Published by Isaac Newton Institute for Mathematical Sciences
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Mathematics
The Isaac Newton Institute is the world's foremost mathematical research centre. Living Proof aims to highlight the diverse people and interconnected topics linked to its many activities. Interviewees range from visiting academics and lecturers to mathematicians, other scientists, musicians, artists, students, and prominent figures within the University of Cambridge and beyond. The podcast typically involves mathematical themes, but is specifically aimed at a general audience. The focus is on the subjects being interviewed and the social stories they have to tell, not just on the significance and details of the research they may be undertaking. We hope there is interest and inspiration here for everyone.- The Isaac Newton Institute for Mathematical Sciences (UK) is an international research centre based in Cambridge, UK. A part of the University of Cambridge, it has been hosting research programmes on mathematical themes since July 1992. Visit > www.newton.ac.uk/news/ini-podcast
Quantum chaos and simple equations with Prof Jens Marklof - Episode #76
Send us Fan Mail A chaotic system is one where the outcome is sensitively dependent on initial conditions. Small disturbances can take the system in new, unpredictable directions. Professor Jens Marklof has built a successful career understanding the mathematics that underpin the chaos of quantum systems. His career, or indeed any academic career, is a kind of chaotic system. You never know which meeting or conversation will send you off in a new direction. In a fascinating conversation, we explore key moments and opportunities in his career, like introducing himself to Peter Sarnak or sharing an office with David Thouless, shaped the scientist he is today. Jens was the Rothschild Distinguished Visiting Fellow for the Isaac Newton Institute's programme on Geometric Spectral Theory . His public lecture, " The quantum centenary: from order to chaos " celebrated the 100th anniversary of quantum mechanics. --- This episode was supported by the quantitative research firm G-Research, which has launched a new series of mathematical puzzles called G-Riddles. It's free to try and could win you a cash prize: https://www.gresearch.com/griddles/ Living Proof is the podcast of the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge. The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period. Produced by Jon Farrow. Edited by Keerthi Raj. Music: 'Origami' by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au
A family of group theorists - Episode #75
Send us Fan Mail A father, two of his children, and a family friend — all mathematicians — made progress on a long-standing problem in group theory by coming together at the Isaac Newton Institute. Listen as Plus Magazine editors Rachel Thomas and Marianne Freiberger interview Roman Sauer, and Uri, Saar, and Shaked Bader to find out more about their research and paths to mathematics. The Operators, Groups, and Graphs programme was in residence at the INI from July to December 2025: https://www.newton.ac.uk/event/ogg/ The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period. newton.ac.uk
Revealing the secrets of Sanskrit mathematics with Prof Clemency Montelle - Episode #74
Send us Fan Mail We talk with Professor Clemency Montelle all about her work decoding the mathematics of ancient manuscripts. In a wide-ranging discussion, we cover some of the concepts that first arose in India, hear about a mentor who hosted meals based on ancient recipes, and learn how important cultural and historical context is for the questions that mathematicians ask. While she was at the INI, Professor Montelle delivered the Kirk Lecture for the Modern History of Mathematics Programme , which you can watch here: https://www.youtube.com/watch?v=sa2kN-li984 --- This episode was supported by the quantitative research firm G-Research, which has launched a new series of mathematical puzzles called G-Riddles. It's free to try and could win you a cash prize: https://www.gresearch.com/griddles/ Living Proof is the podcast of the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge. The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period. Produced by Jon Farrow. Edited by Keerthi Raj. Music: 'Origami' by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au ---- **Correction** At 5:26, the date of the earliest numerical tables is the beginning of the second millenium before the Common Era.
#73 Building digital hearts
Send us Fan Mail Imagine if your doctor had a digital model of your heart, personalised to you and updated with your latest medical information. This isn't science fiction – this revolutionary healthcare is being tested now. In this podcast we speak to Steven Niederer , who leads the CVDNet project developing and testing these ideas, and his colleague Richard Wilkinson , from the University of Nottingham. Richard is one of the organisers of the long research programme, Representing, calibrating & leveraging prediction uncertainty from statistics to machine learning (RCL), held earlier this year at the Isaac Newton Institute for the Mathematical Sciences (INI). We first spoke to Steven back in 2019 when he helped organise the Fickle Heart programme at the INI. In this podcast, Richard and Steven tell us about digital twins, digital hearts, and how the RCL programme and CVDNet build on the work started back in 2019 with the Fickle Heart programme. You can find out more about some of the ideas discussed in this podcast in these short introductions: Maths in a Minute: Mathematical models Maths in a Minute: Differential equations Maths in Minute: Machine learning
#72 Céline Broeckaert and Frank Verstraete
Send us Fan Mail In this episode of Living Proof , we speak with Céline and Frank about their book: Why nobody understands quantum physics - and everyone needs to know something about it . They share insights into their writing journey and how each of their backgrounds contributed to the final project. We met Céline and Frank at the Isaac Newton Institute for Mathematical Sciences in Cambridge, where Frank is co-organising the research programme Quantum field theory with boundaries, impurities, and defects . "I have learnt that even if you are not a master in mathematics and science you are still able to grasp the essence." This is Céline Broeckaert talking, believe it or not, about the famously difficult theory of quantum mechanics. Céline knows what she's talking about. She's not a physicist, in fact she's a Romance languages scholar, author and playwright. Yet she's written a book about quantum mechanics together with her physicist husband Frank Verstraete, Leigh Trapnell Professor of Quantum Physics at the University of Cambridge. The book is called Why nobody understands quantum physics - and everyone needs to know something about it . And it's good timing: quantum mechanics celebrates its 100th birthday this year . See here for an article Plus Magazine published previously about Frank's work. For a brief introduction to quantum mechanics see A ridiculously short introduction to some very basic quantum mechanics . To find out more about the overlap of maths and art, see here .
#71 Moustapha Fall
Send us Fan Mail In this episode of the Living Proof podcast we're delighted to meet Moustapha Fall . Moustapha is the Center President of the African Institute for Mathematical Sciences (AIMS) in Senegal and winner of a prestigious 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 the 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, here . The same team of authors has also drawn up recommendations on how to fight fraudulent publishing . We met Moustapha when he visited the Isaac Newton Institute for Mathematical Sciences in Cambridge.
#70 Codina Cotar and some amazing mathematical art
Send us Fan Mail Earlier this year the the anomalous mathematical patterns sci-art competition attracted some jaw-dropping entries . The competition was held in connection to the Stochastic systems for anomalous diffusion research programme which took place at the Isaac Newton Institute for Mathematical Sciences (INI) in Cambridge last year. In this episode of Living Proof, we talk to 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 competition - This article explores some of the mathematics behind the competition, including randomness, diffusion, and many particle systems. The Fields Medals 2022: Maryna Viazovska - This article looks at the mathematics of sphere packings, which won a Fields Medal for the mathematician Maryna Viazovska. Maths in a Minute: Fluid dynamics - A very bried introduction to the mathematics of liquids and gases. A ridiculously short introduction to some very basic quantum mechanics - This article does what the title suggests. A brief history of quantum field theory - A deeper look at the theory that arose from quantum mechanics.
#69 Ekaterina Eremenko on Olga Ladyzhenskaya’s Life in Math
Send us Fan Mail In this episode of Living Proof, we speak with renowned filmmaker Ekaterina Eremenko about her film "Portrait of Olga Ladyzhenskaya" , which tells the story of the legendary Russian mathematician celebrated for her groundbreaking work in partial differential equations and fluid dynamics. Ekaterina shares what inspired her to bring Ladyzhenskaya’s life to the screen, explores the creative process behind the film, and reflects on the powerful intersection of art and science. The film was screened at the Isaac Newton Institute for Mathematical Sciences to celebrate International Women in Mathematics Day 2025 .
#68 Hunting through higher dimensions with Zhouli Xu
Send us Fan Mail Welcome to the latest episode of Living Proof , our podcast produced in collaboration with Plus.maths.org – you can find all the content from the collaboration here . On May 30th 2024 seminar goers at Princeton University witnessed a thrilling moment. The mathematician Zhouli Xu of the University of California, LA, announced that, together with colleagues he had sorted out the 126th dimension. Not in general, but in regards to a problem that has taunted mathematicians since the 1960s. The problem involves strange shapes and is called the Kervaire invariant problem , after the mathematician Michel Kervaire. In this episode, Zhouli takes us on a trip into higher dimensions, giving us a gist of what this long-standing problem is all about and retracing some of the long, and sometimes arduous, journey towards a proof. We met Zhouli when he visited the Isaac Newton institute for Mathematical Sciences (INI) in Cambridge to take part in a research programme called Equivariant homotopy theory in Context . To find out more abut the topics discussed in this podcast see: Maths in a minute: Topology The hypersphere in four dimensions Telescope topology
#67 The meaning is in the arrows with Adina Goldberg
Send us Fan Mail Welcome to the latest episode of Living Proof , our podcast produced in collaboration with Plus.maths.org In this podcast we hope to give you some interesting information. This information is encoded in terms of 0s and 1s – the classical bits in your computer or phone. But what if instead we were using a quantum computer? Then we'd be dealing with quantum bits, or qubits , opening up exciting new possibilities. And quantum information theory is the area of mathematics that explores how we can do that. Adina Goldberg was one of the participants at a recent research programme in this area at the Isaac Newton Institute for Mathematical Sciences . In this episode we speak to Adina about her work and how her intriguing motto – "the meaning is in the arrows" – applies to her research, her career path, and the way she looks at life. You can find out more about quantum information in this short introduction and delve into the details of information theory in this collection of content . Make sure you visit
#66 A conversation with Sarah Hart
Send us Fan Mail Welcome to the latest episode of Living Proof , our podcast produced in collaboration with Plus.maths.org In this episode we spoke to Sarah Hart, a mathematician interested in not just the maths itself, but also its connections to other areas of literature and art. She's done an amazing number of things throughout her career — from research in pure mathematics and heading up a maths department, to being the first woman Gresham Professor of Geometry and President of the British Society for the History of Mathematics. Sarah has also written a fascinating book, called Once upon a prime: The wondrous connections between mathematics and literature , and she gave a talk at this year's Cambridge Festival, with the intriguing title Life in Lilliput – The Mathematics of Fictional Realms that was held at the INI. Sarah also participates in the Modern History of Mathematics research programme that is currently taking place at the INI. In this episode, Sarah tells us many things she has done and how they all fit together, and gives some advice for budding mathematicians of all ages: "keep pursuing all the things you love doing, and one day it may turn out that they all fit together." To find out more about some of the things mentioned in this podcast see the following links: Sarah Hart: Once upon a prime — In this episode of Maths on the Move podcast Sarah talks about her book and the connections between maths and literature. Maths in three minutes: Groups — This article gives a brief introduction to Sarah's research area. Life in Lilliput – The Mathematics of Fictional Realms — Click this link to watch a recording of Sarah's Cambridge Festival talk at the INI.
#64 Communicating mathematics with the INI and Hannah Fry
Send us Fan Mail Welcome to the latest episode of Living Proof , our podcast produced in collaboration with Plus.maths.org In this episode, we dive into the importance of communicating mathematics to a broader audience, a growing priority within the maths community. Sara Khan, Communications Manager at the Isaac Newton Institute, shares how the INI is championing mathematics communication. Then, Rachel Thomas and Marianne Freiberger, editors of Plus.maths.org, revisit their conversation with Hannah Fry, who has recently taken on the role of Professor of the Public Understanding of Mathematics at the University of Cambridge. To learn more about the organizations and events mentioned in this episode that support mathematics communication, check out the following links: The Mathsci-comm network , funded by an INI Network grant, connects individuals working in or with an interest in communicating complex mathematics and data science to non-expert audiences. The network is managed by Plus.maths.org editors Marianne Freiberger and Rachel Thomas, alongside Maha Kaouri from the Newton Gateway to Mathematics . The Communicating Mathematical and Data Sciences — What Does Success Look Like? workshop, organized by the Mathsci-comm network, was held at the INI in November 2024. It was at this event that Hannah Fry announced her move to Cambridge. The Graduate Training Workshop for the Mathematical Sciences , hosted by the Newton Gateway to Mathematics, took place at the INI in February 2025, with a key focus on communication. This session was led by Plus.maths.org editors Marianne Freiberger and Rachel Thomas, along with Alison Kiddle and Katie Steckles, and followed a pilot event in October 2024. The Talking Maths in Public (TMiP) conference, held biennially in the UK, brings together those who work in or contribute to communicating mathematics to the public. TMiP 2025 will be held at the University of Warwick from 28th to 30th August 2025, with an option to attend online.
#65 Diving into maths with Emmy Noether
Send us Fan Mail Welcome to the latest episode of Living Proof , our podcast produced in collaboration with Plus.maths.org In this episode, we talked to famous Maths historian, David E. Rowe , who provided scientific advice for the play Diving into math with Emmy Noether, which was staged as part of the Modern History of Mathematics research programme and the Inclusivity in the Mathematical Sciences workshop at the INI. We dive deep into the life and work of Emmy Noether, and about what it's like putting mathematics on stage. The play is produced by Portrait Theater Vienna in co-operation with Freie Universität Berlin, directed by Sandra Schueddekopf, and features Anita Zieher as Emmy Noether. Read article Emmy Noether: a creative mathematical genius produced by Plus magazine as part of their collaboration with INI.
#63 Exploring anomalous diffusion: an interview with Aleks Mijatovic and Codina Cotar
Send us Fan Mail In the latest episode of Living Proof, Dan Aspel speaks to Aleks Mijatovic (Warwick, Alan Turing Institute) and Codina Cotar (UCL) about the Stochastic systems for anomalous diffusion programme. They’ll be speaking about the theme and challenges of their highly interdisciplinary six-month research project, but the conversation starts with comments on some truly remarkable headwear… Stochastic systems for anomalous diffusion programme: https://www.newton.ac.uk/event/ssd/ Submit a proposal for an INI programme: https://www.newton.ac.uk/events/submit-a-proposal/ 00:00 - Introduction 00:41 - Welcome, an insight into “flamboyant” hat designs 03:53 - Explaining the concept of anomalous diffusion 07:05 - Connections to physics, biology, statistical mechanics and more 10:00 - The logistical support at INI in Cambridge: “I’ve never been so relaxed in my life!” 13:20 - “The freedom this place affords us is great, and fertile ground for such things to happen” 17:52 - Solutions vs questions 20:44 - Personal highlights of the programme
#62 Exploring Twistor Theory - an interview with Lionel Mason and Maciej Dunajski
Send us Fan Mail In the latest episode of Living Proof, Dan Aspel speaks to Professors Lionel Mason (Oxford) and Maciej Dunajski (Cambridge) of the Twistor Theory programme ( https://www.newton.ac.uk/event/twt ). Over the 30 minutes, they share their experiences of the scale and challenges of this far-reaching topic that - amongst other things - aims to unify general relativity and quantum mechanics. 00:00 - Introduction 00:42 - Welcome 01:48 - “I have been excited about this programme for 40 years”, introducing the topic 05:18 - Successes of the programme, the attendance of Roger Penrose 06:30 - Connecting Twistor Theory with the Kennedy assassination, a short history of the field 10:28 - The many languages of mathematics 13:45 - Periods of acceleration within the field, “… the 70s must have been truly exciting”, the collaboration between Penrose and Michael Atiyah 17:50 - “Roger makes no secret of the fact that he disapproved of String Theory” 19:48 - What applications can one expect from Twistor Theory? 27:14 - Personal highlights of the month-long programme, celebrating 30 years of collaboration
#61 Organising an INI Satellite Programme: an interview with Professors Mark Blyth and Sasha Korobkin
Send us Fan Mail In the latest episode of Living Proof, Dan Aspel speaks to Professors Mark Blyth and Sasha Korobkin , organisers of the INI Satellite Programme “ The mathematics of multiphase flows with applications ” (https://www.newton.ac.uk/event/mfa/). In the conversation, Mark and Sasha explain the programme’s research themes and share their insights into the challenges and rewards of organising an INI programme at your home institution - in their case the University of East Anglia in Norwich. 00:00 - Introduction 00:49 - Welcome, overview of the programme, UEA and Norwich as a venue 07:22 - Social aspect of INI programmes 09:20 - Structure of the programme, starting with a summer school 13:02 - Central workshop of the programme: “New directions in multiphase flows” (https://www.newton.ac.uk/event/mfaw02/), connections with industry 16:30 - The challenges of running a satellite programme, without the infrastructure provided in Cambridge 20:50 - Discussing the two-year lead time from proposal to preparation to hosting the month-long programme, the importance of planning far in advance 22:45 - Success of the science during a month-long programme 26:38 - Personal highlights: “I was amazed we made it through the month without any catastrophes”, lecture on beer tapping 29:25 - Final thoughts, looking to the future
#60 Exploring 'Mathlib' and the digitisation of mathematics: an interview with Professor Kevin Buzzard
Send us Fan Mail In the latest episode of Living Proof, Dan Aspel speaks to Professor Kevin Buzzard of Imperial College London. Inspired by a lecture given by Thomas Hales at INI’s Big Proof ( https://www.newton.ac.uk/event/bpr/ ) programme in 2017, Kevin has spent the past seven years working alongside fellow enthusiasts on the “Maths Library” project. In this conversation he explains the project in detail, touching on why the programming language of Lean was chosen, and how it interacts with his recent five-year grant to check the proof of Fermat’s Last Theorem. If you have been inspired by Kevin’s story, make sure to visit the October 2024 INI research programme Big Specification ( https://www.newton.ac.uk/event/bsp/ ), much of which will be available to watch via live stream on newton.ac.uk 00:00 - Introduction 00:48 - Welcome, explaining the concept behind the “Maths Library”, digitising mathematics 04:20 - “It’s like asking if a submarine can swim” 07:55 - Harnessing the involvement of undergraduates 09:45 - Discussing the motivation, end goals and challenges of the project 17:28 - “The other question is: how far is it going to go? This is an ongoing topic of debate” 20:21 - A minimal, pessimistic prediction of expected progress in 10 years’ time 29:30 - A five-year grant to prove Fermat’s Last Theorem 36:55 - “I’d like to think I’m making the proof of Fermat’s Last Theorem more beautiful” 38:48 - “The goal is to make tools that, together with AI techniques, will turn mathematics on its head” 40:10 - Discussing “Lean” as a functional programming language 44:50 - “The INI Big Proof programme (2017) changed my life completely” ( https://www.newton.ac.uk/event/bpr/ ) 52:50 - “If you hadn’t streamed it, I never would have seen it”, a transformation from a “second-rate number theorist” to business class flights, four-star hotels and chauffeur-driven cars on an international lecture tour 54:48 - “I still wake up every morning thinking ‘I want to prove Fermat’s Last Theorem’”
“Meet the…Simons Postdoctoral Fellows” mini series #12 Dr Luke Davis
Send us Fan Mail Established in 2021, the INI Postdoctoral Fellowships in Mathematics scheme enables “exceptional early career researchers in the mathematical sciences” to gain “experience, independence and new connections on their way to a successful academic career”. In this episode of Living Proof, Dan Aspel speaks to Dr Luke Davis to learn about his journey through mathematics so far, and to find out what being awarded this Fellowship – which involves spending six months on the INI research programme “ Stochastic systems for anomalous diffusion ” – means to him personally. 00:00 - Introduction 00:38 - Welcome 01:55 - Taking part in “Stochastic systems for anomalous diffusion” ( https://www.newton.ac.uk/event/ssd/ ) 05:54 - What does an early career researcher bring to an INI research programme? And what can they gain? 10:50 - Why transition from physics to mathematics? 13:40 - The experience of working at INI, “a place engineered for people to think, to talk” 15:04 - The future, the University of Edinburgh
#59 Meeting the three mathematics medalists from the STEM for Britain awards 2024
Send us Fan Mail In this episode of Living Proof, Dan Aspel is joined by three guests: Daniel Gardham (Surrey), Katherine Benjamin (Oxford), and Francisco de Melo Virissimo (LSE), all of whom won medals as podium finishers at the 2024 STEM for Britain awards at the UK parliament in March. The conversation covers their success in the highly competitive poster exhibition, how it felt to present their mathematical research to politicians and the public, and what the future holds for each of them from this point onwards. > https://stemforbritain.org.uk/ > https://www.newton.ac.uk/news/ini-news/stem-for-britain-winners-2024/ 00:00 - Introduction 02:20 - How does it feel to have won medals at STEM for Britain? 04:40 - What attracted you to the event? 08:10 - What’s it like presenting mathematical research to MPs and politicians? 12:10 - Learning to communicate key information quickly and more efficiently, and comparisons with academic settings 16:40 - Could all academics benefit from this kind of experience? 19:00 - How would pure maths fare at en event such as STEM for Britain? 20:50 - A strong field of finalist posters, but little time to enjoy them 23:30 - The experience of visiting Parliament and the atmosphere of the event 27:27 - What does the future hold for each of you?
“Meet the…Simons Postdoctoral Fellows” mini series #11 Dr S. J. Kole
Send us Fan Mail Now in its third year, the INI Postdoctoral Fellowships in Mathematics scheme enables “exceptional early career researchers in the mathematical sciences” to gain “experience, independence and new connections on their way to a successful academic career”. In this episode of Living Proof, Dan Aspel speak to Dr Swapnil Jaideo (SJ) Kole to learn about her journey through mathematics so far, and to find out what being awarded this Fellowship – which involves spending three months on the INI research programme " New statistical physics in living matter: non equilibrium states under adaptive control " and nine months working with Professor Michael Cates at Cambridge University’s Department for Applied Maths and Theoretical Physics – means to her personally.
Producer's note
Steal the structure. Not the show.
Keep the useful structure, then change the audience, point of view, and voice until the idea is unmistakably yours.
