Mathematics studies that are independent of any application outside mathematics
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18 episodes with Pure mathematics
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3 episodes with Pure mathematics
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2 episodes with Pure mathematics
2 episodes with Pure mathematics
Head on over to https://cell.ver.so/TOE and use coupon code TOE at checkout to save 15% on your first order. Get ready to witness a turning point in mathematical history: in this episode, we dive into the AI breakthroughs that stunned number theorists worldwide. Join us as Professor Yang-Hue Hi discusses the murmuration conjecture, shows how DeepMind, OpenAI, and EpochAI are rewriting the rules of pure math, and reveals what happens when machines start making research-level discoveries faster than any human could. AI is taking us beyond proof straight into the future of discovery. As a listener of TOE you can get a special 20% off discount to The Economist and all it has to offer! Visit https://www.economist.com/toe Join My New Substack (Personal Writings): https://curtjaimungal.substack.com Listen on Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e Timestamps: 00:00 Introduction to a New Paradigm 01:34 The Changing Landscape of Research 03:30 Categories of Machine Learning in Mathematics 06:53 Researchers: Birds vs. Hedgehogs 09:36 Personal Experiences with AI in Research 11:44 The Future Role of Academics 14:08 Presentation on the AI Mathematician 16:14 The Role of Intuition in Discovery 18:00 AI's Assistance in Vague Problem Solving 18:48 Newton and AI: A Historical Perspective 20:59 Literature Processing with AI 24:34 Acknowledging Modern Mathematicians 26:54 The Influence of Data on Mathematical Discovery 30:22 The Riemann Hypothesis and Its Implications 31:55 The BST Conjecture and Data Evolution 33:29 Collaborations and AI Limitations 36:04 The Future of Mathematics and AI 38:31 Image Processing and Mathematical Intuition 41:57 Visual Thinking in Mathematics 49:24 AI-Assisted Discovery in Mathematics 51:34 The Murmuration Conjecture and AI Interaction 57:05 Hierarchies of Difficulty 58:43 The Memoration Breakthrough 1:00:28 Understanding the BSD Conjecture 1:01:45 Diophantine Equations Explained 1:03:39 The Cubic Complexity 1:19:03 Neural Networks and Predictions 1:21:36 Breaking the Birch Test 1:24:44 The BSD Conjecture Clarified 1:26:21 The Role of AI in Discovery 1:30:29 The Memoration Phenomenon 1:32:59 PCA Analysis Insights 1:35:50 The Emergence of Memoration 1:38:35 Conjectures and AI's Role 1:41:29 Generalizing Biases in Mathematics 1:44:55 The Future of AI in Mathematics 1:49:28 The Brave New World of Discovery Links Mentioned: - Topology and Physics (book): https://amzn.to/3ZoneEn - Machine Learning in Pure Mathematics and Theoretical Physics (book): https://amzn.to/4k8SXC6 - The Calabi-Yau Landscape (book): https://amzn.to/43DO7H0 - Yang-Hui's bio and published papers: https://www.researchgate.net/profile/Yang-Hui-He - A Triumvirate of AI-Driven Theoretical Discovery (paper): https://arxiv.org/abs/2405.19973 - Edward Frenkel explains the Geometric Langlands Correspondence on TOE: https://www.youtube.com/watch?v=RX1tZv_Nv4Y - Stone Duality (Wiki): https://en.wikipedia.org/wiki/Stone_duality - Summer of Math Exposition: https://some.3b1b.co/ - Machine Learning meets Number Theory: The Data Science of Birch–Swinnerton-Dyer (paper): https://arxiv.org/pdf/1911.02008 - The L-functions and modular forms database: https://www.lmfdb.org/ - Epoch AI FrontierMath: https://epoch.ai/frontiermath/the-benchmark - Mathematical Beauty (article): https://www.quantamagazine.org/mathematical-beauty-truth-and-proof-in-the-age-of-ai-20250430/ SUPPORT: - Become a YouTube Member (Early Access Videos): https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join - Support me on Patreon: https://patreon.com/curtjaimungal - Support me on Crypto: https://commerce.coinbase.com/checkout/de803625-87d3-4300-ab6d-85d4258834a9 - Support me on PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 SOCIALS: - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs #science Learn more about your ad choices. Visit megaphone.fm/adchoices
Pure mathematics: the tranquil wilderness of logic where numbers frolic without purpose. No real-world applications here—just soothing abstractions to lull you into oblivion. Great for sleep, boredom, or philosophical insomnia relief. Want More? Request a topic: https://www.icantsleeppodcast.com/request-a-topic Listen ad-free & support: https://icantsleep.supportingcast.fm/ Shop sleep-friendly products: https://www.icantsleeppodcast.com/sponsors This content is derived from the Wikipedia article on Pure Mathematics, available under the Creative Commons Attribution-ShareAlike (CC BY-SA) license. Read the full article: Wikipedia - Pure Mathematics. Learn more about your ad choices. Visit megaphone.fm/adchoices
In this episode, we dive into the world of international touring and performance with Cliff and Susan. From their most memorable shows to their secrets for maintaining musical versatility, we explore the highs and lows of life on the road. With their unique blend of energy, enthusiasm, and expertise, Cliff and Susan share insights on adapting to diverse cultural audiences, managing a demanding tour schedule, and overcoming challenges. Tune in for a behind-the-scenes look at the lives of these globetrotting musicians, and get ready to be inspired by their passion, creativity, and dedication to their craft. Whether you're a music lover, an aspiring performer, or simply looking for a dose of creativity and inspiration, this episode is sure to delight! If Charlie Daniels married a female Jerry Lee Lewis, you have Cliff and Susan, a married country duo from Little Rock, Arkansas. The duo captivates audiences worldwide with their piano, fiddle, and guitar performances. Their lively, request-driven, and interactive shows keep crowds entertained for hours as they masterfully deliver diverse musical genres to people of all ages. With over 2,000 songs in their arsenal, their musical versatility is truly impressive.Cliff Prowse, a singer, songwriter, multi-instrumentalist, arranger, and producer, has been creating music for decades. He started at a young age honing his skills in the town square of Mt. View, Arkansas, to recording, living, and performing in Nashville, TN. Cliff's versatility as a multi-instrumentalist has led to many collaborations with award-winning artists. He has produced over 30 artists and continues writing, arranging, and creating.Susan Erwin Prowse, a singing piano entertainer, boasts a thriving international music career spanning two decades, with two albums released out of Nashville. Since 2003, Susan has followed her music passion and left the corporate world as a Radio Frequency Engineer to travel the world entertaining in high-energy piano bars. Susan took 10 years of classical piano lessons starting at the age of 6. She is an honors graduate of the University of Central Arkansas with a degree in Pure Mathematics.Cliff and Susan met on stage in Little Rock, Arkansas, in 2016 and immediately formed their music duo. Love blossomed, and they eloped in Las Vegas in 2017. Cliff & Susan have toured internationally in over seven countries, performing more than 200 shows per year. The duo released their debut single, "Drivin' Me Crazy," in April 2020. Their signature song, "Fiddle & Keys," released in January 2023, caught the attention of Governor Mike Huckabee, and lead to an invitation to perform on his nationally televised Huckabee Show in February 2023. On October 6, 2023, they released “Neon Dreams” as a single leading up to their 12-song song debut album, “Fiddle & Keys,” released on October 27, 2023. Their debut album charted Top 40 Apple Country Albums Chart upon release. They've opened for national acts such as ZZ Top and Niko Moon.In 2017, Cliff and Susan incorporated Big Red Dog Productions, a music production and artist development company based in Little Rock, Arkansas. As an extension of their artistic brand, their e-commerce store, Rainy Ray, features their handmade jewelry, apparel, and artwork. Their annual Yadaloo Music & Arts Festival won Arkansas's Best New Festival of the Year in 2019. It led to them winning the Arkansas Country Music Award's Promoter of the Year. The duo has hosted the Cliff & Susan Podcast since 2021, offering insights into their lives while educating, entertaining, and inspiring listeners. In 2022, they launched the Entertainers Academy to help independent artists build profitable music careers and stay up-to-date in the ever-evolving music industry. Cliff and Susan reside in Little Rock, Arkansas, with their three adorable dogs, Booker, Charlie, and Gibby. :)https://www.susanerwin.com/news http://instagram.com/cliffandsusan http://www.facebook.com/cliffandsusan http://twitter.com/cliff_and_susan http://www.youtube.com/@cliffandsusan https://www.tiktok.com/@cliffandsusan http://www.linkedin.com/in/susanerwinprowse http://pinterest.com/susanerwinprowse http://soundcloud.com/cliffandsusanBecome a supporter of this podcast: https://www.spreaker.com/podcast/i-am-refocused-radio--2671113/support.
In Today's episode of Moment of Truth, Saurabh sits down with Brian Chau, Executive Director of Alliance for the Future and author of the "AI Pluralism" Newsletter, to discuss all things artificial intelligence including OpenAI's ChatGPT, Google's Gemini, market competitors like Anthropic, the Great Power conflict with China, US regulation of the industry, current AI legislation and executive orders, the threat of censorship, and much more.#BrianChau #AllianceForTheFuture #AFFuture #AI #OpenAI #Google #Microsoft #Amazon #Apple #Anthropic #JoeBiden #ArtificialIntelligence #Censorship #InnovationBrian Chau is the executive director of Alliance for the Future. Brian has a background in Pure Mathematics and has won international awards in computer science. He is a former machine learning engineer and the current author of the AI Pluralism newsletter, a popular newsletter on Artificial Intelligence.Learn more about Brian Chau's work:https://www.affuture.org/https://substack.com/@cactushttps://twitter.com/psychosortBecome a 'Truther' or 'Statesman' to get access to exclusive perks. Watch ALL EPISODES a day before everyone else, and enjoy members-only bonus content: youtube.com/channel/UC4qmB5DeiFxt53ZPZiW4Tcg/join––––––Follow American Moment across Social Media:Twitter – https://twitter.com/AmMomentOrgFacebook – https://www.facebook.com/AmMomentOrgInstagram – https://www.instagram.com/ammomentorg/YouTube – https://www.youtube.com/channel/UC4qmB5DeiFxt53ZPZiW4TcgRumble – https://rumble.com/c/ammomentorCheck out AmCanon:https://www.americanmoment.org/amcanon/Follow Us on Twitter:Saurabh Sharma – https://twitter.com/ssharmaUSNick Solheim – https://twitter.com/NickSSolheimAmerican Moment's "Moment of Truth" Podcast is recorded at the Conservative Partnership Campus in Washington DC, produced by American Moment Studios, and edited by Jake Mercier and Jared Cummings.Subscribe to our Podcast, "Moment of Truth"Apple Podcasts – https://podcasts.apple.com/us/podcast/moment-of-truth/id1555257529Spotify – https://open.spotify.com/show/5ATl0x7nKDX0vVoGrGNhAj Hosted on Acast. See acast.com/privacy for more information.
Professor Amie Wilkinson, from the Department of Mathematics, studies smooth dynamical systems, ergodic theory, and mathematical chaos. Although she met an unsupportive advisor in college, her love for pure maths stayed strong, and she saw herself pursuing graduate school even more while working after college. Tune in to hear Professor Wilkinson talks about her career path and how she became a University of Chicago professor.
On this day in 1996, FBI agents raided the remote Montana cabin of Theodore “Ted” Kaczynski.See omnystudio.com/listener for privacy information.
Read the full transcript here. What should the goals of math education be? What does it mean to "think well"? Is math real? Why are feelings of bewilderment or confusion so common in math classes but not as common in other subjects? Schools now generally offer reading and writing instruction separately — even though both are important for language use — because the skill sets they require can differ so widely; so how might math education benefit from drawing a similar distinction? What should math classes impart to students that will enable them to engage as citizens with complex or controversial issues? What does it mean to ask good questions in math? Can math teach empathy? What is category theory? Can most people learn most things if they just have the right teacher and/or educational materials?Eugenia Cheng is a mathematician, educator, author, public speaker, columnist, concert pianist, composer, and artist. She is Scientist In Residence at the School of the Art Institute of Chicago. She won tenure in Pure Mathematics at the University of Sheffield, UK, and is now Honorary Visiting Fellow at City, University of London. She has previously taught at the Universities of Cambridge, Chicago, and Nice, and holds a PhD in pure mathematics from the University of Cambridge. Alongside her research in Category Theory and undergraduate teaching, her aim is to rid the world of "math phobia". Eugenia was an early pioneer of math on YouTube, and her videos have been viewed around 15 million times to date. She has also written several books, including: How to Bake Pi (2015); Beyond Infinity (2017); The Art of Logic (2018); x + y : A Mathematician's Manifesto for Rethinking Gender (2020); The Joy of Abstraction: A Exploration of Math, Category Theory, and Life (2022); Is Math Real? How Simple Questions Lead Us to Mathematics' Deepest Truths (2023); and two children's books: Molly and the Mathematical Mysteries and Bake Infinite Pie with x + y. She also writes the "Everyday Math" column for the Wall Street Journal and has completed mathematical art commissions for Hotel EMC2, 6018 North, the Lubeznik Center, and the Cultural Center, Chicago. She is the founder of the Liederstube, an intimate oasis for art song based in Chicago. As a composer she has been commissioned by GRAMMY-nominated soprano Laura Strickling and is one of the composers for the LYNX Amplify series, setting work by autistic poets who are primarily non-speaking. Learn more about her at her website, eugeniacheng.com. [Read more]
Please support us https://www.patreon.com/mlst https://discord.gg/aNPkGUQtc5 https://twitter.com/MLStreetTalk Lance Da Costa aims to advance our understanding of intelligent systems by modelling cognitive systems and improving artificial systems. He's a PhD candidate with Greg Pavliotis and Karl Friston jointly at Imperial College London and UCL, and a student in the Mathematics of Random Systems CDT run by Imperial College London and the University of Oxford. He completed an MRes in Brain Sciences at UCL with Karl Friston and Biswa Sengupta, an MASt in Pure Mathematics at the University of Cambridge with Oscar Randal-Williams, and a BSc in Mathematics at EPFL and the University of Toronto. Summary: Lance did pure math originally but became interested in the brain and AI. He started working with Karl Friston on the free energy principle, which claims all intelligent agents minimize free energy for perception, action, and decision-making. Lance has worked to provide mathematical foundations and proofs for why the free energy principle is true, starting from basic assumptions about agents interacting with their environment. This aims to justify the principle from first physics principles. Dr. Scarfe and Da Costa discuss different approaches to AI - the free energy/active inference approach focused on mimicking human intelligence vs approaches focused on maximizing capability like deep reinforcement learning. Lance argues active inference provides advantages for explainability and safety compared to black box AI systems. It provides a simple, sparse description of intelligence based on a generative model and free energy minimization. They discuss the need for structured learning and acquiring core knowledge to achieve more human-like intelligence. Lance highlights work from Josh Tenenbaum's lab that shows similar learning trajectories to humans in a simple Atari-like environment. Incorporating core knowledge constraints the space of possible generative models the agent can use to represent the world, making learning more sample efficient. Lance argues active inference agents with core knowledge can match human learning capabilities. They discuss how to make generative models interpretable, such as through factor graphs. The goal is to be able to understand the representations and message passing in the model that leads to decisions. In summary, Lance argues active inference provides a principled approach to AI with advantages for explainability, safety, and human-like learning. Combining it with core knowledge and structural learning aims to achieve more human-like artificial intelligence. https://www.lancelotdacosta.com/ https://twitter.com/lancelotdacosta Interviewer: Dr. Tim Scarfe TOC 00:00:00 - Start 00:09:27 - Intelligence 00:12:37 - Priors / structure learning 00:17:21 - Core knowledge 00:29:05 - Intelligence is specialised 00:33:21 - The magic of agents 00:39:30 - Intelligibility of structure learning #artificialintelligence #activeinference
Yang-Hui He is a mathematical physicist and pioneer in the usage of artificial intelligence and machine learning in pure mathematics and theoretical physics.Today's topics include:* The mathematical foundations of the laws of nature* Misconceptions about geometry* The search for a ‘theory of everything', leading to the rise of string theory* Artificial intelligence and its applications in fundamental sciences* And Yang's pioneering use of machine learning in string theory and beyondYang's books:* Machine Learning in Pure Mathematics and Theoretical Physics* Topology And Physics* The Calabi–Yau Landscape: From Geometry, to Physics, to Machine LearningSUPPORT & CONNECT:- Follow and leave a 5-star review- LinkedIn: https://www.linkedin.com/in/matthewgeleta/- Twitter: https://twitter.com/MatthewGeleta- Donate: https://bit.ly/donate-to-paradigmPODCAST INFO:- Spotify: https://spoti.fi/3IVDF2W- Apple Podcasts: https://apple.co/3oEZYmJ- Google Podcasts: https://bit.ly/paradigm-on-google- YouTube: https://bit.ly/paradigm-on-youtube- RSS: https://api.substack.com/feed/podcast/1656558/s/65176.rss Get full access to Paradigm at paradigmpodcast.substack.com/subscribe
Support Us On Patreon: patreon.com/TheTangentTerritory Follow The Tangent Territory: https://twitter.com/tangenterritory Maths Beyond Limits Camp: https://mathsbeyondlimits.eu/ Entirely produced by the host. Books mentioned in the episode: 1. A Brief History of Time, Stephen Hawking: https://tinyurl.com/2p889t8j 2. A Concise Introduction to Pure Mathematics, Martin Liebeck: https://tinyurl.com/38f8sux9 3. Topics in Algebra, I.N. Herstein: https://tinyurl.com/4dvpea2y
My guest is Ross Farrelly. Ross is the Director of Data Science and Artificial Intelligence for IBM Asia Pacific. He works with companies throughout the region to develop and execute on their strategies to adopt and realise the benefits of predictive analytics and AI. He has a Master of Applied Statistics, a Masters of Applied Ethics, a first class honours degree in Pure Mathematics and a PhD in Information Systems.Some of the highlights of our conversation include exploring the ethical questions that AI provokes, the explosion of ChatGPT, how AI is helping the planet, and what organisational leaders need to be understanding about AI to lead more effectively in today's world.Enjoy the conversation. You can reach out to Ross directly at: https://www.linkedin.com/in/rossfarrelly To learn more about what it takes to be an evolved leader, and to check out our other podcast episodes, go to: https://www.evolvedstrategy.com.au Please note, the views and opinions expressed in this podcast are the personal opinions of the speakers and do not necessarily reflect the views or positions of any entities they represent.
Paul Erdős (1913 – 1996) is one of the most celebrated mathematicians of the 20th century. During his long career, he made a number of impressive advances in our understanding of maths and developed whole new fields in the subject. He was born into a Jewish family in Hungary just before the outbreak of World War I, and his life was shaped by the rise of fascism in Europe, anti-Semitism and the Cold War. His reputation for mathematical problem solving is unrivalled and he was extraordinarily prolific. He produced more than 1,500 papers and collaborated with around 500 other academics. He also had an unconventional lifestyle. Instead of having a long-term post at one university, he spent much of his life travelling around visiting other mathematicians, often staying for just a few days. With Colva Roney-Dougal Professor of Pure Mathematics at the University of St Andrews Timothy Gowers Professor of Mathematics at the College de France in Paris and Fellow of Trinity College, Cambridge and Andrew Treglown Associate Professor in Mathematics at the University of Birmingham The image above shows a graph occurring in Ramsey Theory. It was created by Dr Katherine Staden, lecturer in the School of Mathematics at the Open University.
Paul Erdős (1913 – 1996) is one of the most celebrated mathematicians of the 20th century. During his long career, he made a number of impressive advances in our understanding of maths and developed whole new fields in the subject. He was born into a Jewish family in Hungary just before the outbreak of World War I, and his life was shaped by the rise of fascism in Europe, anti-Semitism and the Cold War. His reputation for mathematical problem solving is unrivalled and he was extraordinarily prolific. He produced more than 1,500 papers and collaborated with around 500 other academics. He also had an unconventional lifestyle. Instead of having a long-term post at one university, he spent much of his life travelling around visiting other mathematicians, often staying for just a few days. With Colva Roney-Dougal Professor of Pure Mathematics at the University of St Andrews Timothy Gowers Professor of Mathematics at the College de France in Paris and Fellow of Trinity College, Cambridge and Andrew Treglown Associate Professor in Mathematics at the University of Birmingham The image above shows a graph occurring in Ramsey Theory. It was created by Dr Katherine Staden, lecturer in the School of Mathematics at the Open University.
Support me by becoming wiser and more knowledgeable – check out books by or related to these intellectuals for sale on Amazon: Terence Tao - https://amzn.to/4cACjHV Jacob Lurie - https://amzn.to/3U5NIZr Simon Donaldson - https://amzn.to/3x99r9w Maxim Kontsevich - https://amzn.to/3VxbPRL If you purchase a book through this link, I will earn a 4.5% commission and be extremely delighted. But if you just want to read and aren't ready to add a new book to your collection yet, I'd recommend checking out the Internet Archive, the largest free digital library in the world. If you're really feeling benevolent you can buy me a coffee or donate over at https://ko-fi.com/theunadulteratedintellect. I would seriously appreciate it! __________________________________________________ Terence Chi-Shen Tao (born 17 July 1975) is an Australian mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory. Tao was born to ethnic Chinese immigrant parents and raised in Adelaide. Tao won the Fields Medal in 2006 and won the Royal Medal and Breakthrough Prize in Mathematics in 2014. He is also a 2006 MacArthur Fellow. Tao has been the author or co-author of over three hundred research papers. He is widely regarded as one of the greatest living mathematicians and has been referred to as the "Mozart of mathematics". Jacob Alexander Lurie (born December 7, 1977) is an American mathematician who is a professor at the Institute for Advanced Study. Lurie is a 2014 MacArthur Fellow. Simon Kirwan Donaldson (born 20 August 1957) is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. He is currently a permanent member of the Simons Center for Geometry and Physics at Stony Brook University in New York, and a Professor in Pure Mathematics at Imperial College London. Maxim Lvovich Kontsevich (born 25 August 1964) is a Russian and French mathematician and mathematical physicist. He is a professor at the Institut des Hautes Études Scientifiques and a distinguished professor at the University of Miami. He received the Henri Poincaré Prize in 1997, the Fields Medal in 1998, the Crafoord Prize in 2008, the Shaw Prize and Breakthrough Prize in Fundamental Physics in 2012, and the Breakthrough Prize in Mathematics in 2015. Richard Lawrence Taylor (born 19 May 1962) is a British mathematician working in the field of number theory. He is currently the Barbara Kimball Browning Professor in Humanities and Sciences at Stanford University. Taylor received the 2015 Breakthrough Prize in Mathematics "for numerous breakthrough results in the theory of automorphic forms, including the Taniyama–Weil conjecture, the local Langlands conjecture for general linear groups, and the Sato–Tate conjecture." He also received the 2007 Shaw Prize in Mathematical Sciences for his work on the Langlands program with Robert Langlands. He also served on the Mathematical Sciences jury for the Infosys Prize from 2012 to 2014. Yuri Borisovich (Bentsionovich) Milner (born 11 November 1961) is a Soviet-born Israeli entrepreneur, investor, physicist and scientist . He is a cofounder and former chairperson of internet company Mail.Ru Group (now VK) and a founder of investment firm DST Global. Through DST Global, Milner is an investor in Byju's, Facebook, Wish, and many others. In 2012 Milner's personal investments included a stake in 23andMe, Habito, Planet Labs, minority stake in a real estate investments startup, Cadre in 2017. Audio source here --- Support this podcast: https://podcasters.spotify.com/pod/show/theunadulteratedintellect/support
Natascha McIntyre Hall has an Executive Role in the Development & Construction industry, and was nominated as one of the Top 5 most influential female clients to work with in 2022. Yes: She made it up the ladder in a very male industry. She also has a Masters in Pure Mathematics. And her current major goal & driver is to redefine profit in the industry, from solely monetary to the true benefit to a community through inclusive design. So you should definitely meet her. My personal reasons, why she is a role model to me: Her outspokenness, the openness & passion she talks about the topics important to her. Also, our shared acknowledgment that we have to make the best of our time & think it's important to talk to strangers. As a start, due to current developments, we also talked about the role model function of Queen Elisabeth II. So what did she do? She showed people what was possible. She drove the King of Saudi Arabia around behind the steering wheel, changed the law of succession, had a big heart for her horses as well as dogs. All this by devoting her own life to a role/career that she even did not pick herself. With massive amount of self-discipline. So what is Natascha's advice to climb the career ladder? What are her notable achievements & further plentiful ideas to make housing more socially profitable? She gives detailed hands-on-learnings, how to approach the needs of people & why a diversity of ideas is vital to make a project inclusive. Big hint: Gen Z is hugely important as well to create the living of the future. Finally, we discuss, why it is important to be outspoken, and to live your life, because „life is when you have other plans.“. My favourite quote: „The ability to speak the truth is sometimes a blessing but sometimes a curse.“ Have fun.⭐️ LET'S CONNECT:
Libo Valencia is a mathematics educator in New York with over a dozen years of experience. Libo is a passionate teacher who strongly believes that understanding mathematics can help all students develop critical thinking and problem-solving skills that can be utilized outside the classroom. His upcoming book Math Play on CodeBreaker Publishing will provide any educator practical ideas for expanding a child's perspective of math beyond assignments to engagement.Libo is known for his use of different technologies to engage his students and bring math concepts to life. He currently teaches at Horace Greeley High School in Chappaqua, CUNY Lehman College, and Mercy College. As a mathematics educator, he has taught a wide range of subjects, from remedial algebra classes to upper-level calculus. Libo holds a Bachelor of Arts in Mathematics, a Master of Arts in Pure Mathematics, and a Master of Science in Educational Leadership. Resources mentioned during the episode:Desmos: desmos.comGeogebra: geogebra.orgArticle for Math Assoc of America: engaging-students-with-a-desmos-art-projectConnect with Libo :Website mathplay4all.comTwitter: @MrValencia24Blogs by Libo: blog.savvas.com/contributors/libardo-valencia/Follow ideas for #MathPlay on TwitterChris Woods is the host of the STEM Everyday Podcast... Connect with him:Website: dailystem.comTwitter: @dailystemInstagram: @dailystemYouTube: youtubeGet Chris's book Daily STEM on AmazonSupport the show
How can we make sense of what we're told about risk? We're bombarded with messages on subjects ranging from COVID to the economy from people that range from genuine experts to those with no expertise but strong opinions. On this episode, I'm speaking to Professor David Spiegelhalter.David is Chair of the Winton Centre for Risk and Evidence Communication within the Department of Pure Mathematics and Mathematical Statistics at Cambridge University. The Centre is dedicated to improving the way that quantitative evidence is used in society. Listeners in the UK will almost certainly have seen or heard David. Since the start of the pandemic he's been a regular fixture on TV and radio, helping to make sense of the things we're being told about the virus. In a world of self-appointed experts whose only qualification is from the University of YouTube and untrustworthy politicians telling us they're "following the science", he's been a voice of clarity and common sense. In our discussion, we explore what drives David's interest in statistics, why we like to see connections between things that might not actually be there, why the mantra of “following the science” is nonsensical and whether there is such a thing as coincidence. David also provides plenty of practical tips for communicating and interpreting messages about risk. As you might expect for someone who specialises in risk communication, David is really good at getting his message across in ways we can all understand. My huge thanks to long-time friend of the show Roger Miles, who helped to make this conversation possible.To find out more about David, visit his academic website: https://wintoncentre.maths.cam.ac.uk/about/people/professor-sir-david-spiegelhalter/or his personal website: https://www.statslab.cam.ac.uk/~david/You'll find his books in all good bookstores. For more information, visit:The Art of Statistics — https://www.penguin.co.uk/books/294857/the-art-of-statistics-by-spiegelhalter-david/9780241258767COVID by Numbers — https://www.penguin.co.uk/authors/126755/david-spiegelhalterFor video content, I recommend:Communicating statistics in the time of COVID — https://www.youtube.com/watch?v=JW9plVfanjoFalse Positives — https://www.youtube.com/watch?v=XmiEzi54lBIBe Prepared To Show Your Working — https://www.youtube.com/watch?v=E12_F4xeOHwIn our discussion, we also refer to the episode featuring Tim Harford on using Data to Make Smarter Decisions. You can hear that here: https://www.humanriskpodcast.com/tim-harford-on-using-data/
In this episode, Mark and Georgia spoke to Professor Sir David Spiegelhalter, who is currently Chair of the Winton Centre for Risk and Evidence Communication, based within the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. Prior to this, he was the Winton Professor for the Public Understanding of Risk in the Statistical Laboratory within the same department. He completed his undergraduate degree in statistics at the University of Oxford, later moving to University College London to complete his MSc and PhD in mathematical statistics under the supervision of Sir Adrian Smith. His research interests include use of Bayesian methods in medical statistics, and the monitoring and comparing of clinical and public-health outcomes and their associated publication as performance indicators. Currently, he is working on improving the way in which risk and statistical evidence is taught and discussed in society. He has hosted and appeared on various TV and radio shows such as BBC Horizon and Desert Island Discs, and has also published several books. You can find Professor Spiegelhalter on Twitter @d_spiegel, or his personal home page: https://www.statslab.cam.ac.uk/~david/ (where you can find the video of him on Winter Wipeout!). The BlueSci Podcast is run by the Cambridge University Science Magazine. This episode was hosted by Georgia Nixon and Mark Grimes. Visit www.bluesci.co.uk to access our free magazine, and find out how to get involved. If you enjoyed this episode, please subscribe and leave a review or rating! we welcome your feedback and suggestions via email: podcast(at)bluesci.co.uk. You can also follow us on Twitter on @bluescipod or Instagram @bluescicam.
131 Technology beyond Government with Dimitri Kusnezov . Dr. Dmitri Kusnezov received A.B. degrees in Physics and in Pure Mathematics with highest honors from UC Berkeley. Following a year of research at the Institut fur Kernphysik, KFA-Julich, in Germany, he attended Princeton University earning his MS in Physics and Ph.D. in Theoretical Nuclear Physics. At Michigan State University, he conducted postdoctoral research and then became an instructor. In 1991, he joined the faculty of Yale University as an assistant professor in physics, becoming an associate professor in 1996. He has served as a visiting professor at numerous universities around the world. Dr. Kusnezov has published over 100 articles and a book. He joined federal service at the National Nuclear Security Administration in late 2001 and is a member of the Senior Executive Service and is also a Visiting Researcher at Yale. He currently serves as Deputy Under Secretary for A.I. and Technology. We talk about How did culture have to evolve to be conducive for discovery to take place? How is technology being utilized in decision making at all levels in the government? How does one make complex decisions? How can a young company get access to Washington DC resources and connections? And much more Connect with Dimitri Kusnezov https://www.linkedin.com/in/dimitri-kusnezov-097a9b68/
Dr. Julian Sahasrabudhe is a University Lecturer (Assistant Professor in the American/Canadian system) in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge, Cambridge, United Kingdom. Dr. Sahasrabudhe is the recipient of the 2021 European Prize in Combinatorics. In a conversation with students from Simon Fraser University, Amritha Raj Kizhakkeputhukulathil Ramanan, Brian Krammer, and Anmol Anmol Singh, Dr. Sahasrabudhe talks about how it was to be a late bloomer in mathematics, some of the places that he visited and the people that he met on his academic journey, and about his current research interests.
Dr. Donald Robertson is a Neumann Research Fellow in Pure Mathematics in the Department of Mathematics at the University of Manchester, Manchester, United Kingdom. Dr. Robertson is interested in ergodic theory and its application to combinatorial problems. In a conversation with students from Simon Fraser University, Anmol Anmol Singh, Amritha Raj Kizhakkeputhukulathil Ramanan, and Brian Krammer, Dr. Robertson talks about why he preferred mathematics over physics, tells about the importance of communication in mathematics, and talks about connections between ergodic theory and Ramsey theory.
Mahe Zehra Husain a.k.a MZ is a trained mathematician and data scientist with a passion for creativity and color since a very young age. At the age of nineteen she started her Masters in Pure Mathematics and in 2008 left for the University of Texas at Austin to pursue her Masters degree in Operations Research. She scored a 4.0 in three out of four semesters while working on her art E-Books which are now available on amazon. After returning from her masters she joined FiveRivers Technology as Manager Operations and Co-founder of pepper.pk which was FRTs first mobile app unit. In 2011 under her leadership and UI/UX team, FRT started creating world number one apps. Several newspapers and channels highlighted their work and their team started working for names like Samsung and local tel-co giants. She introduced data science analytics, Virtual Reality (VR), Artificial Intelligence (AI) and Internet of Things (IoT) at FRT and was the key person in building its team and grew the team and revenue 300%. She became FRTs first female CEO in 2017, one of a handful of tech CEOs in Pakistan. She holds a consulting position as Chief Data Scientist at Ballogy and she also works as managing editor of a US based AI Magazine “Cognitive Times.” Since a young age Husain believes she has a chaotic brain that runs in 50 different directions at the same time! So she harnessed her creative side and indulged herself into arts, crafts and painting. She's been using her right brain to balance her left brain dominated life and she says it brings balance to her life and makes her feel alive. She runs her creative blog and has released several creative e-books and courses some of which have been best sellers on Amazon a number of times. She also exhibited at the Maker Faire in NYC with her new stencil product and is Pakistan's first Certified Zentangle Teacher. Husain says that she wants to empower the youth of Pakistan specially young women, so she has started working on an entrepreneurial book which will be launched this year in 2021 and is aiming towards constructing a multipurpose campus in Lahore which will act as a more inviting and refreshing workspace along with a learning hub for young tech entrepreneurs. She is currently working on some cutting edge data science projects while running her e-book publishing label MZ Creates on the side.
This ID the Future wraps up a lively four-part series between religious skeptic Michael Shermer and Return of the God Hypothesis author and philosopher of science Stephen Meyer. Here Meyer underscores the fact that every worldview must posit something as the prime reality, and he argues that positing mind (rather than matter) as the prime reality solves far more problems in science, and not just in origins science. What about the idea of a multiverse to explain the fine tuning of the laws and constants of physics? Meyer concedes that this is a solution of sorts, but it comes at a tremendous cost, which he explains. That's just a taste of where Meyer and Shermer go in this final segment. Read More › Source
I grew up reading the Choose Your Own Adventure series but it had been years — decades even! — since I'd read a game book. Then I stumbled upon the fascinating book Meanwhile by Jason Shiga and was completely sucked back into this incredible genre. When you open Meanwhile you are a young boy on his way to an ice-cream shop. If you get vanilla? You go home. The end! But if you get chocolate? You plunge into thousands of endlessly splintering storylines. You meet a mad scientist. You jump in a time travel machine. The fate of the world is suddenly at stake! I have no idea how someone could imagine a book this complex and yet so elegant to experience. I was sucked in. So I reach out to Jason Shiga and was grateful that he agreed to come on 3 Books. Jason is a Japanese-American cartoonist who incorporates puzzles, mysteries and unconventional — very unconventional — narrative techniques into his work. He grew up in California and studied Pure Mathematics at the University of Berkeley. Jason has been the ‘Maze Specialist' for McSweeney's Quarterly (founded by Dave Eggers, our guest in Chapter 81!), written for Nickelodeon, SpongeBob SquarePants, and much more. He's also won a number of awards including the Eisner and the Ignatz and has written a number of additional books, including Book Hunter and Demon. What are we going to talk about on this show? Well there is a lot to learn including: what is a Japanese chicken commune? How does children's literature address taboos we have around death? How can a love of puzzles inform creativity? What are moral dilemmas and what can we learn from them? What is the ‘classic trolley problem'? What is the relationship between books and video games? What is the state of the game book industry? How do we think about playing with a book? And, of course, what are Jason Shiga's three most formative books? Let's turn the page into Chapter 87 now … What You'll Learn: Why is death taboo in children's literature? What is pure mathematics? How can a love of puzzles and brain teasers inform creative work? What is elegance of form? What is an interactive form of literature? What can we learn from moral dilemmas and the state of humanity today? Why are moral choices so good for game books? What's the classic trolley problem? How can books and video games co-exist? What is the state of the game book industry today? How can we encourage our kids to get into game books? How does one play with a book? You can find show notes and more information by clicking here: https://www.3books.co/chapters/87 Leave us a voicemail. Your message may be included in a future chapter: 1-833-READ-A-LOT. Sign up to receive podcast updates here: https://www.3books.co/email-list 3 Books is a completely insane and totally epic 15-year-long quest to uncover and discuss the 1000 most formative books in the world. Each chapter discusses the 3 most formative books of one of the world's most inspiring people. Sample guests include: Brené Brown, David Sedaris, Malcolm Gladwell, Angie Thomas, Cheryl Strayed, Rich Roll, Soyoung the Variety Store Owner, Derek the Hype Man, Kevin the Bookseller, Vishwas the Uber Driver, Roxane Gay, David Mitchell, Vivek Murthy, Mark Manson, Seth Godin, Judy Blume and Quentin Tarantino. 3 Books is published on the lunar calendar with each of the 333 chapters dropped on the exact minute of every single new moon and every single full moon all the way up to 5:21 am on September 1, 2031. 3 Books is an Apple "Best Of" award-winning show and is 100% non-profit with no ads, no sponsors, no commercials, and no interruptions. 3 Books has 3 clubs including the End of the Podcast Club, the Cover to Cover Club, and the Secret Club, which operates entirely through the mail and is only accessible by calling 1-833-READ-A-LOT. Each chapter is hosted by Neil Pasricha, New York Times bestselling author of The Book of Awesome, The Happiness Equation, Two-Minute Mornings, etc. For more info check out: https://www.3books.co
Kumar Rashad has been a Jefferson County public school teacher for the last 17 years. He has a Master of Arts, in Teacher Education and Professional Development from the University of Louisville and a Bachelor of Science in Pure Mathematics from Kentucky State University. He is currently a Math Resource Teacher at Breckenridge Metropolitan High School. He was recognized by JCPS as one of 10 Employees at the Educators of Color Celebration in January, 2021. Kumar also serve on the Board of Directors for both Jefferson County Teachers Association and Kentucky Educators Association. In addition, Kumar Rashad is a member of the Association for the Study of African American Life and History.
In this week's episode, the tit is moving (again) so Ruben Bryan and Colin walk through the finer points why DeFi insurance DAOs also need insurance, we give another toot to El Sal legal tender law, Tips on Twitter, and, finally, an analysis of the first live Dapp on Cardano testnet! Look out!From CoinTelegraph, In a candid open letter, the lead contributor of Cover and Ruler Protocol, 'œDeFi Ted,' announced the protocol will close its virtual doors in the near future, citing a mass developer exit as the primary reason for the project's conclusion. Launched earlier this year, the Ethereum-based decentralized finance (DeFi) insurance marketplace enabled users to stake Cover tokens as collateral and receive insurance payouts if their assets in other DeFi protocols are hacked or rug-pulled. In December 2020, the Cover protocol suffered a catastrophic exploit when a hacker minted 40 quintillion tokens, stratospherically increasing the token supply and effectively rendering the project valueless, a hypothesis confirmed with the consequential 97% price plummet. in a drastic turn of events becoming more commonplace in the market, the hacker consciously returned the funds, and attached the stern message, 'œNext time, take care of your own shit.' Despite the compassionate return of funds, serious damage was inflicted on the protocol both in terms of tokenomics value and cultural reputability.From FastCompany.com, On Sept. 7, 2021, El Salvador will become the first country to make bitcoin legal tender. The government even went a step further in promoting the cryptocurrency's use by giving $30 in free bitcoins to citizens who sign up for its national digital wallet, known as Chivo, or 'œcool' in English. Foreigners who invest three bitcoins in the country'"currently about $140,000'"will be granted residency. Legal tender refers to money'"typically coins and banknotes'"that must be accepted if offered in payment of a debt. The front of every U.S. banknote states, 'œThis note is legal tender for all debts public and private.' This statement has been enshrined in federal law in various forms since the late 1800s.In celebration of the El Sal law, a grassroots twitter effort has started to gain momentum for a market buy of $30 per person. From Michael Saylor, 'œOn September 7, El Salvador will officially begin using #Bitcoin as its national currency alongside the U.S. dollar. Every cyber hornet I know is planning to buy $30 in BTC tomorrow in solidarity with the people of #ElSalvador and their leader @nayibbukele. Will you join us?Twitter is now testing the ability to tip users in Bitcoin through Jack Maller's lightning network app Strike, according to The Block and a post on MacRumors. According to The Block, the new lightning service will be Strike enabled and also support Square's forthcoming hardware wallet. The company also lists Blue Wallet and Wallet of Satoshi as examples of custodial wallets and Breez, Muun, Phoenix and Zap as examples of non-custodial wallets. Twitter will also use Strike to produce Bitcoin invoices. For now, Twitter users will need a Strike account to receive tips in Bitcoin. "We use Strike to generate Bitcoin Lightning invoices so you'll need to connect your account to accept Bitcoin tips,' the instructions read. The Bitcoin developments at Twitter follow through with promises by CEO Jack Dorsey made in July. It was implied then that Bitcoin would be enabled in the Tip Jar service. He suggested also that BitcoinFrom @Sassal0X on twitter, The first dapp went live on Cardano today and ADA fanboys are finally discovering that you can't peer review your way out of fundamental issues. From the r/Cardano reddit, 'œLooks good, but when i try to swap things, all im getting is 'œTransaction Fail: UTXOs are being used this block. Please wait 20-40 seconds and try again' Reply : Unfortunately, and I hate to say it because it might be a bit painful, critic have been discussing this for years trying to understand how in the world Cardano is going to implement smart contracts with a UTXO model (which effectively means an app like Uniswap can only handle one TX per block). They've yet to an answer to this question. ' People need to ask such stuff to Charles on his YouTube AMA streams, rather than his thoughts on Afghanistan or something. Reply: They did and he laughed it off. Said people should learn more about eUTXO and it's a non-issue. --- Reply from @LarsBrunjes, the 'œDirector of Education at @InputOutputHK' and PhD in Pure Mathematics 'œYou are right, this is an issue. But our scientists are already thinking of 'œconcurrent state machines' that can address this.The Securities and Exchange Commission is investigating the startup behind one of the biggest cryptocurrency exchanges, as regulators probe further into parts of the digital-asset market that have resisted oversight, according to people familiar with the matter. Regulators are examining Uniswap Labs, the main developer of the world's largest decentralized exchange, called Uniswap, the people said. Enforcement attorneys are seeking information about how investors use Uniswap and how it is marketed, the people said. A spokesman for Uniswap Labs said the company is 'œcommitted to complying with the laws and regulations governing our industry and to providing information to regulators that will assist them with any inquiry.' An SEC spokeswoman declined to comment, saying the agency doesn't confirm or deny investigations. The developers often say they no longer control the protocols, which could diminish their liability under securities laws. SEC Chairman Gary Gensler has said DeFi projects aren't immune from regulatory scrutiny. They may still be controlled by developers or middlemen that benefit from incentives such as trading fees and digital tokens that give holders governance rights over the program, he has said. '" https://archive.is/ewYN
In today's episode of the podcast we are interviewing Christina Trexler who is going to talk to us about computer science and sexism in this career. Christina Trexler, known as xtinacomputes on Tiktok and Instagram, is an undergraduate student at the University of Arkansas majoring in both Pure Mathematics and Computer Science, and currently is a visiting student at the Massachusetts Institute of Technology's Center for Brains, Minds, and Machines. She is a researcher in the McDermott Lab for Computational Audition where she operates at the intersection of psychology, neuroscience, and engineering to design more effective machine systems for recognizing and interpreting sound. When COVID-19 struck the US, Christina decided to spend her isolation making TikTok memes about programming and women in STEM, where she was able to grow an audience of over 100 thousand people. Connect with us on social media: Christina Trexler: @xtinacomputes on all platforms Engineering Gals: @engineeringgals Amy Kaur: @amydeepkaur Lara Huyapaya: @larahuapaya MUSIC by: Not The King - Faded - Royalty Free Vlog Music @coreygagn --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/engineeringgals/support
Dr. Eugenia Cheng is Scientist In Residence at the School of the Art Institute of Chicago. She won tenure in Pure Mathematics at the University of Sheffield, UK, where she is now an Honorary Fellow. Alongside her research in Category Theory and undergraduate teaching her aim is to rid the world of “math phobia”. Eugenia is also math columnist for the Wall Street Journal and a concert pianist. Emotions are powerful. In newspaper headlines and on social media, they have become the primary way of understanding the world. With her new book "The Art of Logic: How to Make Sense in a World that Doesn't", Eugenia has set out to show how mathematical logic can help us see things more clearly - and know when politicians and companies are trying to mislead us. This talk, like the book, is filled with useful real-life examples of logic and illogic at work and an essential guide to decoding modern life. Originally published in August of 2018, watch the video of this event via g.co/TalksAtGoogle/TheArtOfLogic.
Mthethwa was born and raised in a village known as eSabhuza in KwaZulu-Natal, South Africa. He has his: Bachelor of Science (BSc) in Mathematics & Statistics, with some Computer Science features BSc Honours in Pure Mathematics (2012), Masters in Pure Mathematics by research (2013-2014) and PhD in Mathematics (2015-2018). He is now a Lecturer & Coordinator in Access Programme at UKZN (2014-2019) Mathematics Engineering Ad Hoc Lecturer (2015-2016) Started Mthethwamatics (2016) Training Coordinator at MiET Africa (2017-2018) Canaan College Maths Consultant (2019) Mathematics Lecturer at UKZN (2019-To Date) Over and above presentations of his research in conferences & Mthethwamatics, he has been invited to speak at the following events; The Youth Business Connect (EThekwini Municipality, Durban) UKhozi FM, Isidlo Sasekuseni Morning Shown and Academic Awards (NSA, Wits).
Mthethwa was born and raised in a village known as eSabhuza in KwaZulu-Natal, South Africa. He has his: Bachelor of Science (BSc) in Mathematics & Statistics, with some Computer Science features BSc Honours in Pure Mathematics (2012), Masters in Pure Mathematics by research (2013-2014) and PhD in Mathematics (2015-2018). He is now a Lecturer & Coordinator in Access Programme at UKZN (2014-2019) Mathematics Engineering Ad Hoc Lecturer (2015-2016) Started Mthethwamatics (2016) Training Coordinator at MiET Africa (2017-2018) Canaan College Maths Consultant (2019) Mathematics Lecturer at UKZN (2019-To Date) Over and above presentations of his research in conferences & Mthethwamatics, he has been invited to speak at the following events; The Youth Business Connect (EThekwini Municipality, Durban) UKhozi FM, Isidlo Sasekuseni Morning Shown and Academic Awards (NSA, Wits).
Estudió Theoretical Physics y Pure Mathematics en Loyola Marymount University, Los Angeles y realizó un Master en Pure Mathematics en Cambridge University. Luciano llevó adelante estudios sobre teorías de la gravedad y agujeros negros. Hoy nos cuenta su experiencia estudiando afuera y especialmente en esta área tan abstracta.
Quantum computing is enigmatic, thrilling, and almost impenetrable from the outside. If you're not a scientist or a mathematician, it's easy to get swept up in the hype. But are these spooky phenomena and mystical properties obscuring us from asking the important questions?In today's episode, we enter the multiverse of quantum computing. HPE Chief Technologist Tony Stranack helps to understand what makes this tech so radically different. We size up quantum supremacy and harnessing decoherence with Dr. Ray Beausoleil, Director of Large-Scale Integrated Photonics Lab at Hewlett Packard Labs. Plus, mathematician, computer scientist and post-quantum cryptographer Dr. Sarah McCarthy explains why we need to shake-up our security now, before it's too late! The long show notes for this episode can be found here: https://community.hpe.com/t5/HPE-Blog-UK-Ireland/Quantum-computing-Superposition-or-qubit-too-far/ba-p/7140416#.YNrAV-hueUk
Welcome to episode 80 of Activist #MMT. Today I talk with sixth-year MMT activist Andrew Chirgwin. Andrew graduated from the University of Sydney with a Bachelors of Science in Chemistry and Pure Mathematics, and a masters in secondary teaching. Andrew's introduction to Modern Money Theory, or MMT, was in 2015 when he stumbled on the blog of University of Newcastle economics professor and original MMT developer, Bill Mitchell. Andrew spent the next nine months reading five years of Bill's blog posts. Those who are familiar with the blog will understand how this is no small feat. (Here's a link to __PART_TWO__.) The heart of our conversation, however, was influenced by a February 2021 Facebook post by Steven Hail (the text of which can be found below). Steven is an economics professor at the University of Adelaide and the author of the 2018 book Economics for Sustainable Prosperity, which is a good introduction to MMT. In the post, Steven discusses how neoclassical economists don't "stay in their lane". What this means is that economists impose themselves onto and dominate conversations about healthcare, when they should be led by healthcare professionals and their patients. They dominate conversations about education that should be led by educators and their students. And to bring it back to today's episode, neoclassical economists dominate conversations about mitigating the climate crisis that should be led by true experts in the field, such as climate scientists, energy specialists, chemists, and so on. This domination is in the form of forcing all conversation and concepts to be expressed in financial terms, as exemplified by the "how're you gonna pay for it?" question. This essentially gives those in power and their economists veto power over every facet of our lives, subjecting us to their biases, ignorance, and ideology. It prevents the true experts from ever being able to complete their highly-complex and critical conversations, and it also keeps the public unaware of the depths of the problems they face. Finance is a purely-human-created concept. Therefore, purely-financial crises are also purely-human-created concepts. This means we can prevent and mitigate financial crises merely by choosing to do so. It also implies that the Great Depression and the Great Financial Crisis are largely man-made disasters, caused and exacerbated by the actions and inactions of those in power and their economists. And yet this is who we allow to dominate highly complex conversations on topics that are largely outside of human control, such as mitigating the climate crisis. In other words, if neoclassical economists can't get their own house in order, then why do we allow them to be in charge of every house?! And of course, when problems are framed in financial terms, then problems that face the rich are always more profitable to solve than those that face the poor. An analogy I keep coming back to is viewing a child only through their report card. Doing this will do nothing to help the student if she is hungry and homeless, and suffering from abuse. It is very unlikely the problems will even be seen. In the same way, forcing the climate crisis and other real-world problems to be seen through a financial lens basically guarantees that these problems will never be acknowledged, let alone properly and fully dealt with. Part two of our conversation turns decidedly dark, as we consider our fate as a species and our choices as parents of young children, if we continue to leave the climate crisis in the hands of neoclassical economists. There's no solving a problem if you don't understand its depth. So buckle up. But that's next week. For now, let's start part one of my conversation with Andrew Chirgwin. Resources Steven Hail's Facebook post (that inspired much of our conversation) and Andrew's Twitter debate with John Hearn can be found below. The 2006 paper by S. Abu Turab Rizvi, Steven Hail, February 2nd, 2021, : Some people I...
Welcome to episode 80 of Activist #MMT. Today I talk with sixth-year MMT activist Andrew Chirgwin. Andrew graduated from the University of Sydney with a Bachelors of Science in Chemistry and Pure Mathematics, and a masters in secondary teaching. Andrew's introduction to Modern Money Theory, or MMT, was in 2015 when he stumbled on the blog of University of Newcastle economics professor and original MMT developer, Bill Mitchell. Andrew spent the next nine months reading five years of Bill's blog posts. Those who are familiar with the blog will understand how this is no small feat. (Here's a link to __PART_TWO__.) The heart of our conversation, however, was influenced by a February 2021 Facebook post by Steven Hail (the text of which can be found below). Steven is an economics professor at the University of Adelaide and the author of the 2018 book Economics for Sustainable Prosperity, which is a good introduction to MMT. In the post, Steven discusses how neoclassical economists don't "stay in their lane". What this means is that economists impose themselves onto and dominate conversations about healthcare, when they should be led by healthcare professionals and their patients. They dominate conversations about education that should be led by educators and their students. And to bring it back to today's episode, neoclassical economists dominate conversations about mitigating the climate crisis that should be led by true experts in the field, such as climate scientists, energy specialists, chemists, and so on. This domination is in the form of forcing all conversation and concepts to be expressed in financial terms, as exemplified by the "how're you gonna pay for it?" question. This essentially gives those in power and their economists veto power over every facet of our lives, subjecting us to their biases, ignorance, and ideology. It prevents the true experts from ever being able to complete their highly-complex and critical conversations, and it also keeps the public unaware of the depths of the problems they face. Finance is a purely-human-created concept. Therefore, purely-financial crises are also purely-human-created concepts. This means we can prevent and mitigate financial crises merely by choosing to do so. It also implies that the Great Depression and the Great Financial Crisis are largely man-made disasters, caused and exacerbated by the actions and inactions of those in power and their economists. And yet this is who we allow to dominate highly complex conversations on topics that are largely outside of human control, such as mitigating the climate crisis. In other words, if neoclassical economists can't get their own house in order, then why do we allow them to be in charge of every house?! And of course, when problems are framed in financial terms, then problems that face the rich are always more profitable to solve than those that face the poor. An analogy I keep coming back to is viewing a child only through their report card. Doing this will do nothing to help the student if she is hungry and homeless, and suffering from abuse. It is very unlikely the problems will even be seen. In the same way, forcing the climate crisis and other real-world problems to be seen through a financial lens basically guarantees that these problems will never be acknowledged, let alone properly and fully dealt with. Part two of our conversation turns decidedly dark, as we consider our fate as a species and our choices as parents of young children, if we continue to leave the climate crisis in the hands of neoclassical economists. There's no solving a problem if you don't understand its depth. So buckle up. But that's next week. For now, let's start part one of my conversation with Andrew Chirgwin. Resources Steven Hail's Facebook post (that inspired much of our conversation) and Andrew's Twitter debate with John Hearn can be found below. The 2006 paper by S. Abu Turab Rizvi, The Sonnenschein-Mantel-Debreu: Results after Thirty Years Steven Hail, February 2nd, 2021, Facebook post: Some people I respect think you should value our ecosystem in financial terms and then manage a portfolio of natural assets the way a fund manager might use portfolio theory to manage a diversified portfolio of financial assets. I could not disagree with them more profoundly. Never mind the fact that this buys into the notion of a simple link between GDP per capita and well-being, which should have been dismissed by now in all high income countries, where there is demonstrably no such link. Never mind that they habitually use a measure of ecological footprint which allows rich countries to 'export' their pollution to poor countries, allowing them to claim that ecological impact does not rise as GDP rises beyond a certain point. My biggest problem with this approach is the idea that the financial economics of portfolio management implies the safe management of anything - let alone the natural environment. Portfolio theory requires measurable risks and known probability distributions, or in other words the absence of complexity, non-linearities, feedbacks and fundamental uncertainties. The complexity and feedbacks and resulting uncertainties of financial systems is the reason we have so many endogenously driven financial crises in our history. The thing about financial crises is you can recover from them. Our natural environment is far more complex, has far more feedbacks and non-linearities and connections, and is as a result far more uncertain than our financial system. So if you can't trust economists to manage the financial system so that it remains healthy and robust, why would you imagine that by financialising ecosystem services, you will be able to trust them to manage that far more complex 'portfolio'? It is a profound mistake to financialise the natural world, in my opinion. Instead, we should identify where it is safe to be, add a big margin to allow for unavoidable uncertainty (if we can), and then set limits on what we can tolerate. Dollars shouldn't come into the limits. Then we should take a step back and identify what we need to allow people to have the best possible chance of a good, secure, just, engaged life. To an extent, this has been done in the UN Sustainable Development goals, but it is done better in Kate Raworth's doughnut, which can be and is being applied at national, regional and local levels. What is someone who has spent a career training finance professionals doing saying we ought not to be applying the tools of financial management to our natural environment? I am saying it is entirely inappropriate, misleading and liable to bias the narrative, policies and outcomes in potentially dangerous ways. Andrew's conversation with economist John Hearn Many line breaks have been removed. Andrew: What is a stock of income? Hearn: There is no stock of income only a stock of money. Andrew: Flow of incomes become stocks of money. Accounting 101 Hearn: Accounting 101 is wrong. A stock of money is used to measure a flow of income. Economics always teaches accountants not the other way round. Andrew: Accounting is incorrect? So your conjecture here can't even stand up to basic bookkeeping? The net sum of flows is a stock. Hence the net sum of incomes is a stock of incomes, and the stock of incomes is savings or money. Hearn: Accounting is bean counting it does not require any understanding of what it is counting. Flows are not stocks so there is no hence. Andrew: If accounting is just beam counting, how do you measure any of your work? Economic activity is measured using accounting... that's how Taxes are determined, savings calculated, policy assessed into potential outcomes. Your statement here is like saying "physics ignores distance" Hearn: Economists understand simple accounting, accountants rarely understand economics. Andrew: That's a nice hasty generalisation there. You seem to be shaky on elementary accounting Professor, especially about credit creation by balance sheet expansion. Hearn: Test me. Andrew: Credits are created with a matching debts. Currency is is therefore both a credit and a debt. Money, as a credit issued by other entities, are both a credit and debt. Hence currency, and all other money, are debts created by balance sheet expansions. Hearn: Yes it is double entry bookkeeping. A deposit at a bank is double entered as an asset and liability. It is not the currency. Money can be created by a net increase in newly created loans. Fiat money is not a debt, commodity backed currency is. Andrew: Fiat money is a debt, because it is also a credit. It is a balance sheet expansion of a different balance sheet. I thought you said you were good at accounting... Hearn: Think assets and liabilities as these appear on a balance sheet not credit and debit. Andrew: That's another red herring professor. You should be running a cafe at this rate. Red herring for everyone. Currency and other money are accounted for on balance sheets along with other credits as assets of the balance ledger. Stop trying to play coy. Hearn: Explain how the Aussie dollars in your wallet are a debt Andrew: Because the federal government created a credit by balance sheet expansion, hence making them also a debt. Hearn: Think liability not debt, asset not credit. Andrew: See my other response. This is a red herring and we both know it professor. Liabilities, and debts, are accounted for on the balance sheet as much as assets and credits. Your accumulated credits appear as assets. But again, a red herring to avoid the actual topic. Andrew: It's also their liability to me. The Treasurer signed it. Hearn: How will the Treasury fulfil its liability to you? Andrew: When they contract their balance sheet. Until they are willing to do so, they recognise the liability exists because they recognise the asset existing. Hearn: You are wasting your time and your intellect trying to play word games rather than understanding what you are talking about. Spend the rest of the day trying to understand that fiat money is not debt and commodity backed currency is. Come back tomorrow when it is solved. Andrew: Apparently, Professor, balance sheet contractions and expansions bother you. The collection of an national import duty is a balance sheet contraction of the Issuer of Currency. The collection of a fee for operating a company by the national government as above. The issuing of a, now very limited, UK Passport comes with a contraction of the balance sheet of the UK Government. The settling of a debt incurred from a court case at the National Law level comes with a contraction of the balance sheet of the national government. Four concrete examples all generalised as: "The liability to me will be expunged when I do something that the Currency Issuer will contract its balance sheet in response."
Po-Shen Loh is a Professor of Mathematics at Carnegie Mellon University with research interests in combinatorics, probability theory, and computer science. He is also the coach of the United States International Math Olympiad team and it was under his guidance he led his teams to secure first place in 2015, 16, 18, and 19. He is also the founder of Expii, an online platform that teaches young students basic concepts of math and science. He is also the founder of the NOVID app that has an innovative way of contact tracing in order to reduce the spread of coronavirus.NOVID App: https://www.novid.org/More about Po: https://www.poshenloh.com/About the Host:I am a Ph.D. student at Arizona State University, doing research on building Interpretable AI models for Medical Diagnosis.LinkedIn: https://www.linkedin.com/in/shahjay22/You can reach out to https://www.public.asu.edu/~jgshah1/ for any queries.Stay tuned for upcoming podcasts!#mathematics #research #coronavirus #covid***Disclaimer: The information contained in this video represents the views and opinions of the speaker and does not necessarily represent the views or opinions of any institution. It does not constitute an endorsement by any Institution or its affiliates of such video content.***
In this episode, Robert Martichenko, an award-winning business author, shares his career journey that started as a postgraduate with a degree in Pure Mathematics to finding his fit in freight and logistics. He discussed why the relationship between shippers and logistics companies have been deteriorating as a direct result of the customers perceiving a lack of innovation and improvement. Robert helps us see the importance of Visual Management and the significance of high-quality data for making a good decision. https://theleaneffectpodcast.com/ https://www.facebook.com/TheLeanEffectPodcast https://www.facebook.com/groups/272448766629082/ https://www.linkedin.com/company/the-lean-effect-podcast/ Insta: @theleaneffectpodcast Twitter @TheLeanEffect Guest: Robert Martichenko robert@leancor.com https://www.linkedin.com/in/robertmartichenko/ Host: Mark Dejong: https://www.linkedin.com/in/mark-de-jong-investor-lean-advisor-0288695/ Mark@4ppartners.ca https://www.4ppartners.ca Phone: 1-778-807-9691
For the next few weeks, we shall have a series where we amplify the voices of young women. They too have powerful stories to share, and lessons to teach. For whatever reason we tend to perpetuate the gap in the generation divide. But we need to start talking to each other. We need to listen and actually hear what the other says, we need to embrace each other. I have been fortunate enough to meet some phenomenal young women, who have reminded me not to make assumptions on outward appearances. To seek the truth first. My first guest is the Beautiful Timi Aluko from Nigeria. For years, Timi went undiagnosed of Polycystic Ovarian Syndrome, this caused her to have a hormonal imbalance and uncontrollable weight gain for years. As a result she experienced body shaming, bullying and depression. At 25 years of age, Timi has proudly overcome her tormentors. How? Well I guess you have to listen. Timi Aluko is the founder of Aso, an African Textile production firm. The Program Coordinator of Nigerian National Committee of the United World College, and a virtual assistant for business executives and professionals. She graduated with Honours from the University of Ibadan with a bachelor's degree in Pure Mathematics. Timi is currently a fellow of the Google African Developers Scholarship Program for Associate Google Cloud Certification and the Tony Elumelu Entrepreneurship Programme. She is enthusiastic about early child education and fascinated by poetry, history, myths and facts.⠀⠀ Quotes "I decide what you say to me and what it means to me" "They [bullies] cannot stand to hear, No, you cannot talk to me that way" "When you have self love you won't allow people to create an image of you, You create an image of yourself." "You can have self love without being selfish" "Sometimes how people see you is a reflection of themselves" "Understanding that My uniqueness is much more than my flaws" "Vulnerability should not be a burden" Connect with Timi https://www.instagram.com/shoptimialuko/ https://flutterwave.com/store/timialukoapparels KNOW your Roots, Grow your Purpose LINKS: www.instagram.com/chulu_bydesign www.facebook.com/chulubydesign Join the Africana Woman Visionaries: https://www.facebook.com/groups/708489836426989 Africana Woman Blog: https://www.africanawoman.com/
In this episode of Teen Glendale Empowerment Now Talks (G.E.N.) hosts Melissa and Desiree sit down with David Zearbaugh, mathematician, IT technician, and librarian. David talks about his experiences while getting his BA in Pure Mathematics during his college years and how he discovered his interest in becoming a librarian.
In this talk Vicky Neale gives a glimpse of the undergraduate Pure Maths courses through the lens of elliptic curves. Our Open Days are intended to give an insight in to Maths at Oxford, whether you are a potential applicant or are just curious.
ACEMS' Yanan Fan is a statistician at UNSW. But in this episode, she reaches out to three women in STEM - Dr Alina Ostafe: Senior Lecturer in Pure Mathematics at UNSW, Dr Sarah Martell: Senior Lecturer in Astrophysics at UNSW, and Prof Emma Johnston: Professor of Marine Ecology & Ecotoxicology, Dean of Science at UNSW, and President of Science & Technology in Australia (STA). Discover what their science is like, why maths is so important, and the importance of getting more women into STEM.The Random Sample is a podcast by the Australian Research Council Centre of Excellence for Mathematical and Statistical frontiers. In this show, we share stories about mathematics, statistics and the people involved. To learn more about ACEMS, visit https://acems.org.au.See omnystudio.com/listener for privacy information.
In this episode of The Big Questions, we talk big … big, big, bigger than big … how about about infinitely big! Dr Eugenia Cheng is Scientist In Residence at the School of the Art Institute of Chicago, has tenure in Pure Mathematics at the University of Sheffield, UK. She holds a PhD in pure mathematics from the University of Cambridge, is a concert pianist, pioneer of math on YouTube and author of math books, “How to Bake Pi” and “Thinking Better: The Art of Logic in an Illogic World”. Connect with Adam Spencer at: https://twitter.com/adambspencer Find LiSTNR on Facebook: https://www.facebook.com/LiSTNRau/ Follow LiSTNR on Instagram: https://www.instagram.com/listnrau/ Follow LiSTNR Australia on Twitter: https://twitter.com/listnrau Download the LiSTNR app from the Apple and Google Play app stores. Or go to listnr.com See omnystudio.com/listener for privacy information.
Melvyn Bragg and his guests discuss randomness and pseudorandomness.Randomness is the mathematics of the unpredictable. Dice and roulette wheels produce random numbers: those which are unpredictable and display no pattern. But mathematicians also talk of 'pseudorandom' numbers - those which appear to be random but are not. In the last century random numbers have become enormously useful to statisticians, computer scientists and cryptographers. But true randomness is difficult to find, and mathematicians have devised many ingenious solutions to harness or simulate it. These range from the Premium Bonds computer ERNIE (whose name stands for Electronic Random Number Indicator Equipment) to new methods involving quantum physics.Digital computers are incapable of behaving in a truly random fashion - so instead mathematicians have taught them how to harness pseudorandomness. This technique is used daily by weather forecasters, statisticians, and computer chip designers - and it's thanks to pseudorandomness that secure credit card transactions are possible.With:Marcus du SautoyProfessor of Mathematics at the University of OxfordColva Roney-DougalSenior Lecturer in Pure Mathematics at the University of St AndrewsTimothy GowersRoyal Society Research Professor in Mathematics at the University of CambridgeProducer: Thomas Morris.
Melvyn Bragg and guests John Barrow, Colva Roney-Dougal and Marcus du Sautoy explore the unintended consequences of mathematical discoveries, from the computer to online encryption, to alternating current and predicting the path of asteroids.In his book The Mathematician's Apology (1941), the Cambridge mathematician GH Hardy expressed his reverence for pure maths, and celebrated its uselessness in the real world. Yet one of the branches of pure mathematics in which Hardy excelled was number theory, and it was this field which played a major role in the work of his younger colleague, Alan Turing, as he worked first to crack Nazi codes at Bletchley Park and then on one of the first computers.Melvyn Bragg and guests explore the many surprising and completely unintended uses to which mathematical discoveries have been put. These include:The cubic equations which led, after 400 years, to the development of alternating current - and the electric chair.The centuries-old work on games of chance which eventually contributed to the birth of population statistics.The discovery of non-Euclidean geometry, which crucially provided an 'off-the-shelf' solution which helped Albert Einstein forge his theory of relativity.The 17th-century theorem which became the basis for credit card encryption.In the light of these stories, Melvyn and his guests discuss how and why pure mathematics has had such a range of unintended consequences.John Barrow is Professor of Mathematical Sciences at the University of Cambridge and Professor of Geometry at Gresham College, London; Colva Roney-Dougal is Lecturer in Pure Mathematics at the University of St Andrews; Marcus du Sautoy is Charles Simonyi Professor for the Public Understanding of Science and Professor of Mathematics at the University of Oxford.
Melvyn Bragg and guests discuss the strange mathematics of probability where heads or tails is a simple question with a far from simple answer. Gambling may be as old as the hills but probability as a mathematical discipline is a relative youngster. Probability is the field of maths relating to random events and, although commonplace now, the idea that you can pluck a piece of maths from the tumbling of dice, the shuffling of cards or the odds in the local lottery is a relatively recent and powerful one. It may start with the toss of a coin but probability reaches into every area of the modern world, from the analysis of society to the decay of an atom. With Marcus du Sautoy, Professor of Mathematics at the University of Oxford; Colva Roney-Dougal, Lecturer in Pure Mathematics at the University of St Andrews; Ian Stewart, Professor of Mathematics at the University of Warwick
Melvyn Bragg and guests discuss the contribution Indian mathematicians have made to our understanding of the subject. Mathematics from the Indian subcontinent has provided foundations for much of our modern thinking on the subject. They were thought to be the first to use zero as a number. Our modern numerals have their roots there too. And mathematicians in the area that is now India, Pakistan and Bangladesh were grappling with concepts such as infinity centuries before Europe got to grips with it. There's even a suggestion that Indian mathematicians discovered Pythagoras' theorem before Pythagoras. Some of these advances have their basis in early religious texts which describe the geometry necessary for building falcon-shaped altars of precise dimensions. Astronomical calculations used to decide the dates of religious festivals also encouraged these mathematical developments. So how were these advances passed on to the rest of the world? And why was the contribution of mathematicians from this area ignored by Europe for centuries?With George Gheverghese Joseph, Honorary Reader in Mathematics Education at Manchester University; Colva Roney-Dougal, Lecturer in Pure Mathematics at the University of St Andrews; Dennis Almeida, Lecturer in Mathematics Education at Exeter University and the Open University.
Melvyn Bragg and guests discuss the mathematical structures that lie within the heart of music. The seventeenth century philosopher Gottfried Leibniz wrote: 'Music is the pleasure the human mind experiences from counting without being aware that it is counting'. Mathematical structures have always provided the bare bones around which musicians compose music and have been vital to the very practical considerations of performance such as fingering and tempo. But there is a more complex area in the relationship between maths and music which is to do with the physics of sound: how pitch is determined by force or weight; how the complex arrangement of notes in relation to each other produces a scale; and how frequency determines the harmonics of sound. How were mathematical formulations used to create early music? Why do we in the West hear twelve notes in the octave when the Chinese hear fifty-three? What is the mathematical sequence that produces the so-called 'golden section'? And why was there a resurgence of the use of mathematics in composition in the twentieth century? With Marcus du Sautoy, Professor of Mathematics at the University of Oxford; Robin Wilson, Professor of Pure Mathematics at the Open University; Ruth Tatlow, Lecturer in Music Theory at the University of Stockholm.
Melvyn Bragg and guests discuss negative numbers, a history of mystery and suspicion. In 1759 the British mathematician Francis Maseres wrote that negative numbers "darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple". Because of their dark and mysterious nature, Maseres concluded that negative numbers did not exist, as did his contemporary, William Friend. However, other mathematicians were braver. They took a leap into the unknown and decided that negative numbers could be used during calculations, as long as they had disappeared upon reaching the solution. The history of negative numbers is one of stops and starts. The trailblazers were the Chinese who by 100 BC were able to solve simultaneous equations involving negative numbers. The Ancient Greeks rejected negative numbers as absurd, by 600 AD, the Indians had written the rules for the multiplication of negative numbers and 400 years later, Arabic mathematicians realised the importance of negative debt. But it wasn't until the Renaissance that European mathematicians finally began to accept and use these perplexing numbers. Why were negative numbers considered with such suspicion? Why were they such an abstract concept? And how did they finally get accepted? With Ian Stewart , Professor of Mathematics at the University of Warwick; Colva Roney-Dougal , Lecturer in Pure Mathematics at the University of St Andrews; Raymond Flood , Lecturer in Computing Studies and Mathematics at Kellogg College, Oxford.
Melvyn Bragg and guests discuss prime numbers: 2, 3, 5, 7, 11, 13, 17 … This sequence of numbers goes on literally forever. Recently, a team of researchers in Missouri successfully calculated the highest prime number - it has 9.1 million digits. For nearly two and a half thousand years, since Euclid first described the prime numbers in his book Elements, mathematicians have struggled to write a rule to predict what comes next in the sequence. The Swiss mathematician Leonhard Euler feared that it is "a mystery into which the human mind will never penetrate." But others have been more hopeful... In the middle of the nineteenth century, the German mathematician Bernhard Riemann discovered a connection between prime numbers and a complex mathematical function called the 'zeta function'. Ever since, mathematicians have laboured to prove the existence of this connection and reveal the rules behind the elusive sequence. What exactly are prime numbers and what secrets might they unlock about our understanding of atoms? What are the rules that may govern the prime sequence? And is it possible that the person who proves Riemann's Hypothesis may bring about the collapse of the world financial system? With Marcus du Sautoy, Professor of Mathematics and Fellow of Wadham College at the University of Oxford; Robin Wilson, Professor of Pure Mathematics at the Open University and Gresham Professor of Geometry; Jackie Stedall, Junior Research Fellow in the History of Mathematics at Queen's College, Oxford.
Melvyn Bragg and guests discuss the nature and existence of mathematical infinity. Jonathan Swift encapsulated the counter-intuitive character of infinity with insouciant style:“So, naturalists observe, a fleaHath smaller fleas on him that preyAnd these hath smaller fleas to bite ‘emAnd so proceed ad infinitum.”Alas, the developing utility mathematicians put to the idea of infinity did not find the English philosopher Thomas Hobbes quite so relaxed. When confronted with a diagram depicting an infinite solid whose volume was finite, he wrote, “To understand this for sense, it is not required that a man should be a geometrician or logician, but that he should be mad”. Yet philosophers and mathematicians have continued to grapple with the unending, and it is a core concept in modern maths.So, what is mathematical infinity? Are some infinities bigger than others? And does infinity exist in nature?With Ian Stewart, Professor of Mathematics at the University of Warwick; Robert Kaplan, co-founder of The Math Circle at Harvard University and author of The Art of the Infinite: Our Lost Language of Numbers; Sarah Rees, Reader in Pure Mathematics at the University of Newcastle.
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