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Maths on the Move

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Maths on the Move
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  • Adventures in Model Land
    You are blue, and are surrounded by other blue people: swirling together in a dot, identical and indistinguishable. From somewhere above you hear the ticking of a clock, and suddenly find yourself and some of your fellows pulled upwards, sucked through a tube arcing high above... Intrigued? That is a description of one ofĀ Jess Enright'sĀ adventures in her mathematical models. This is an exciting new approach that researchers are using to invite people into the worlds of their models, both to communicate their research to the people outside of academia, but also for the researchers themselves to reflect on what aspects of reality these models actually do, and don't, describe. These adventures in model land build on the work ofĀ Erica ThompsonĀ in her book,Ā Escape from Model Land: how mathematical models can lead us astray and what we can do about it.Ā Any mathematical description of a process in the world around us is a mathematical model: whether it's describing the processes in our climate, the spread of a disease through a population or the movement of water across a landscape. They are incredibly useful and key to research in modern mathematics and science. But these mathematical models are, by necessity, simplifications of the real world. Erica's book inspired geoscientistĀ Chris SkinnerĀ to use principles of role-playing games to explore and communicate mathematical models. And this approach was a perfect fit with Jess' experience building board games to communicate her research - we event get to play some in this podcast at the huge UK Games Expo in Birmingham earlier this year! Jess Enright, along with Emma Gort, in action at the UK Games Expo in Birmingham earlier in 2025. (Photo: Rachel Thomas) In this podcast we talk to Jess (a reader in the school of Computing Science at the University of Glasgow and member of the JUNIPER partnership of disease modellers from across the UK), Chris (an independent geoscientist and researcher and a visiting fellow at York St John University)and Erica (Associate Professor of Modelling for Decision Making at University College, London) about their explorations of these ideas. You can find out more information about the ideas discussed in the podcast here: Maths in a Minute: Mathematical model – a brief and an accessible introduction to mathematical models and where they are used. Escape from Model Land: how mathematical models can lead us astray and what we can do about it – Erica's book Adventures in Model Land– the framework, developed by Chris, Erica and Jess, together with Liz Lewis, Rolf Hut and Sam Illingworth, for exploring mathematical models using table-top role-play games You can find some of theĀ adventures in model landĀ and otherĀ gamesĀ that Jess took to the UK Games Expo in Birmingham This podcast is part of ourĀ collaborationĀ withĀ JUNIPER, the Joint UNIversity Pandemic and Epidemic Response modelling consortium. JUNIPER comprises academics from the universities of Cambridge, Warwick, Bristol, Exeter, Oxford, Manchester, and Lancaster, who are using a range of mathematical and statistical techniques to address pressing questions about the control of COVID-19. You can see more content produced with JUNIPERĀ here.
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  • Living Proof: Kevin Buzzard and proof assistants
    There's been a lot of talk recently about whether artificial intelligence is becoming just as good as maths as humans are. But quietly in the background there's been another development regarding the use of computers in maths. It involvesĀ proof assistants: computer programmes that can check whether a mathematical proof is correct; whether it can be derived from a set of basic axioms of mathematics using only the rules of logic. In this episode ofĀ Living proofĀ we meetĀ Kevin Buzzard, an expert on proof assistants at University College London. Kevin explains what proof assistants are, how using them is like playing a computer game, and why they turn maths into a highly collaborative pursuit. He also tells us about his effort to get a proof assistant to check one of the most famous results in all of mathematics — Fermat's Last Theorem — and how proof assistants and AI may team up to provide a powerful tool. We met Kevin in the summer when he was taking part in a research programme calledĀ Big ProofĀ at theĀ Isaac Newton Institute for Mathematical SciencesĀ (INI) in Cambridge. This programme, which attracted some of the best minds in modern mathematics, followed on from aĀ pioneering workshop on the same topicĀ which took place at the INI in 2017. To find out more about the topics mentioned in this podcast, see the following articles: Proof assistants — This two part article, written by our brilliant summer intern Ben Watkins, is based on the interview with Kevin Buzzard and explores what proof assistants are. Maths in a Minute: Coding with Lean — Here's a simple walk-through of how to use a proof assitant called Lean. Pure maths in crisis? — In this article from 2019 Kevin Buzzard explains why he thinks that the standard of proof in research maths might not be as high as mathematicians would like to believe. How to (im)prove mathematics — This article explores how the simple notion of counting ends in a revolutionary new way of doing maths using proof assistants. This article is based on a talk by Terence Tao at aĀ 2024 workshopĀ at the INI which celebrated the mathematics of Tim Gowers as well as his 60th birthday. A very old problem turns 30! — This article explores Fermat's famous last theorem as well as the mathematics its proof has given rise to. It comes with aĀ podcastĀ featuring Andrew Wiles, who proved the result, and people who are now working on its legacy. You can find more background reading in ourĀ collection on proof assistants. This content forms part of our collaboration with theĀ Isaac Newton InstituteĀ for Mathematical Sciences (INI) – you can find all the content from the collaborationĀ here. The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. VisitĀ www.newton.ac.ukĀ to find out more.
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  • Living Proof: Moustapha Fall
    In this episode of theĀ Living ProofĀ podcast we're delighted to meetĀ Moustapha Fall. Moustapha is the Center President of theĀ African Institute for Mathematical Sciences (AIMS) in SenegalĀ and winner of a prestigiousĀ Ramanujan Prize for Young Mathematicians from Developing Countries. He also plays an important role on the international stage as Member-at-Large of the Executive Committee of theĀ International Mathematical Union. Moustapha talks to us about about the amazing institution that is AIMS, about his outreach activities and advice for budding mathematicians, and about the challenges that face mathematicians in sub-Saharan Africa. You can find the IMU-ICIAM report on fraudulent publishing, which Moustapha mentions in the podcast,Ā here. The same team of authors has also drawn upĀ recommendations on how to fight fraudulent publishing.
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  • Living proof: Codina Cotar and some amazing mathematical art
    Earlier this year the theĀ anomalous mathematical patterns sci-art competitionĀ attracted someĀ jaw-dropping entries. The competition was held in connection to theĀ Stochastic systems for anomalous diffusionĀ research programme which took place at theĀ Isaac Newton Institute for Mathematical SciencesĀ (INI) in Cambridge last year.Ā  In this episode ofĀ Maths on the MoveĀ we talk toĀ Codina Cotar, who co-organised the INI programme and helped put on the competition. Codina explains the maths which served as inspiration and discusses some of the winning entries. From coffee to quantum mechanics and from dance to diffusion, find out how mathematics, nature and art are inextricably linked. Note that the in-person exhibition at the INI is now scheduled for March 2026. The entries discusses in this podcast are shown below. To find out more about some of the mathematical topics mentioned in this podcast see: The Sci-art competitionĀ - This article explores some of the mathematics behind the competition, including randomness, diffusion, and many particle systems. The Fields Medals 2022: Maryna ViazovskaĀ - This article looks at the mathematics of sphere packings, which won a Fields Medal for the mathematician Maryna Viazovska. Maths in a Minute: Fluid dynamicsĀ - A very bried introduction to the mathematics of liquids and gases. A ridiculously short introduction to some very basic quantum mechanicsĀ - This article does what the title suggests. A brief history of quantum field theoryĀ - A deeper look at the theory that arose from quantum mechanics. Dye Diffusion in WaterĀ by Henrique Biasi. Find out moreĀ here. Ā  A microcosm of milkĀ by Christian Casaljay. Find out moreĀ here. Ā  Work by Lilia Bakanova, which which won the category for textile, sculpture and other medium. Find out moreĀ here. Ā  Ā 
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  • Topological data analysis with Michael Hill
    The mathematical area ofĀ topologyĀ is all about figuring out what truly defines a shape. Famously, topologists consider a coffee cup to be the same as a doughnut because one can be turned into the other without cutting or gluing — what defines and relates these two shapes for a topologist is that they have a single hole. As you might imagine, if you have ever tried to drink coffee out of a doughnut, topology has traditionally been part of pure mathematics.Ā Topological data analysisĀ (TDA), however, opens up a world of applications by applying ideas from topology to vast data sets, helping us to understand their "shape" and draw out important features. In this episode ofĀ Maths on the MoveĀ we talk to algebraic topologistĀ Michael HillĀ about some of the fascinating uses of topological data analysis — from understanding breast cancer to making sure that voting is fair. We talked to Michael after he gave a brilliantĀ Rothschild lectureĀ at the Isaac Newton Institute for Mathematical Sciences (INI) in Cambridge. He was at the INI to attend the research programmeĀ Equivariant homotopy theory in context. To find out more about the topics mentioned in this podcast see: Maths in a minute: Topology — a quick introduction to topology. Understanding life with topology — a quick introduction to TDA and some of its uses. Euromaths: Heather Harrington — An episode of ourĀ Maths on the moveĀ podcast giving and introduction to topological data analysis. Watch Mike Hill'sĀ Rothschild lecture at the INI. Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survivalĀ - The paper by Nicolau, Levine and Carlesson, mentioned by Michael in the podcast, which uses TDA to identify a novel type of breast cancer. The Data and Democracy Lab — mentioned by Mike in the podcast. Also, here is an image illustrating the intuition behind topological data analysis. As discs drawn around a bunch of points arranged in a circle increase in radius, they eventually overlap to form a ring, and later overlap to form a single blob. Ā  This podcast forms part of our collaboration with theĀ Isaac Newton Institute for Mathematical SciencesĀ (INI) – you can find all the content from the collaborationĀ here. The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. VisitĀ www.newton.ac.ukĀ to find out more.
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About Maths on the Move

Maths on the Move, the podcast from plus.maths.org, will bring you the latest news from the world of maths, plus interviews and discussions with leading mathematicians and scientists about the maths that is changing our lives. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.
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