engagement. This is being presented as one of those moments when shareholders can directly influence the direction of the company.The message is not complicated: Read the information available Consider the company's recent progress Assess the risks around the proposed board changes Vote In governance terms, that is the crux of it. A listed company only functions properly when shareholders take an active interest in major decisions, especially when those decisions concern leadership, strategy and accountability.The bigger picture for PhysiomicsStrip away the corporate drama, and the underlying story is a relatively straightforward one.Physiomics is a specialist life sciences consultancy working in mathematical modelling and biostatistics for drug development. It has come through a difficult period for the wider life sciences sector and is now reporting stronger financial performance, with signs that it could deliver a record year.At exactly that moment, it faces an activist-led attempt to replace the board.Management's view is that this is the wrong intervention at the wrong time. The company says it is making progress, the business environment is becoming more supportive, and a disruptive governance change without a clearly articulated alternative plan would introduce unnecessary risk.Whether shareholders agree is, of course, a matter for them. But the issues at stake are now clear: Business momentum Board stability Strategic clarity Governance quality Those are not side issues. They go to the heart of whether Physiomics can build on its recent progress and sustain the upward trajectory management believes is now underway.

Aaron joins Jeremiah to talk about the Sounders and why the underlying numbers are likely underrating the team. In the second segment the two preview the Sporting KC match and spoiler alert - they're not great!Sponsor

Aaron joins Jeremiah to talk about the Sounders and why the underlying numbers are likely underrating the team. In the second segment the two preview the Sporting KC match and spoiler alert - they're not great!Sponsor

In today's math classrooms, there's a growing expectation: students should be able to use and connect multiple mathematical representations. From visual models to symbolic notation, this practice is becoming a key part of high-quality math instruction. But for many teachers, this shift feels challenging—especially when their own experience with math was primarily abstract and procedural.So what happens when you're asked to teach in a way you didn't experience yourself? When you're expected to connect visual, physical, contextual, and symbolic representations—but don't feel like you have the tools or confidence to do it? For many educators, this creates an experience gap. And without support, it can feel overwhelming. The reality is, this isn't just about learning new strategies—it's about rethinking what it means to understand math, and being willing to learn alongside your students.In this episode, you'll explore:What it really means to connect mathematical representationsThe difference between strategies and representationsWhy many teachers feel unprepared for this shift—and what to do about itHow learning alongside students can strengthen your practiceThe role of networks and collaboration in building confidenceWhat teachers, coaches, and leaders can do to support this workIf you've been asked to implement connected representations in your math classroom but aren't sure where to start, this episode will help you build clarity, confidence, and a path forward.Not sure what matters most when designing math improvement plans? Take this assessment and get a free customized report: https://makemathmoments.com/grow/ Math coordinators and leaders – Ready to design your math improvement plan with guidance, support and using structure? Learn how to follow our 4 stage process. https://growyourmathprogram.com Looking to supplement your curriculum with problem-based lessons and units? Make Math Moments Problem Based Lessons & Units Show Notes PageLove the show? Text us your big takeaway! Get a Customized Math Improvement Plan For Your District.Are you district leader for mathematics? Take the 12 minute assessment and you'll get a free, customized improvement plan to shape and grow the 6 parts of any strong mathematics program.Take the assessmentAre you wondering how to create K-12 math lesson plans that leave students so engaged they don't want to stop exploring your math curriculum when the bell rings? In their podcast, Kyle Pearce and Jon Orr—founders of MakeMathMoments.com—share over 19 years of experience inspiring K-12 math students, teachers, and district leaders with effective math activities, engaging resources, and innovative math leadership strategies. Through a 6-step framework, they guide K-12 classroom teachers and district math coordinators on building a strong, balanced math program that grows student and teacher impact. Each week, gain fresh ideas, feedback, and practical strategies to feel more confident and motivate students to see the beauty in math. Start making math moments today by listening to Episode #139: "Making Math Moments From Day 1 to 180.

Ireland saw success at this year's European Girls Mathematical Olympiad: secondary school student Róisín Spratt won bronze, achieving Ireland's 10th ever medal.She joins Seán to discuss her experience.

Ben Lorica speaks with Tudor Achim, cofounder of Harmonic, about the fast progress of AI for mathematical reasoning and what it would take to build “mathematical superintelligence.” Subscribe to the Gradient Flow Newsletter

What if math felt less like drudgery and more like discovery? In this episode, we explore “mathematical imagination” and the many ways math is already alive in everyday family life. We talk about counting, measuring, predicting, sports, video games, art, nature, and how curiosity can turn numbers into something meaningful. We also share practical ways to make formal math time more inviting, from manipulatives and mystery-based activities to math tea times and even bubblegum math. If you've ever wanted to help your child experience math as a language for describing the world, this conversation is for you. Listen in, then come tell us what math looks like in your home.Resources:Explore the Journey North Mystery Class archivesEncounter solar system planet sizes and distances in this fun activityFind our favorite books for kids and parents in the Brave Writer Book ShopVisit Julie's Substack to find her special podcast for kids (and a lot more!) Purchase Julie's newest book, Help! My Kid Hates WritingFind community at the Brave Learner Home Learn more about the Brave Writer Literature & Mechanics programsStart a free trial of CTCmath.com to try the math program that's sure to grab and keep your child's attentionSubscribe to Julie's Substack newsletters, Brave Learning with Julie Bogart and Julie Off Topic, and Melissa's Catalog of EnthusiasmsSign up for our Text Message Pod Ring to get podcast updates and more!Send us podcast topic ideas by texting us: +1 (833) 947-3684Interested in advertising with us? Reach out to media@bravewriter.comConnect with Julie:Instagram: @juliebravewriterThreads: @juliebravewriterBluesky: @bravewriter.comFacebook: facebook.com/bravewriterConnect with Melissa:Website: melissawiley.comSubstack: melissawiley.substack.comInstagram: @melissawileybooksBluesky: @melissawiley.bsky.socialProduced by NOVA

This episode starts with a simple idea from the binary logic of computer science, and ends up somewhere much closer to home.Every computer program runs on basic on/off decisions. 1 or 0. True or false. And as it turns out, that's exactly how a child makes sense of the world. Questions to: Am I good, worthy, smart, special, different, normal (and plenty more) are answered definitively one way or the other. In this episode, I unpack how those early binary decisions form the structure of insecurity and how most adults go their whole lives without examining this core coding. I'll also show you how the strategies you've built to avoid having your worst fear about yourself confirmed operate like mathematical equations. Precise. Predictable. And completely invisible once they're running.And most importantly:Why the solution is not to flip the answer from “not enough” to “enough”… but to dismantle the binary logic altogether.I also share a very real and painful example from my own life this week that would have triggered binary logic, had I not already dismantled it. Plus:The first official Insecurity Project patron saint, andA brand new version of the Hidden Insecurity Diagnostic to help you see your deepest patterningIf you've ever tried to ‘positive think' your way out of insecurity or try to replace one belief with another, this will show you why that never quite works, and what to do instead.

Can you predict exactly where a world leader will be born 700 years from now? Can you predict the exact price he'll be betrayed for, or the specific method of his execution before that method even exists?The Prophet, we look at the Mathematical Proof. We're moving past "religious stories" and looking at Statistical Probability. We'll explore the 300+ specific prophecies fulfilled by Jesus Christ and look at the astronomical odds that one man could "accidentally" fulfill even eight of them. For the husband, this is the proof that God isn't just "watching" history—He is writing it. Isaiah 46:10 – "I make known the end from the beginning, from ancient times, what is still to come."

She can read original texts in Greek, Latin, Sanskrit, Arabic, and Cuneiform. 

A chat with Alexa leads Pete to contemplate what it looks like to lead his best mathematical life.  But what does that mean?  In this episode, Pete and Noah discuss ways to view mathematics not as a rigid school subject, but as a "grand adventure" that is constantly present in your life. Leave us a voice message Find us on Twitter Send us an email

Dr Conor Boland, a researcher from Dublin City University joins Emile Donovan to explain.

Do humans project mathematical order onto nature? Or was it there all along? On this classic ID The Future from the vault, host Andrew McDiarmid concludes his three-part conversation with Dr. Melissa Cain Travis about her book Thinking God's Thoughts: Johannes Kepler and the Miracle of Cosmic Comprehensibility. In Part 3, we look at how Kepler's ideas and work can inform the scientific enterprise today. This is Part 3 of a 3-part discussion. Source

Watch the best scene reading: https://www.youtube.com/watch?v=vFwco66VXrU For centuries, mathematicians chased an elusive dream: one formula that explains the mystery of Saturn's rings, rotating celestial spheres, and spinning tops. The puzzle was known as The Mathematical Mermaid. Many men tried and failed. Then, one extraordinary mind defied tradition and dared to solve it. —— Subscribe to the podcast: https://twitter.com/wildsoundpod https://www.instagram.com/wildsoundpod/ https://www.facebook.com/wildsoundpod

In this essay, Vincent Bouchard and Asia Matthews discuss how contemporary anarchism can be used as a framework to rethink how we teach mathematics at the university level. At its core, anarchism aims at aligning thoughts and actions, and we argue that an anarchist viewpoint on undergraduate mathematics may offer a path toward a more equitable, horizontal and human-centred approach. This is not an essay about math: this is about how it is taught, and why it matters! Vincent Bouchard is Professor in the Department of Mathematical and Statistical Sciences at the University of Alberta (personal website: https://sites.ualberta.ca/~vbouchar/). Vincent's publication list is freely available on arXiv.org at https://arxiv.org/a/bouchard_v_1.html . Asia Matthews is a professor of mathematics and interdisciplinary educator. She worked at Quest University Canada until recently, and is now a free agent. You can find her on LinkedIn at https://www.linkedin.com/in/asiamatthews/. Asia and Vincent's recent publication, "An Anarchist Approach to the Undergraduate Mathematics Curriculum", on which this essay is based, was published in the Canadian Journal of Science, Mathematics and Technology Education (2025) and is freely available on arXiv at https://arxiv.org/abs/2505.18811. Anarchist Essays is brought to you by Loughborough University's Anarchism Research Group and the journal Anarchist Studies. Follow us on Bluesky @anarchismresgroup.bsky.social Our music comes from Them'uns (featuring Yous'uns). Artwork by Sam G.

Why is the cosmos intellectually accessible to us? On this classic ID The Future from vault, host Andrew McDiarmid continues his conversation with Dr. Melissa Cain Travis about her book Thinking God's Thoughts: Johannes Kepler and the Miracle of Cosmic Comprehensibility. In Part 2, Travis illuminates Kepler's university years to show us how his study of mathematics and astronomy complemented his interest in theology. We learn about obstacles he overcame during his education and how an unexpected appointment to assist imperial mathematician Tycho Brahe jump-started his career as an astronomer and gave him the tools he needed to develop and advance his revolutionary ideas. Travis unpacks Kepler's major works, from Mysterium Cosmographicum to his magnum opus Harmonices Mundi. She also tracks for us the progression of Kepler's ideas to show us how he became a key figure in the transition from ancient astronomy to a true celestial physics. This is Part 2 of a 3-part discussion. Source

A look at internal strategies where a company spends approximately $1,000 per hour on social media ads for themselves and their clients. Frank outlines a comprehensive framework for creating "social media campaigns that sell" by moving away from aggressive "buy now" tactics and toward a system of intent-based marketing. The core philosophy focuses on building goodwill and trust through long-form content before ever making an offer. Key Takeaways Target the 30-90 Day Window: Most advertisers compete for the 5% of the market ready to buy today. The real profit lies in the 45% who will be ready in the next 30 to 90 days. Long-Form Video (3-6 Minutes): Videos under three minutes lack the depth to build a bond, while those over six minutes often lose social media users' attention. Empathy and Specificity: Don't use generic "motivational" content. Speak directly to the frustrations, desires, and emotions of your specific ideal prospect. Low Production, High Relatability: High-end "Hollywood" production can feel like an ad and trigger resistance. Authentic iPhone-style videos often perform better on social platforms. The Two-Step Ad Sequence: Split your campaign into Value Ads (content-rich, no call-to-action) and Sales Ads (the offer). Only show Sales Ads to people who consumed the Value Ads. Content as a Filter: Use broad targeting and let the video content itself act as the filter. If someone watches a significant portion of a specific video, they have identified themselves as a qualified lead. The Relationship is the Trigger: Sales copy is important, but the relationship and trust built during the "Value" phase are what ultimately trigger the purchase. Timestamps 00:00 - Intro and agency context on ad spend. 01:55 - Targeting the neglected 45% of the market (the 30-90 day buyers). 04:50 - Why long-form video (3-6 minutes) is the sweet spot for building trust. 07:20 - Why you should avoid generic "motivational" content. 09:01 - Being the "narrator" of your prospect's movie. 11:22 - Pre-framing: Controlling how prospects judge your "book" by its cover. 14:19 - Why relationships outperform sales copy every time. 16:21 - The synergy between Value-Oriented Ads and Sales-Oriented Ads. 20:47 - The fundamental question: What must you demonstrate to be true? 24:09 - Q&A: Budgeting for high-ticket services ($2,500+). 26:07 - Q&A: How many value videos are needed before an offer? 28:40 - The "Three Buckets" of audience retargeting (Stranger, Warm, Offer). 32:09 - Why organic follower count is irrelevant in the paid ad game. 34:31 - Using content to replace traditional Facebook targeting and "opt-in" forms. 37:00 - Mathematical breakdown of acquisition costs and ROI.

Vlad Tenev (Robinhood co-founder/CEO) and Tudor Achim (former helm.ai CTO) are the founders of Harmonic, an AI lab pioneering the path toward mathematical superintelligence. Together, they developed Aristotle, a model that eliminates hallucinations by reasoning in Lean code rather than natural language. By shifting from probabilistic guesses to formal logic, Aristotle produces 100% verified mathematical outputs. The model recently demonstrated its breakthrough capabilities by achieving gold-medal performance at the International Math Olympiad. In this episode of Summation, Vlad, Tudor, and Auren discuss:Why AI models struggled at math for so long How Aristotle helped 10x the total corpus of formally verified Erdos problems in just a few months Why formal verification will make all software dramatically saferHow the first Millennium Prize problem will be solved by 2027-2028You can find Auren Hoffman on X at @auren, Vlad Tenev on X at @vladtenev, and Tudor Achim on X at @tachim

The Lunar Society: Read the notes at at podcastnotes.org. Don't forget to subscribe for free to our newsletter, the top 10 ideas of the week, every Monday --------- We begin the episode with the absolutely ingenious and surprising way in which Kepler discovered the laws of planetary motion.People sometimes say that AI will make especially fast progress at scientific discovery because of tight verification loops.But the story of how we discovered the shape of our solar system shows how the verification loop for correct ideas can be decades (or even millennia) long.During this time, what we know today as the better theory can actually make worse predictions.And the reasons it survives this epistemic hell is some mixture of judgment and heuristics that we don't even understand well enough to actually articulate, much less codify into an RL loop. Hope you enjoy!Watch on YouTube; read the transcript.Sponsors- Jane Street loves challenging my audience with different creative puzzles. One of my listeners, Shawn, solved Jane Street's ResNet challenge and posted a great walk-through on X. If you want to try one of these puzzles yourself, there's one live now at janestreet.com/dwarkesh.- Labelbox can get you rubric-based evals, no matter your domain. These rubrics allow you to give your model feedback on all the dimensions you care about, so you can train how it thinks, not just what it thinks. Whatever you're focused on—math, physics, finance, psychology or something else—Labelbox can help. Learn more at labelbox.com/dwarkesh.- Mercury just released a new feature called Insights. Insights summarizes your money in and out, showing you your biggest transactions and calling out anything worth paying attention to. It's a super low-friction way to stay on top of your business. Learn more at mercury.com/insights.Timestamps(00:00:00) – Kepler was a high temperature LLM(00:11:44) – How would we know if there's a new unifying concept within heaps of AI slop?(00:26:10) – The deductive overhang(00:30:31) – Selection bias in reported AI discoveries(00:46:43) – AI makes papers richer and broader, but not deeper(00:53:00) – If AI solves a problem, can humans get understanding out of it?(00:59:20) – We need a semi-formal language for the way that scientists actually talk to each other(01:09:48) – How Terry uses his time(01:17:05) – Human-AI hybrids will dominate math for a lot longer Get full access to Dwarkesh Podcast at www.dwarkesh.com/subscribe

We begin the episode with the absolutely ingenious and surprising way in which Kepler discovered the laws of planetary motion.People sometimes say that AI will make especially fast progress at scientific discovery because of tight verification loops.But the story of how we discovered the shape of our solar system shows how the verification loop for correct ideas can be decades (or even millennia) long.During this time, what we know today as the better theory can actually make worse predictions.And the reasons it survives this epistemic hell is some mixture of judgment and heuristics that we don't even understand well enough to actually articulate, much less codify into an RL loop. Hope you enjoy!Watch on YouTube; read the transcript.Sponsors- Jane Street loves challenging my audience with different creative puzzles. One of my listeners, Shawn, solved Jane Street's ResNet challenge and posted a great walk-through on X. If you want to try one of these puzzles yourself, there's one live now at janestreet.com/dwarkesh.- Labelbox can get you rubric-based evals, no matter your domain. These rubrics allow you to give your model feedback on all the dimensions you care about, so you can train how it thinks, not just what it thinks. Whatever you're focused on—math, physics, finance, psychology or something else—Labelbox can help. Learn more at labelbox.com/dwarkesh.- Mercury just released a new feature called Insights. Insights summarizes your money in and out, showing you your biggest transactions and calling out anything worth paying attention to. It's a super low-friction way to stay on top of your business. Learn more at mercury.com/insights.Timestamps(00:00:00) – Kepler was a high temperature LLM(00:11:44) – How would we know if there's a new unifying concept within heaps of AI slop?(00:26:10) – The deductive overhang(00:30:31) – Selection bias in reported AI discoveries(00:46:43) – AI makes papers richer and broader, but not deeper(00:53:00) – If AI solves a problem, can humans get understanding out of it?(00:59:20) – We need a semi-formal language for the way that scientists actually talk to each other(01:09:48) – How Terry uses his time(01:17:05) – Human-AI hybrids will dominate math for a lot longer Get full access to Dwarkesh Podcast at www.dwarkesh.com/subscribe

On this classic ID The Future out of the vault, host Andrew McDiarmid kicks off a three-episode discussion with Dr. Melissa Cain Travis about her recent book Thinking God's Thoughts: Johannes Kepler and the Miracle of Cosmic Comprehensibility. A fellow at Discovery Institute's Center for Science and Culture, Dr. Travis serves as Affiliate Faculty at Colorado Christian University's Lee Strobel Center for Evangelism and Applied Apologetics, where she teaches courses in the history and philosophy of science. In Part 1, learn why Kepler was instrumental in transforming classical astronomy into a true celestial physics. Like others before him, Kepler perceived a remarkable resonance between the rational order of the material world, mathematics, and the human mind. In response, he developed a three-part cosmic harmony of archetype, copy, and image to explain this unity. Travis unpacks his tripartite harmony for us. This is Part 1 of a 3-part discussion. Source

This week on Game Crunch: Pokopia, Blue Prince, Marathon. All this and more on the latest Game Crunch! Until next week - Game On!

Math is one of the subjects that gets the most attention in American education, but how well do we actually understand what good math instruction should look like? Should math classes consist of students solving problem after problem, or should math classes also include opportunities for discussion and group work? Should students learn a topic […]

Data scientists often jump straight to machine learning when tackling a new problem. But there's a foundational step that can dramatically increase your chances of project success and create more reliable business value. Mathematical modelling from first principles provides a low-cost scaffolding that can make your machine learning work more robust.In this Value Boost episode, Dr. Tim Varelmann joins Dr. Genevieve Hayes to explain how building models from physics principles, like mass and energy conservation, creates a modular foundation that reduces computational costs and makes your work easier to understand.In this episode, we explore:1. What mathematical modelling from first principles actually means [01:20]2. How to build modular models with different resolution levels [04:39]3. When to add machine learning to first principles models [08:18]4. The practical first step to incorporate this approach into your work [09:23]Guest BioDr Tim Varelmann is the founder of Bluebird Optimization and holds a PhD in Mathematical Optimisation. He is also the creator of Effortless Modeling in Python with GAMSPy, the world's first GAMSPy course.LinksBluebird Optimization WebsiteConnect with Genevieve on LinkedInBe among the first to hear about the release of each new podcast episode by signing up HERE

Math is one of the subjects that gets the most attention in American education, but how well do we actually understand what good math instruction should look like?Should math classes consist of students solving problem after problem, or should math classes also include opportunities for discussion and group work? Should students learn a topic and then move on to the next topic after they have achieved competency, or should teachers strive to teach each topic deeply, giving students many different strategies for solving problems? And if math education in America were dramatically improved, just how good could it be?On this episode of The Report Card, Nat Malkus discusses these questions, and more, with Jon Star. Nat and Jon discuss conceptual understanding and procedural fluency, whether constructivism has a place in the classroom, the value of worked examples, online curricula and the importance of curricular coherence, what mathematical flexibility is and why it matters, whether students can understand problem-solving strategies more or less well, whether math makes students better problem-solvers more generally, Chinese math education, Jon's experience teaching middle school math and how being a researcher informs his teaching, whether math education research is sufficiently accessible to teachers, how to improve American math education, and how good American math education could be.Jon Star is the Carl H. Pforzheimer, Jr. Professor of Teaching and Learning at the Harvard Graduate School of Education and a middle school math teacher.

What does the day-to-day of a math is figureoutable classroom look like? In this episode, Pam and Kim discuss the new book for teachers of Grades 3-5 to transform their teaching. Talking Points:New book release for Grades 3-5!Development of Mathematical ReasoningAdditive ReasoningMultiplicative ReasoningProblem String walkthroughs and videosRich tasks, routines, models and modelingNext steps for teachers, specific to their needs and experienceShark Metaphor Podcast episode: Ep 245: Three Distortions that Ruin Math TeachingCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC 

Is the NBA draft lottery rigged to reward losing? Veteran NBA insider Ric Bucher sits down with Dr. TJ Highley, Associate Professor of Math & Computer Science at LaSalle University, who has developed a groundbreaking anti-tanking formula that could change the NBA forever — and it doesn't involve eliminating the draft.Highley's COLA (Carryover Lottery Allocation) system strips tanking of its incentive by rewarding playoff history instead of regular season losses. Teams would accumulate lottery tickets over time based on sustained failure — not deliberate losing — making intentional tanking mathematically pointless.But Bucher pushes back with 30 years of hard-won NBA knowledge: not every owner wants to win. Some — following the Donald Sterling playbook — are perfectly content selling hope while pocketing profits. Can any formula fix that?Plus: Bucher delivers a candid reassessment of the Denver Nuggets title chances and why the Michael Porter Jr. trade may have cost them more than anyone realized — rebounding. And a sharp takedown of the analytics crowd that thinks they've cracked the code on building a championship team.⏱️ TIMESTAMPS00:00 — Intro & Book Announcement 02:02 — Meet Dr. TJ Highley: The Math Professor Trying to Fix NBA Tanking 03:31 — His NBA Fandom: Spurs to Sixers & "The Process" 05:21 — COLA Explained: How Playoff History Replaces Regular Season Records 07:57 — Has Any NBA Insider Reviewed This System? 09:59 — Simple COLA: A Brand-New Version Revealed for the First Time 13:35 — Should the NBA Abolish the Draft? Ric Says No — Emphatically 15:06 — The Fatal Flaw in Every Anti-Tanking Proposal: Owners Who Don't Want to Win 27:28 — The Donald Sterling Blueprint: How Tanking Became a Business Model 30:10 — Denver Nuggets: Why Ric Is Second-Guessing His Championship Pick 35:01 — The Michael Porter Jr. Trade: What Ric Got Wrong 38:05 — The Hidden Cost: Rebounding and Why It Matters at Crunch Time 43:54 — Final Verdict: Can the Nuggets Come Out of the West? 44:32 — Outro & Sponsor: New Air Club#NBA#NBADraft#Tanking#NBALottery#DenverNuggets#NikolaJokic#RicBucher#OnTheBall#NBAAnalysis#Basketball#MichaelPorterJr#CamJohnson#NBAInsider#SportsPodcast#NBADebate#AntiTanking#COLA#NBAReform#SmallMarketNBA#UnitedWeCastSupport this show http://supporter.acast.com/bucher-and-friends. Hosted on Acast. See acast.com/privacy for more information.

In this episode of Mark & Pete, we explore a fascinating development in modern science: how mathematical models are helping scientists identify genetic material that could dramatically improve the resilience of global food crops.Researchers are increasingly using advanced mathematics, computational biology, and genetic analysis to pinpoint the specific genes responsible for drought tolerance, disease resistance, and environmental adaptability in crops such as wheat, rice, and maize. The goal is simple but crucial: strengthen the world's food supply in the face of climate change, population growth, and unpredictable agricultural conditions.But this technological breakthrough raises bigger questions. When mathematics begins guiding genetic discovery, are we witnessing the next great leap in agricultural science—or are we stepping into a new era where humanity attempts to redesign the natural world?In this episode we unpack how mathematical modelling, genetics, and agricultural science intersect, and why this approach is rapidly becoming one of the most powerful tools in modern crop research. From predictive algorithms that identify useful genetic traits to data-driven plant breeding, the science behind food security is becoming increasingly mathematical.At the same time, we ask an important cultural and philosophical question: what does stewardship of creation look like in an age of genetic precision? The Bible speaks of humanity being placed in the garden “to work it and keep it.” Does modern genetic science fulfil that mandate—or challenge it?This conversation brings together science, ethics, agriculture, and faith, offering a thoughtful look at how technological innovation intersects with biblical ideas about stewardship, responsibility, and wisdom.If you are interested in food security, agricultural science, genetics, biotechnology, climate resilience, and the Christian perspective on science, this episode provides a clear and engaging discussion of one of the most important developments shaping the future of global food production.Keywords:crop resilience genetics, mathematical models genetics, food crop resilience science, agricultural genetics research, genetic material crops, drought resistant crops research, crop breeding algorithms, biotechnology agriculture, global food security science, mathematics in biology, computational genetics agriculture, Christian perspective on science, stewardship of creation agriculture

This is a link post. I would like to thank David Thorstadt for looking over this. If you spot a factual error in this article please message me. The code used to generate the graphs in the article is available to view here. Introduction Say you are an organiser, tasked with achieving the best result on some metric, such as “trash picked up”, “GDP per capita”, or “lives saved by an effective charity”. There are several possible options of interventions you can take to try and achieve this. How do you choose between them? The obvious thing to do is look at each intervention in turn and make your best, unbiased estimate of how each intervention will perform on your metric, and pick the one that performs the best:Image taken from here Having done this ranking, you declare the top ranking program to be the best intervention and invest in it, expecting that that your top estimate will be the result that you get. This whole procedure is totally normal, and people all around the world, including people in the effective altruist community, do it all the time. In actuality, this procedure is not correct. The optimisers curse is [...] ---Outline:(00:26) Introduction(02:17) The optimisers curse explained simply(04:42) Introducing a toy model(08:45) Introducing speculative interventions(12:15) A simple bayesian correction(18:47) Obstacles to simple optimizer curse solutions.(22:08) How Givewell has reacted to the optimiser curse(25:18) Conclusion --- First published: February 11th, 2026 Source: https://forum.effectivealtruism.org/posts/q2TfTirvspCTH2vbZ/the-best-cause-will-disappoint-you-an-intro-to-the Linkpost URL:https://open.substack.com/pub/titotal/p/the-best-cause-will-disappoint-you?r=1e0is3&utm_campaign=post&utm_medium=web&showWelcomeOnShare=true --- Narrated by TYPE III AUDIO. ---Images from the article:Apple Podcasts and Spotify do not show images in the episode description. Try Pocket Casts, or another podcast app.

Vlad Tenev and Tudor Achim from Harmonic explain how they built Aristotle, an AI system that reaches International Mathematical Olympiad gold-medal performance using formally verified Lean proofs. They unpack the architecture behind mathematical superintelligence, including Monte Carlo Tree Search, lemma guessing, and specialized geometry modules. The conversation explores how verifiable reasoning could harden mission-critical software, reshape mathematical practice, and lead to trustworthy superintelligent systems by 2030. Use the Granola Recipe Nathan relies on to identify blind spots across conversations, AI research, and decisions: https://bit.ly/granolablindspot Sponsors: Claude: Claude is the AI collaborator that understands your entire workflow, from drafting and research to coding and complex problem-solving. Start tackling bigger problems with Claude and unlock Claude Pro's full capabilities at https://claude.ai/tcr Framer: Framer is an enterprise-grade website builder that lets business teams design, launch, and optimize their.com with AI-powered wireframing, real-time collaboration, and built-in analytics. Start building for free and get 30% off a Framer Pro annual plan at https://framer.com/cognitive Blitzy: Blitzy is the autonomous code generation platform that ingests millions of lines of code to accelerate enterprise software development by up to 5x with premium, spec-driven output. Schedule a strategy session with their AI solutions consultants at https://blitzy.com Tasklet: Tasklet is an AI agent that automates your work 24/7; just describe what you want in plain English and it gets the job done. Try it for free and use code COGREV for 50% off your first month at https://tasklet.ai CHAPTERS: (00:00) About the Episode (04:58) Math as reasoning (Part 1) (15:22) Sponsors: Claude | Framer (18:51) Math as reasoning (Part 2) (18:51) Inside the Lean language (27:51) Lean intuition and MathLib (Part 1) (34:08) Sponsors: Blitzy | Tasklet (37:08) Lean intuition and MathLib (Part 2) (38:47) Inside Aristotle's architecture (48:33) Scope, boundaries, and applications (54:37) Training, taste, and interpretability (01:08:18) Formal math and software (01:16:50) Limits, entropy, and roadmap (01:25:24) 2030 vision and safety (01:33:38) Outro PRODUCED BY: https://aipodcast.ing

In this conversation, Ravi Vakil discusses the beauty of mathematics, the impact of AI on the field, and the importance of human interaction in mathematical education. He emphasizes the social nature of mathematics and the potential dangers of AI-generated content flooding the mathematical community. The discussion also touches on the future of education, the role of leadership in mathematics, and the balance between mathematics and other disciplines. Throughout, Vakil encourages aspiring mathematicians to embrace the beauty and interconnectedness of the subject.TakeawaysMathematics is fundamentally about curiosity and connection.The beauty of mathematics can be shared and experienced collectively.AI poses both opportunities and challenges for the field of mathematics.Mathematics thrives on social interaction and collaboration.The influx of AI-generated content may dilute the quality of mathematical research.Education in mathematics requires human interaction and cannot be fully replaced by technology.Leadership in mathematics should focus on long-term investments in education.Chapters00:00 Introduction and Setting the Stage01:11 The Beauty of Mathematics03:57 The Intersection of Mathematics and Technology05:41 AI's Role in Mathematics07:36 Emerging Mathematical Ideas in the Age of AI09:12 Community Dynamics in Mathematics13:32 Challenges of AI in Academic Publishing17:08 The Future of Writing and Learning in Mathematics19:42 The Value of Human Interaction in Education22:33 The Future of Mathematics and AI30:15 Leadership in Mathematics and Education35:47 Balancing Mathematics with Liberal Arts39:48 Encouragement for Aspiring MathematiciansFollow Noah on Instagram, Twitter, Bluesky Follow Breaking Math on Substack, Twitter, Instagram, Website, YouTube, TikTokFollow Autumn on Twitter, BlueSky, Instagram, SubstackBecome a guest hereemail: breakingmathpodcast@gmail.com

Understanding history is not about understanding formulas or narratives. Instead, we must understand the people who made history, their motives, and their goals.Original article: https://mises.org/mises-wire/history-not-mathematical-calculation

Understanding history is not about understanding formulas or narratives. Instead, we must understand the people who made history, their motives, and their goals.Original article: https://mises.org/mises-wire/history-not-mathematical-calculation

Two-time Emmy and Three-time NAACP Image Award-winning, television Executive Producer Rushion McDonald interviewed Dr. Jacque Rushin and Robyn Donaldson. Below is a polished, thorough summary of the interview featuring Jacque Rushin and Robyn Donaldson discussing the career and legacy of Dr. Gladys West with Rushion McDonald—along with its purpose, key takeaways, and notable quotes, all drawn directly from the transcript.(Citations reference the uploaded file.) Summary of the Interview On Money Making Conversations Masterclass, Rushion McDonald welcomes Dr. Jacque Rushin (award‑winning business executive, educator, mental health professional, humanitarian) and Robyn Donaldson (2025 Presidential Lifetime Achievement Award honoree for global STEM education) to discuss their celebration of Dr. Gladys B. West, a pioneering mathematician whose work laid the foundation for the GPS (Global Positioning System). The conversation explores the intersection of Juneteenth, Black excellence, STEM education, and Dr. West’s life story, captured in her memoir It Began with a Dream. The guests highlight Dr. West as one of America’s last living “hidden figures”—a brilliant yet historically overlooked Black woman whose mathematical genius revolutionized everyday life. They detail how Dr. West rose from sharecropper roots, excelled academically at Virginia State University, earned her master’s and PhD, spent 39 years contributing to government research, and ultimately developed the algorithms and modeling processes that power GPS. They also describe their collaborative effort to create the Westward Bound Program, a life‑skills and STEM‑focused curriculum inspired by Dr. West’s principles of wisdom, endurance, strategy, and precision. Through humorous, emotional, and deeply insightful dialogue, the episode uplifts Dr. West’s accomplishments while discussing mental health, technology dependence, the importance of exposure to STEM pathways for underserved youth, and how the legacy of Black innovators must remain central in cultural celebrations like Juneteenth. Purpose of the Interview 1. To honor and amplify Dr. Gladys West’s legacy She is a living mathematical pioneer whose GPS contributions transformed global navigation and modern technology. 2. To connect her story to Juneteenth’s spirit of liberation and recognition The guests highlight the “delayed recognition” of Black innovators and the importance of acknowledging hidden figures whose brilliance shaped society. 3. To promote STEM exposure in underserved communities Robyn Donaldson emphasizes equitable access to STEM opportunities so children can compete in a global, tech‑driven world. 4. To introduce and promote the Westward Bound Program The curriculum teaches STEM principles, life skills, and personal development inspired by Dr. West’s methodologies. 5. To highlight themes of resilience, humility, and lifelong learning Dr. West’s quiet determination and academic persistence serve as a blueprint for young people and adults alike. Key Takeaways 1. Dr. Gladys West is a “living hidden figure.” Her research and mathematical modeling are the backbone of GPS, impacting navigation, transportation, military systems, and everyday digital tools. 2. Her journey exemplifies brilliance shaped by humility and hard work. Born in 1930 to sharecropper parents, she excelled academically despite segregation, pursued multiple degrees, and overcame racial and gender barriers in government research settings. 3. Juneteenth is the perfect backdrop for honoring Dr. West. Jacque stresses that Juneteenth represents “delayed freedom,” paralleling the delayed recognition of Black inventors and innovators. 4. STEM exposure is vital to equity. Robyn insists that Black children are fully capable of STEM success—they simply lack exposure, not aptitude. Without STEM skills, young people risk being left behind in a robotics‑driven economy. 5. Technology should complement—not replace—human thinking. Jacque cites Dr. West’s personal preference for physical maps over GPS to maintain cognitive sharpness and critical thinking, a warning about over‑dependence on AI and automation. 6. The Westward Bound Program bridges STEM, life skills, and personal development. Built on the acronym “WEST”—Wisdom, Endurance, Strategy, Tracking—the program supports youth, adults, and entrepreneurs seeking direction and resilience. 7. Mentorship, community, and relationships are central themes. Dr. West’s success was nurtured by professors and role models at her HBCU—mirroring how Jacque and Robyn now uplift the next generation. 8. Her story resonates globally and intergenerationally. From college students to young children to adults, the principles from her memoir and program promote self‑belief, vision, discipline, and perseverance. Notable Quotes (All taken directly from the transcript.) On Dr. West’s impact “She’s a living hidden figure… her accomplishments have actually changed our way of living in every discipline of life.” “Her technology… makes these things possible.” On Juneteenth and recognition “Juneteenth is about the delayed freedom of African Americans… and what Dr. West represents is the quiet, often overlooked brilliance that changes the world.” On STEM access “Our kids are not pursuing high‑paying STEM careers, not because of their aptitude, but simply because they have not been exposed.” On Dr. West’s genius “You don’t have to be loud to be a legacy.” “She is just so humble, but she’s just brilliant. She’s like a mathematical genius.” On technology & mental health “She didn’t want to lose her critical thinking by depending on GPS… everything has a place, and it should complement you, not take over.” On resilience & aspiration “You have to believe there is something greater than what you’re standing in.” “From sharecropper to pioneer—you can be someone from humble beginnings and change the world.” #SHMS #STRAW #BESTSupport the show: https://www.steveharveyfm.com/See omnystudio.com/listener for privacy information.

Two-time Emmy and Three-time NAACP Image Award-winning, television Executive Producer Rushion McDonald interviewed Dr. Jacque Rushin and Robyn Donaldson. Below is a polished, thorough summary of the interview featuring Jacque Rushin and Robyn Donaldson discussing the career and legacy of Dr. Gladys West with Rushion McDonald—along with its purpose, key takeaways, and notable quotes, all drawn directly from the transcript.(Citations reference the uploaded file.) Summary of the Interview On Money Making Conversations Masterclass, Rushion McDonald welcomes Dr. Jacque Rushin (award‑winning business executive, educator, mental health professional, humanitarian) and Robyn Donaldson (2025 Presidential Lifetime Achievement Award honoree for global STEM education) to discuss their celebration of Dr. Gladys B. West, a pioneering mathematician whose work laid the foundation for the GPS (Global Positioning System). The conversation explores the intersection of Juneteenth, Black excellence, STEM education, and Dr. West’s life story, captured in her memoir It Began with a Dream. The guests highlight Dr. West as one of America’s last living “hidden figures”—a brilliant yet historically overlooked Black woman whose mathematical genius revolutionized everyday life. They detail how Dr. West rose from sharecropper roots, excelled academically at Virginia State University, earned her master’s and PhD, spent 39 years contributing to government research, and ultimately developed the algorithms and modeling processes that power GPS. They also describe their collaborative effort to create the Westward Bound Program, a life‑skills and STEM‑focused curriculum inspired by Dr. West’s principles of wisdom, endurance, strategy, and precision. Through humorous, emotional, and deeply insightful dialogue, the episode uplifts Dr. West’s accomplishments while discussing mental health, technology dependence, the importance of exposure to STEM pathways for underserved youth, and how the legacy of Black innovators must remain central in cultural celebrations like Juneteenth. Purpose of the Interview 1. To honor and amplify Dr. Gladys West’s legacy She is a living mathematical pioneer whose GPS contributions transformed global navigation and modern technology. 2. To connect her story to Juneteenth’s spirit of liberation and recognition The guests highlight the “delayed recognition” of Black innovators and the importance of acknowledging hidden figures whose brilliance shaped society. 3. To promote STEM exposure in underserved communities Robyn Donaldson emphasizes equitable access to STEM opportunities so children can compete in a global, tech‑driven world. 4. To introduce and promote the Westward Bound Program The curriculum teaches STEM principles, life skills, and personal development inspired by Dr. West’s methodologies. 5. To highlight themes of resilience, humility, and lifelong learning Dr. West’s quiet determination and academic persistence serve as a blueprint for young people and adults alike. Key Takeaways 1. Dr. Gladys West is a “living hidden figure.” Her research and mathematical modeling are the backbone of GPS, impacting navigation, transportation, military systems, and everyday digital tools. 2. Her journey exemplifies brilliance shaped by humility and hard work. Born in 1930 to sharecropper parents, she excelled academically despite segregation, pursued multiple degrees, and overcame racial and gender barriers in government research settings. 3. Juneteenth is the perfect backdrop for honoring Dr. West. Jacque stresses that Juneteenth represents “delayed freedom,” paralleling the delayed recognition of Black inventors and innovators. 4. STEM exposure is vital to equity. Robyn insists that Black children are fully capable of STEM success—they simply lack exposure, not aptitude. Without STEM skills, young people risk being left behind in a robotics‑driven economy. 5. Technology should complement—not replace—human thinking. Jacque cites Dr. West’s personal preference for physical maps over GPS to maintain cognitive sharpness and critical thinking, a warning about over‑dependence on AI and automation. 6. The Westward Bound Program bridges STEM, life skills, and personal development. Built on the acronym “WEST”—Wisdom, Endurance, Strategy, Tracking—the program supports youth, adults, and entrepreneurs seeking direction and resilience. 7. Mentorship, community, and relationships are central themes. Dr. West’s success was nurtured by professors and role models at her HBCU—mirroring how Jacque and Robyn now uplift the next generation. 8. Her story resonates globally and intergenerationally. From college students to young children to adults, the principles from her memoir and program promote self‑belief, vision, discipline, and perseverance. Notable Quotes (All taken directly from the transcript.) On Dr. West’s impact “She’s a living hidden figure… her accomplishments have actually changed our way of living in every discipline of life.” “Her technology… makes these things possible.” On Juneteenth and recognition “Juneteenth is about the delayed freedom of African Americans… and what Dr. West represents is the quiet, often overlooked brilliance that changes the world.” On STEM access “Our kids are not pursuing high‑paying STEM careers, not because of their aptitude, but simply because they have not been exposed.” On Dr. West’s genius “You don’t have to be loud to be a legacy.” “She is just so humble, but she’s just brilliant. She’s like a mathematical genius.” On technology & mental health “She didn’t want to lose her critical thinking by depending on GPS… everything has a place, and it should complement you, not take over.” On resilience & aspiration “You have to believe there is something greater than what you’re standing in.” “From sharecropper to pioneer—you can be someone from humble beginnings and change the world.” #SHMS #STRAW #BESTSee omnystudio.com/listener for privacy information.

Two-time Emmy and Three-time NAACP Image Award-winning, television Executive Producer Rushion McDonald interviewed Dr. Jacque Rushin and Robyn Donaldson. Below is a polished, thorough summary of the interview featuring Jacque Rushin and Robyn Donaldson discussing the career and legacy of Dr. Gladys West with Rushion McDonald—along with its purpose, key takeaways, and notable quotes, all drawn directly from the transcript.(Citations reference the uploaded file.) Summary of the Interview On Money Making Conversations Masterclass, Rushion McDonald welcomes Dr. Jacque Rushin (award‑winning business executive, educator, mental health professional, humanitarian) and Robyn Donaldson (2025 Presidential Lifetime Achievement Award honoree for global STEM education) to discuss their celebration of Dr. Gladys B. West, a pioneering mathematician whose work laid the foundation for the GPS (Global Positioning System). The conversation explores the intersection of Juneteenth, Black excellence, STEM education, and Dr. West’s life story, captured in her memoir It Began with a Dream. The guests highlight Dr. West as one of America’s last living “hidden figures”—a brilliant yet historically overlooked Black woman whose mathematical genius revolutionized everyday life. They detail how Dr. West rose from sharecropper roots, excelled academically at Virginia State University, earned her master’s and PhD, spent 39 years contributing to government research, and ultimately developed the algorithms and modeling processes that power GPS. They also describe their collaborative effort to create the Westward Bound Program, a life‑skills and STEM‑focused curriculum inspired by Dr. West’s principles of wisdom, endurance, strategy, and precision. Through humorous, emotional, and deeply insightful dialogue, the episode uplifts Dr. West’s accomplishments while discussing mental health, technology dependence, the importance of exposure to STEM pathways for underserved youth, and how the legacy of Black innovators must remain central in cultural celebrations like Juneteenth. Purpose of the Interview 1. To honor and amplify Dr. Gladys West’s legacy She is a living mathematical pioneer whose GPS contributions transformed global navigation and modern technology. 2. To connect her story to Juneteenth’s spirit of liberation and recognition The guests highlight the “delayed recognition” of Black innovators and the importance of acknowledging hidden figures whose brilliance shaped society. 3. To promote STEM exposure in underserved communities Robyn Donaldson emphasizes equitable access to STEM opportunities so children can compete in a global, tech‑driven world. 4. To introduce and promote the Westward Bound Program The curriculum teaches STEM principles, life skills, and personal development inspired by Dr. West’s methodologies. 5. To highlight themes of resilience, humility, and lifelong learning Dr. West’s quiet determination and academic persistence serve as a blueprint for young people and adults alike. Key Takeaways 1. Dr. Gladys West is a “living hidden figure.” Her research and mathematical modeling are the backbone of GPS, impacting navigation, transportation, military systems, and everyday digital tools. 2. Her journey exemplifies brilliance shaped by humility and hard work. Born in 1930 to sharecropper parents, she excelled academically despite segregation, pursued multiple degrees, and overcame racial and gender barriers in government research settings. 3. Juneteenth is the perfect backdrop for honoring Dr. West. Jacque stresses that Juneteenth represents “delayed freedom,” paralleling the delayed recognition of Black inventors and innovators. 4. STEM exposure is vital to equity. Robyn insists that Black children are fully capable of STEM success—they simply lack exposure, not aptitude. Without STEM skills, young people risk being left behind in a robotics‑driven economy. 5. Technology should complement—not replace—human thinking. Jacque cites Dr. West’s personal preference for physical maps over GPS to maintain cognitive sharpness and critical thinking, a warning about over‑dependence on AI and automation. 6. The Westward Bound Program bridges STEM, life skills, and personal development. Built on the acronym “WEST”—Wisdom, Endurance, Strategy, Tracking—the program supports youth, adults, and entrepreneurs seeking direction and resilience. 7. Mentorship, community, and relationships are central themes. Dr. West’s success was nurtured by professors and role models at her HBCU—mirroring how Jacque and Robyn now uplift the next generation. 8. Her story resonates globally and intergenerationally. From college students to young children to adults, the principles from her memoir and program promote self‑belief, vision, discipline, and perseverance. Notable Quotes (All taken directly from the transcript.) On Dr. West’s impact “She’s a living hidden figure… her accomplishments have actually changed our way of living in every discipline of life.” “Her technology… makes these things possible.” On Juneteenth and recognition “Juneteenth is about the delayed freedom of African Americans… and what Dr. West represents is the quiet, often overlooked brilliance that changes the world.” On STEM access “Our kids are not pursuing high‑paying STEM careers, not because of their aptitude, but simply because they have not been exposed.” On Dr. West’s genius “You don’t have to be loud to be a legacy.” “She is just so humble, but she’s just brilliant. She’s like a mathematical genius.” On technology & mental health “She didn’t want to lose her critical thinking by depending on GPS… everything has a place, and it should complement you, not take over.” On resilience & aspiration “You have to believe there is something greater than what you’re standing in.” “From sharecropper to pioneer—you can be someone from humble beginnings and change the world.” #SHMS #STRAW #BESTSteve Harvey Morning Show Online: http://www.steveharveyfm.com/See omnystudio.com/listener for privacy information.

Find me on Substack.Gautam Baid, CFA, is the founder and managing partner of Stellar Wealth Partners India Fund and internationally bestselling author of The Joys of Compounding, who has dedicated over two decades to mastering patient, quality-focused value investing.Episode Sponsor: Fiscal AI is a modern data terminal that gives investors instant access to twenty years of financials, earnings transcripts, and extensive segment and KPI data—use my link for a two-week free trial plus 15% off: https://fiscal.ai/talkingbillions/3:00 - Gautam introduces his six-pillar compounding framework beyond finance: positive thoughts, good health, good habits, wealth, knowledge, and goodwill, explaining how achieving financial independence in 2018 crystallized his understanding that "in life you get what you compound for on a daily basis."8:00 - Deep dive into compounding positive thoughts through avoiding negative emotions and toxic people while associating with high-quality minds, celebrating small wins to create momentum toward long-term goals.12:00 - Health habits discussion: consume less sugar and junk food, exercise 3-4 times weekly for one hour, sleep 7-8 hours daily—fundamentals that aren't sexy but "just work" when implemented consistently.15:00 - Mathematical equation for wealth: addition (monthly savings) + subtraction (eliminate greed/biases) + division (asset allocation) + multiplication (time horizon) = exponential compounding power.20:00 - Pattern recognition in investing develops through building a "large mental database of businesses and industries through years and decades" allowing identification of opportunities in any market condition.25:00 - Compounding goodwill principle from Guy Spear and Moneesh Pabrai: being genuinely helpful without expectations creates competitive advantage, especially in money management where nice people are rare.42:00 - India investment opportunity: demographic dividend with median age of 29, rising disposable incomes, strong domestic consumption, and companies expanding to overseas markets at 50-100% higher margins.52:00 - Corporate governance revolution in India: promoters now realize good governance earns 25-30x P/E multiples versus 5-6x for poor governance—"it pays to be honest" creates 5x more wealth for insiders.55:00 - Investment journal advice: $10 journal purchased in 2014 became "one of the best value investments" by documenting decisions, tracking mistakes, and archiving market panic commentary for pattern recognition during future corrections.Podcast Program – Disclosure StatementBlue Infinitas Capital, LLC is a registered investment adviser and the opinions expressed by the Firm's employees and podcast guests on this show are their own and do not reflect the opinions of Blue Infinitas Capital, LLC. All statements and opinions expressed are based upon information considered reliable although it should not be relied upon as such. Any statements or opinions are subject to change without notice.Information presented is for educational purposes only and does not intend to make an offer or solicitation for the sale or purchase of any specific securities, investments, or investment strategies. Investments involve risk and unless otherwise stated, are not guaranteed.

The Gödel Problem: A Mathematical Argument Against AI Thought, The Mind and the Machine, Episode 7 by Thomas Aquinas College Lectures & Talks

Contribute to the East West Lecture Series fundraiser: theeastwestseries.com Today, Dr. Jacobs tackles the common objection: Was ancient Christianity infiltrated by Greek philosophy, such that it required a reformation or restoration? The answer is a resounding no. Follow Dr. Jacobs as he tracks the history through Old and New Testaments, German Idealism, and of course, a little realism and nominalism dusted on top for good measure. All the links: Substack: https://nathanajacobs.substack.com/Instagram: https://www.instagram.com/thenathanjacobspodcastWebsite: https://www.nathanajacobs.com/X: https://x.com/NathanJacobsPodSpotify: https://open.spotify.com/show/0hSskUtCwDT40uFbqTk3QSApple Podcast: https://podcasts.apple.com/us/podcast/the-nathan-jacobs-podcastFacebook: https://www.facebook.com/nathanandrewjacobsAcademia: https://vanderbilt.academia.edu/NathanAJacobs00:00:00 Intro 00:02:05 The case for Hellenistic or Platonized Christian baggage 00:06:49 German idealism 00:15:21 Hegel and the Church Fathers 00:20:08 The leftist Hegelians, atheism, and Christianity 00:26:18 The protestant application00:30:42 Open theism 00:35:16 Hebrew ideas vs Greek ideas 00:42:00 Mathematical truth vs Philosophical truth00:50:07 Realism and nominalism 00:56:03 The Septuagint and the Jewish shift away 01:03:58 Are the Church Fathers platonists? 01:19:19 Idealism in Old Testament studies 01:25:11 Cases in the New Testament 

Joel David Hamkins is a mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity, and he’s the #1 highest-rated user on MathOverflow. He is also the author of several books, including Proof and the Art of Mathematics and Lectures on the Philosophy of Mathematics. And he has a great blog called Infinitely More. Thank you for listening ❤ Check out our sponsors: https://lexfridman.com/sponsors/ep488-sc See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc. Transcript: https://lexfridman.com/joel-david-hamkins-transcript CONTACT LEX: Feedback – give feedback to Lex: https://lexfridman.com/survey AMA – submit questions, videos or call-in: https://lexfridman.com/ama Hiring – join our team: https://lexfridman.com/hiring Other – other ways to get in touch: https://lexfridman.com/contact EPISODE LINKS: Joel’s X: https://x.com/JDHamkins Joel’s Website: https://jdh.hamkins.org Joel’s Substack: https://www.infinitelymore.xyz Joel’s MathOverflow: https://mathoverflow.net/users/1946/joel-david-hamkins Joel’s Papers: https://jdh.hamkins.org/publications Joel’s Books: Lectures on the Philosophy of Mathematics: https://amzn.to/3MThaAt Proof and the Art of Mathematics: https://amzn.to/3YACc9A SPONSORS: To support this podcast, check out our sponsors & get discounts: Perplexity: AI-powered answer engine. Go to https://www.perplexity.ai/ Fin: AI agent for customer service. Go to https://fin.ai/lex Miro: Online collaborative whiteboard platform. Go to https://miro.com/ CodeRabbit: AI-powered code reviews. Go to https://coderabbit.ai/lex Chevron: Reliable energy for data centers. Go to https://chevron.com/power Shopify: Sell stuff online. Go to https://shopify.com/lex LMNT: Zero-sugar electrolyte drink mix. Go to https://drinkLMNT.com/lex MasterClass: Online classes from world-class experts. Go to https://masterclass.com/lexpod OUTLINE: (00:00) – Introduction (01:58) – Sponsors, Comments, and Reflections (15:40) – Infinity & paradoxes (1:02:50) – Russell’s paradox (1:15:57) – Gödel’s incompleteness theorems (1:33:28) – Truth vs proof (1:44:52) – The Halting Problem (2:00:45) – Does infinity exist? (2:18:19) – MathOverflow (2:22:12) – The Continuum Hypothesis (2:31:58) – Hardest problems in mathematics (2:41:25) – Mathematical multiverse (3:00:18) – Surreal numbers (3:10:55) – Conway’s Game of Life (3:13:11) – Computability theory (3:23:04) – P vs NP (3:26:21) – Greatest mathematicians in history (3:40:05) – Infinite chess (3:58:24) – Most beautiful idea in mathematics

In the 1800s, it seemed like mathematics was a solved problem. The paradoxes in the field were resolved, and even areas like advanced calculus could be taught consistently and reliably at any school. It was clearly understandable in a way that abstract fields like philosophy weren’t, and it was on its way to solving humanity’s problems. Mathematical work on electromagnetism made modern electrical engineering and power systems possible. New research in algebra created the logical basis for future computer science and digital circuits. But then new problems appeared. In the early 20th century, mathematicians made discoveries that showed them enough to know how little they really knew. Bertrand Russell showed that at its edges, math fell apart. It couldn’t fully define itself on its own terms without becoming logically inconsistent. He gave the analogy of a small-town barber who shaves everyone who doesn't shave himself; the question is, who shaves the barber—if he shaves himself, he breaks the rule, but if he doesn't shave himself, he must, by the rule, shave himself? In today’s episode, I’m speaking to Jason Bardi, author of The Great Math War: How Three Brilliant Minds Fought for the Foundations of Mathematics and we explore the story of three competing efforts by mathematicians to resolve this crisis. What do you do if math, the most logical of all sciences, becomes illogical at a certain point? Bertrand Russell thought the problem could be solved with even more logic, we just hadn’t tried hard enough. David Hilbert thought redemption lay in accepting mathematics as a formal game of arbitrary rules, no different from the moves and pieces in chess. And L. E. J. Brouwer argued math is entirely rooted in human intuition—and that math is not based on logic but rather logic is based on math. Set against the backdrop of one of the most turbulent periods of European history (from the late 19th century through World War I, the 1920s, the Great Depression, and the early days of World War II), we look at what happens when rock-solid truths don’t seem so rock solid anymore.See omnystudio.com/listener for privacy information.

Drift off with calm, bedtime reading that gently explores mathematical finance while supporting sleep and easing insomnia. This calm, bedtime reading blends clear explanations with a steady rhythm, helping sleep come more easily for listeners experiencing insomnia or restless nights. As Benjamin reads, you'll learn about models, probability, and how mathematics shapes modern finance, all presented in a soothing, unhurried way. His calm cadence is designed for bedtime reading and sleep, offering peaceful, fact-filled education without dramatics or performance. This episode supports insomnia relief, stress reduction, and anxious minds while letting curiosity quietly fade into rest. Press play, relax, and allow learning to guide you toward sleep. Happy sleeping! Read with permission from Mathematical finance, Wikipedia (https://en.wikipedia.org/wiki/Mathematical_finance), licensed under CC BY-SA 4.0. Learn more about your ad choices. Visit megaphone.fm/adchoices