Podcasts about mathematical logic

In this episode, host Farzana Baduel engages in an enlightening conversation with Andrew Bruce Smith, a leading expert in artificial intelligence and its applications in digital PR, social media, SEO, and analytics. Andrew Bruce Smith brings over 38 years of experience to the table, having strategically integrated AI into digital communications programmes for some of the world's largest brands. With a strong foundation in Philosophy and Mathematical Logic, Andrew has pioneered the adoption of AI content tools and has shared his expertise with over 3000 organisations, including NATO, NHS, Specsavers, Sky, Jaguar Land Rover, and Disney. In This Episode, We Explore: Andrew's pioneering work in AI programming languages and content tools. Integrating AI into digital communications for global brands. The challenges and opportunities of adopting AI in PR. How AI can enhance PR campaigns and creativity. The future of AI in media relations, content production, and account management Ethical considerations in using AI to combat fake news and misinformation. Recommendations for AI tools and emerging technologies in the PR industry. Connect with Andrew: LinkedIn: Andrew Bruce Smith Twitter: @andismit Website: Escherman Follow Dan & Farzana on Social Media: Twitter & Instagram: @Dangoldmedia | @FarzanaBaduel Executive Producer: David Olajide - david@curzonpr.com Podcast Manager and Editor: Ikechukwu Mgbenwelu- ike.mgbenwelu@gmail.com  Disclaimer: Views expressed by the guest are their own and not necessarily endorsed by the FUSE podcast.

In this week's episode, I speak with Damien Desfontaines, also known by the pseudonym “Ted”, who is the Staff Scientist at Tumult Labs, a startup leading the way on differential privacy. In Damien's career, he has led an Anonymization Consulting Team at Google and specializes in making it easy to safely anonymize data. Damien earned his PhD and wrote his thesis at ETH Zurich, as well as his Master's Degree in Mathematical Logic and Theoretical Computer Science.Tumult Labs' platform makes differential privacy useful by making it easy to create innovative privacy and enabling data products that can be safely shared and used widely. In this conversation, we focus our discussion on Differential Privacy techniques, including what's next in its evolution, common vulnerabilities, and how to implement differential privacy into your platform.When it comes to protecting personal data, Tumult Labs has three stages in their approach. These are Assess, Design, and Deploy. Damien takes us on a deep dive into each with use cases provided.Topics Covered:Why there's such a gap between the academia and the corporate worldHow differential privacy's strong privacy guarantees are a result of strong assumptions; and why the biggest blockers to DP deployments have been eduction & usabilityWhen to use "local" vs "central" differential privacy techniquesAdvancements in technology that enable the private collection of dataTumult Labs' Assessment approach to deploying differential privacy, where a customer defines its 'data publication' problem or questionHow the Tumult Analytics platform can help you build different privacy algorithms that satisfies 'fitness for use' requirementsWhy using gold standard techniques like differential privacy to safely release, publish, or share data has value far beyond complianceHow data scientists can make the analysis & design more robust to better preserve privacy; and the tradeoff between utility on very specific tasks & number of tasks that you can possibly answerDamien's work assisting the IRS & DOE deploy differential privacy to safely publish and share data publicly via the College Scorecards projectHow to address security vulnerabilities (i.e. potential attacks) to differentially private datasetsWhere you can learn more about differential privacyHow Damien sees this space evolving over the next several yearsResources Mentioned:Join the Tumult Labs SlackLearn about Tumult LabsGuest Info:Connect with Damien on LinkedInLearn more on Damien's websiteFollow 'Ted' on Twitter Privado.ai Privacy assurance at the speed of product development. Get instant visibility w/ privacy code scans.Shifting Privacy Left Media Where privacy engineers gather, share, & learnDisclaimer: This post contains affiliate links. If you make a purchase, I may receive a commission at no extra cost to you.Copyright © 2022 - 2024 Principled LLC. All rights reserved.

Today I had the pleasure of talking to Joe Mileti, associate professor of mathematics at Grinnell College. Even if you are not "into" math, you will enjoy this conversation. We talked about how math is not what you think it is. It's not just memorizing formulas and grinding. It's about thinking and, like all thinking, it involves abstraction, logic, using analogies and metaphors, and a bunch of imagination. We also talked about how math is about talking to other mathematicians and doing a kind of "brainstorming."  Joes's new book is Modern Mathematical Logic (Cambridge UP, 2022). Marshall Poe is the founder and editor of the New Books Network. He can be reached at marshallpoe@newbooksnetwork.com. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/new-books-network

Today I had the pleasure of talking to Joe Mileti, associate professor of mathematics at Grinnell College. Even if you are not "into" math, you will enjoy this conversation. We talked about how math is not what you think it is. It's not just memorizing formulas and grinding. It's about thinking and, like all thinking, it involves abstraction, logic, using analogies and metaphors, and a bunch of imagination. We also talked about how math is about talking to other mathematicians and doing a kind of "brainstorming."  Joes's new book is Modern Mathematical Logic (Cambridge UP, 2022). Marshall Poe is the founder and editor of the New Books Network. He can be reached at marshallpoe@newbooksnetwork.com. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Today I had the pleasure of talking to Joe Mileti, associate professor of mathematics at Grinnell College. Even if you are not "into" math, you will enjoy this conversation. We talked about how math is not what you think it is. It's not just memorizing formulas and grinding. It's about thinking and, like all thinking, it involves abstraction, logic, using analogies and metaphors, and a bunch of imagination. We also talked about how math is about talking to other mathematicians and doing a kind of "brainstorming."  Joes's new book is Modern Mathematical Logic (Cambridge UP, 2022). Marshall Poe is the founder and editor of the New Books Network. He can be reached at marshallpoe@newbooksnetwork.com. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/science

Today I had the pleasure of talking to Joe Mileti, associate professor of mathematics at Grinnell College. Even if you are not "into" math, you will enjoy this conversation. We talked about how math is not what you think it is. It's not just memorizing formulas and grinding. It's about thinking and, like all thinking, it involves abstraction, logic, using analogies and metaphors, and a bunch of imagination. We also talked about how math is about talking to other mathematicians and doing a kind of "brainstorming."  Joes's new book is Modern Mathematical Logic (Cambridge UP, 2022). Marshall Poe is the founder and editor of the New Books Network. He can be reached at marshallpoe@newbooksnetwork.com. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/science-technology-and-society

Today I had the pleasure of talking to Joe Mileti, associate professor of mathematics at Grinnell College. Even if you are not "into" math, you will enjoy this conversation. We talked about how math is not what you think it is. It's not just memorizing formulas and grinding. It's about thinking and, like all thinking, it involves abstraction, logic, using analogies and metaphors, and a bunch of imagination. We also talked about how math is about talking to other mathematicians and doing a kind of "brainstorming."  Joes's new book is Modern Mathematical Logic (Cambridge UP, 2022). Marshall Poe is the founder and editor of the New Books Network. He can be reached at marshallpoe@newbooksnetwork.com.

On this ID the Future, host Wesley J. Smith talks with polymath and Human Nature author David Berlinski about the philosophy of mathematics, the corruption of science, the burning of Notre Dame, modern Europe's curious incapacity to build graceful, beautiful structures, and what's driving the devolution of Western society. But before any of that, Berlinski relates the dramatic story of how his parents, European Jews, escaped the Nazis only by the skin of their teeth. This is Part 1 of a two-part conversation borrowed with permission from Wesley J. Smith's Humanize podcast. Source

Edward Hirsch is working at Steklov Institute of Mathematics in St. Petersburg now heading the Laboratory of Mathematical Logic. He also holds a part-time professor position in the new department of Mathematics and Computer Science at St. Petersburg State University. Edward's research interests include algorithms and computational complexity. He is a co-founder of the theoretical computer science conference series CSR (International Computer Science Symposium in Russia), geographically bounded meetings conducted according to "international standards". He is the author of many articles and an advisor to many students. ================================ SUPPORT & CONNECT: Support on Patreon: https://www.patreon.com/denofrich Twitter: https://twitter.com/denofrich Facebook: https://www.facebook.com/denofrich YouTube: https://www.youtube.com/denofrich Instagram: https://www.instagram.com/den_of_rich/ Hashtag: #denofrich © Copyright 2022 Den of Rich. All rights reserved.

Edward Hirsch is working at Steklov Institute of Mathematics at St. Petersburg now heading the Laboratory of Mathematical Logic. He also holds a part-time professor position in the new department of Mathematics and Computer Science at St. Petersburg State University. Edward's research interests include algorithms and computational complexity. He is a co-founder of the theoretical computer science conference series CSR (International Computer Science Symposium in Russia), geographically bounded meetings conducted according to "international standards". He is an author of many articles and advisor to many students.================================PODCAST INFO:Podcast website: https://www.uhnwidata.com/podcastApple podcast: https://apple.co/3kqOA7QSpotify: https://spoti.fi/2UOtE1AGoogle podcast: https://bit.ly/3jmA7ulSUPPORT & CONNECT:Support on Patreon: https://www.patreon.com/denofrichTwitter: https://www.instagram.com/denofrich/Instagram: https://www.instagram.com/denofrich/Facebook: https://www.facebook.com/denofrich

Podcast Why Truth Requires Proof Is Culture Copyright2021.mp3PODCAST 120 WHY TRUTH REQUIRES PROOF IS CULTURE  is a textual analysis viewed through many lens which is grounded in numerous theories and captured and framed in podcast 120 and verbalized in 13 chapters of publication 231, in ISBN 978-976-96689-1-1.Truth can only be seen by those with truth in them. He who does not have Truth in his heart, will always be blind to her.” and there's your proof.” “Fashion does not have to prove that it is serious. It is the proof that intelligent frivolity can be something creative and positive WORKS CITED  Alberto Vanzo, "Kant on the Nominal Definition of Truth", Kant-Studien, 101 (2010), pp. 147–66.Alexis G. Burgess and John P. Burgess (2011). Truth (hardcover) (1st ed.). Princeton University Press. ISBN 978-0-691-14401-6. Retrieved October 4, 2014. a concise introduction to current philosophical debates about truthAlfred North Whitehead, Dialogues, 1954: Prologue.Alfred Tarski, Introduction to Logic and to the Methodology of the Deductive Sciences (ed. Jan Tarski). 4th Edition. Oxford Logic Guides, No. 24. New York and Oxford: Oxford University Press, 1994, xxiv + 229 pp. ISBN 0-19-504472-XAsay, Jamin. "Truthmaker Theory". Internet Encyclopedia of Philosophy.Baudrillard's attribution of this quote to Ecclesiastes is deliberately fictional. "Baudrillard attributes this quote to Eccle-siastes. However, the quote is a fabrication (see Jean Baudrillard. Cool Memories III, 1991–95. London: Verso, 1997). Editor's note: In Fragments: Conversations With François L'Yvonnet. New York: Routledge, 2004:11, Baudrillard acknowledges this 'Borges-like' fabrication." Cited in footnote #4 in Smith, Richard G., "Lights, Camera, Action: Baudrillard and the Performance of Representations" Archived 2018-04-25 at the Wayback Machine, International Journal of Baudrillard Studies, Volume 2, Number 1 (January 2005)Baudrillard, Jean. "Simulacra and Simulations", in Selected Writings Archived 2004-02-09 at the Wayback Ma-chine, ed. Mark Poster, Stanford University Press, 1988; 166 ffBeebee, Helen; Dodd, Julian. Truthmakers: The Contemporary Debate. Clarendon Press. pp. 13–14.Chaitin, Gregory L., The Limits of Mathematics (1997) 1–28, 89 ff.Chaitin, Gregory L., The Limits of Mathematics (1997) esp. 89 ff.Cicéron, Marcus Tullius Cicero; Bouhier, Jean (1812). Tusculanes (in French). Nismes: J. Gaude. p. 273. OCLC 457735057.Compare 1 Thessalonians 5:21: "Prove all things [...]."Cupillari, Antonella. The Nuts and Bolts of Proofs. Academic Press, 2001. Page 3.David, Marion (2005). "Correspondence Theory of Truth" in Stanford Encyclopedia of PhilosophyDefinition of digitization at WhatIs.comDefinition of proof | Dictionary.com". www.dictionary.com.Die Wahrheit ist die Bewegung ihrer an ihr selbst." The Phenomenology of Spirit, Preface, ¶ 48Digitization/digitisation" in Collins English DictionaryElliott Mendelson; Introduction to Mathematical Logic; Series: Discrete Mathematics and Its Applications; Hard-cover: 469 pages; Publisher: Chapman and Hall/CRC; 5 edition (August 11, 2009); ISBN 1-58488-876-8.Etymology, Online. "Online Etymology"Evidence, proof, and facts: a book of sources by Peter Murphy 2003 ISBN 0199261954 pages 1–2Foucault, M. "The Order of Things", London: Vintage Books, 1970 (1966)Garrido, Angel (2012). "A Brief History of Fuzzy Logic". Revista EduSoft., EditorialGittens, William  Anderson  Author, Cinematographer Dip.Com., Arts. B.A. Media Arts SpecSupport the show (http://www.buzzsprout.com/429292)

#artificialintelligence #artificialgeneralintelligence #agi #intelligentmachine #turingmachine #narrowai #generalai #superai Dr Pei Wang, Ph.D. is an Associate Professor of Computer and Information Sciences at Temple University and is the Chief Executive Editor of the Journal of Artificial General Intelligence (JAGI). His research interests include artificial intelligence and cognitive science, especially on unified theories of intelligence, formal models of rationality, reasoning under uncertainty, learning and adaptation, knowledge representation, and real-time decision making. Pei authored Formalization of Evidence: A Comparative Study. Non-Axiomatic Logic (NAL) Specification, Cognitive Logic versus Mathematical Logic, The Logic of Intelligence, Recommendation Based on Personal Preference, Toward a Unified Artificial Intelligence, What Do You Mean by “AI”?, Editorial: What Makes JAGI Special, The Limitation of Bayesianism, Wason's Cards: What is Wrong?, Case-by-Case Problem Solving, From NARS to a Thinking Machine, and Artificial General Intelligence and Classical Neural Network. Pei earned his B.S. in Computer Science at Peking University in 1983, his M.S. in Computer Science at Peking University in 1986, and his Ph.D. in Computer Science & Cognitive Science at Indiana University in 1995. https://cis.temple.edu/~pwang/ https://www.linkedin.com/in/pei-wang-3a46241/ https://lifeboat.com/ex/bios.pei.wang Prelude -0:00 to 0:46 Intro - 0:47 to 1:19 Can you define what's AI, AGI & ASI - 1:20 to 7:42 What is the current progress of narrow intelligence that excites you the most - 7:43 to 15:40 What architecture/framework would be the path ahead for building Artificial General Intelligence- 15:41 to 22:32 Who amongst your peers are on the right path towards building an Intelligent machine - 22:33 to 24:50 Is there a curriculum/course for Artificial General Intelligence - 24:51 to 25:44 will understanding our brains lead to AGI - 25:45 to 28:14 Would robotic embodiment, understanding consciousness play a role in building an intelligent machine - 28:15 to 29:50 will we require something more than a classical computer to build AGI- Neuromorphic or Quantum computing - 29:51 to 30:41 Will AGI be an existential risk - 30:42 to 32:40 When will we have AGI & How would it transform our society- 32:41 to 35:05 What excites you the most about AGI- 35:06 to 36:36 Outro - 36:37 to 38:03

Professor Peter Koellner is a leading Logician and Philosopher based at Harvard University. He has made very important contributions to areas surrounding Mathematical Logic and today he was kind enough to join me for a discussion on Penrose's arguments against the prospects of mechanizing the mind (given Kurt Gödel's work on Incompleteness). Note: I am sorry for the occasional internet connection problems. I hope the relevant parts can still be understood! Conversation Outline: 00:00 What are the Incompleteness Theorems?01:59 Why are Gödel's results relevant for discussions concerning the mind?03:28 Connections between Turing Machines and Formal Systems04:20 When we talk about whether the mind can be mechanized or not, what do we mean? 06:56 Should Cognitive Scientists (or Philosophers of Mind) be interested in this discussion?09:45 The First Generation of Arguments against The Prospects of Mechanizing the Mind19:52 Three Versions of The Mechanistic Thesis21:55 What makes Penrose's New Argument harder to evaluate in theory EA+T?22:56 Penrose's Formulation of The Argument (Quote from his Book)27:49 What are the explicit assumptions behind Penrose's New Argument?32:14 What are the indeterminate statements that Penrose uses in the argument? 36:10 Do you think we'll ever have an adequate formal theory of type-free truth which settles Gödel's First Disjunct (the one targeted by Penrose)? 37:18 Do you think your opponent would accept bringing the key notions of relative provability, absolute provability and truth in the setting of effectively formalized theories? 42:25 Why do you think Penrose does not abandon his New Argument, despite resistance from mathematical logicians?44:35 Unlike Lucas or Penrose, some authors such as Hofstadter use Gödel's results to illuminate the workings of the mind. Do you think the Incompleteness Theorems have anything worthwhile to say here?Enjoy!Apple Podcasts:https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135Spotify: https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10Google Podcasts:https://podcasts.google.com/?q=philosophical%20trialsInstagram: https://www.instagram.com/tedynenu/

Henk Barendregt received his doctorate in Mathematical Logic in 1971, and continued studying studied Zen meditation and Vipasssana meditation until 2006. As occupant of the chair of Foundations of Mathematics and Computer Science at Nijmegen University, he studied meditation and its neuropsychologic....

Episode: 1899 Kurt Gödel: A mathematician brings us down to earth.  Today, a mathematician brings us down to earth.

Joel David Hamkins is an American Mathematician who is currently Professor of Logic at the University of Oxford. He is well known for his important contributions in the fields of Mathematical Logic, Set Theory and Philosophy of Mathematics. Moreover, he is very popular in the mathematical community for being the highest rated user on MathOverflow. Outline of the conversation:00:00 Podcast Introduction00:50 MathOverflow and books in progress04:08 Mathphobia05:58 What is mathematics and what sets it apart?08:06 Is mathematics invented or discovered (more at 54:28)09:24 How is it the case that Mathematics can be applied so successfully to the physical world?12:37 Infinity in Mathematics16:58 Cantor's Theorem: the real numbers cannot be enumerated24:22 Russell's Paradox and the Cumulative Hierarchy of Sets29:20 Hilbert's Program and Godel's Results35:05 The First Incompleteness Theorem, formal and informal proofs and the connection between mathematical truths and mathematical proofs40:50 Computer Assisted Proofs and mathematical insight44:11 Do automated proofs kill the artistic side of Mathematics?48:50 Infinite Time Turing Machines can settle Goldbach's Conjecture or the Riemann Hypothesis54:28 Nonstandard models of arithmetic: different conceptions of the natural numbers1:00:02 The Continuum Hypothesis and related undecidable questions, the Set-Theoretic Multiverse and the quest for new axioms1:10:31 Minds and computers: Sir Roger Penrose's argument concerning consciousnessTwitter: https://twitter.com/tedynenu

  Far too often, we evaluate math ability in high schoolers solely on the basis of grades and level of math learned. A more accurate assessment of a student’s potential on challenging math tasks--including those posed on tests like the SAT and ACT--should consider mathematical maturity.  Amy and Mike invited author and test prep professional Dr. Steve Warner to define what this means and explain the link between mathematical maturity and test success.  What are five things you will learn in this episode? What is mathematical maturity? How can you determine your "level" of mathematical maturity? Can mathematical maturity be improved? How does mathematical maturity relate to standardized test scores? What steps can students seeking higher levels of mathematical maturity take? MEET OUR GUEST Dr. Steve Warner, a New York native, earned his Ph.D. at Rutgers University in Pure Mathematics in May 2001. After Rutgers, Dr. Warner joined the Penn State Mathematics Department as an Assistant Professor and in September 2002, he returned to New York to accept an Assistant Professor position at Hofstra University. By September 2007, Dr. Warner had received tenure and was promoted to Associate Professor. He has taught undergraduate and graduate courses in Precalculus, Calculus, Linear Algebra, Differential Equations, Mathematical Logic, Set Theory, and Abstract Algebra. From 2003 – 2008, Dr. Warner participated in a five-year NSF grant, “The MSTP Project,” to study and improve mathematics and science curriculum in poorly performing junior high schools. He also published several articles in scholarly journals, specifically on Mathematical Logic. Dr. Warner has nearly two decades of experience in general math tutoring and tutoring for standardized tests such as the SAT, ACT, GRE, GMAT, and AP Calculus exams. He has tutored students both individually and in group settings. In February 2010 Dr. Warner released his first SAT prep book “The 32 Most Effective SAT Math Strategies,” and in 2012 founded Get 800 Test Prep. Since then Dr. Warner has written books for the SAT, ACT, SAT Math Subject Tests, AP Calculus exams, and GRE. In 2018 Dr. Warner released his first pure math book called “Pure Mathematics for Beginners.” Since then he has released several more books, each one addressing a specific subject in pure mathematics. Dr. Steve Warner can be reached at steve@SATPrepGet800.com LINKS Gaining Mathematical Maturity Dr. Warner’s extensive catalog of math prep books ABOUT THIS PODCAST Tests and the Rest is THE college admissions industry podcast. Explore all of our episodes on the show page.

An invited talk by the Emeritus Hillman University Professor of Computer Science, Philosophy and Mathematical Logic at Carnegie Mellon University at FLoC2018

Once again, a candidate nominated by Ludwig-Maximilians-Universität (LMU) München has been awarded one of the coveted Alexander von Humboldt Professorships. The philosopher and mathematician Hannes Leitgeb, Professor of Mathematical Logic and Philosophy of Mathematics at the University of Bristol (UK), was selected to receive the accolade by an expert committee set up by the Humboldt Foundation. The prize, which is worth 5 million Euros, is financed by the Federal Ministry for Education and Research, and is the most richly endowed award of its kind in Germany. Leitgeb is one of the leading proponents of an approach to problems in logic, philosophy and the foundations of the scientific method that exploits insights from both philosophical analyses and mathematical theories of provability. In effect, he formulates philosophical questions as precisely posed mathematical propositions, allowing him not only to come up with solutions, but also to explain them with the utmost clarity. Hannes Leitgeb becomes the LMU’s third Humboldt Professor, joining Ulrike Gaul (Systems Biology) and Georgi Dvali (Astrophysics). Leitgeb is one of the most prominent scholars worldwide who tackle analytical philosophy and cognitive sciences with the help of mathematical logic. This multi-pronged approach is motivated by the conviction that philosophical investigations can best be advanced if their fundamental assumptions can be recast as mathematical models that make them more transparent and simpler to describe. As a Humboldt Professor at LMU, Leitgeb will provide the basis for the planned Munich Center for Mathematical Philosophy, Language and Cognition, in which postgraduate and postdoctoral students in the fields of Philosophy, Logic and Mathematics will work together on common problems. The new Center will also collaborate with the Munich Center for Neuroscience, Brain and Mind (MCN). This institution was established in 2007, as the result of an internal competition (LMUinnovativ) to identify innovative ways of tackling questions related to the mind-brain problem. Its members utilize the whole spectrum of disciplines relevant to the neurosciences, from molecular biology, through systemic neurobiology, psychology and neurology, to philosophy. By fostering cooperation between widely diverse areas of study, the two Centers hope to make internationally significant contributions to theoretical and empirical brain sciences. Hannes Leitgeb's interdisciplinary orientation will help further sharpen the profile of the LMU’s Faculty of Philosophy by renewing its long-standing focus on the intersection between philososphy, logic and foundations of science, which is closely associated with the work of Wolfgang Stegmuller. This focus will also be given a future-oriented and internationally apparent impetus. Leitgeb first forged a firm link between philosophical logic and the cognitive sciences in his book “Inference on the Low Level. An Investigation into Deduction, Nonmonotonic Reasoning, and the Philosophy of Cognition”. Here he showed that, under certain circumstances, state transitions in neural networks can be understood as simple ‘if ... then’ inferences. These in turn are known to follow laws governing the behaviour of logical systems that have emerged from studies in the philosophy of language and in theoretical computer science. Leitgeb is currently working on a monograph devoted to Rudolf Carnap’s “The Logical Structure of the World”. He hopes to give this classic text a new lease of life by highlighting the relevance of Carnap’s insights for modern scientific research. One of the aims of this latest endeavour is to discover how to transform theoretical scientific models into propositions framed in terms of our immediate sensory perceptions. To this end, Leitgeb is developing a theory of probability that permits valid inferences about systems which are themselves capable of generating statements about their own probability. Hannes Leitg...

Melvyn Bragg and guests discuss an iconic piece of 20th century maths - Gödel's Incompleteness Theorems. In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations, called axioms, had been shaken. They were deemed to be inconsistent and possibly paradoxical. At the conference, a young man called David Hilbert set out a plan to rebuild the foundations of maths – to make them consistent, all encompassing and without any hint of a paradox. Hilbert was one of the greatest mathematicians that ever lived, but his plan failed spectacularly because of Kurt Gödel. Gödel proved that there were some problems in maths that were impossible to solve, that the bright clear plain of mathematics was in fact a labyrinth filled with potential paradox. In doing so Gödel changed the way we understand what mathematics is and the implications of his work in physics and philosophy take us to the very edge of what we can know.With Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford; John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry and Philip Welch, Professor of Mathematical Logic at the University of Bristol.

Melvyn Bragg and guests discuss an iconic piece of 20th century maths - Gödel’s Incompleteness Theorems. In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations, called axioms, had been shaken. They were deemed to be inconsistent and possibly paradoxical. At the conference, a young man called David Hilbert set out a plan to rebuild the foundations of maths – to make them consistent, all encompassing and without any hint of a paradox. Hilbert was one of the greatest mathematicians that ever lived, but his plan failed spectacularly because of Kurt Gödel. Gödel proved that there were some problems in maths that were impossible to solve, that the bright clear plain of mathematics was in fact a labyrinth filled with potential paradox. In doing so Gödel changed the way we understand what mathematics is and the implications of his work in physics and philosophy take us to the very edge of what we can know.With Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford; John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry and Philip Welch, Professor of Mathematical Logic at the University of Bristol.

Melvyn Bragg and guests discuss an iconic piece of 20th century maths - Gödel’s Incompleteness Theorems. In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations, called axioms, had been shaken. They were deemed to be inconsistent and possibly paradoxical. At the conference, a young man called David Hilbert set out a plan to rebuild the foundations of maths – to make them consistent, all encompassing and without any hint of a paradox. Hilbert was one of the greatest mathematicians that ever lived, but his plan failed spectacularly because of Kurt Gödel. Gödel proved that there were some problems in maths that were impossible to solve, that the bright clear plain of mathematics was in fact a labyrinth filled with potential paradox. In doing so Gödel changed the way we understand what mathematics is and the implications of his work in physics and philosophy take us to the very edge of what we can know.With Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford; John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry and Philip Welch, Professor of Mathematical Logic at the University of Bristol.