Living Proof: the Isaac Newton Institute podcast

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Field-altering, AI-assisted mathematical results are coming out every day. The pace is blistering. How are the maths and theoretical computer science community handling this rapid change? For some, they're choosing collaboration.

We spoke with Dr Robert Robere, one of the participants in the current Logical Foundations of Complexity programme, to learn more about how their community is changing the way it collaborates to make progress, together.

Having recently been granted tenure, Dr Robere is at an inflection point in his career. He is no longer in the start-up phase, but nor is he yet considered senior. He is visiting the INI during his first sabbatical, and AI is radically shifting the mathematical landscape. This is mirroring his experience when he started his first faculty position during COVID, which radically shifted the way people work.

Dr Robert Robere is an associate professor in the School of Computer Science at McGill University in Montreal, Canada. He completed his undergraduate in Newfoundland before moving to Toronto for graduate studies under the supervision of Turing Award winner Stephen Cook and Toniann Pitassi.

He now runs his own group focused on using mathematical tools to understand the nature of computation. We caught up with him while he was in Cambridge for two months on an INI programme.

The episode was recorded on September 29, 2026.

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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

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AI is fundamentally mathematical, and AI systems are changing what is possible in mathematics. This is a turbulent time for the field.

We spoke with Professor Gitta Kutyniok, who visited the INI in August as part of the Operator methods for dynamical systems programme. An expert in the mathematics underpinning AI, she had a fascinating take on the impact of AI on research, education, and society more widely.

Professor Kutyniok holds theChair for Mathematical Foundations of Artificial Intelligence at LMU Munich, where she focuses on "the intersection of mathematics and artificial intelligence, aiming for both a mathematical understanding of artificial intelligence and artificial intelligence for mathematical problems."

The episode was recorded on August 6, 2026.

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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

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Human behaviour is messy. People aren't always perfectly rational and don't always have the right information to make perfect decisions.

But can mathematics help us model the way people will act in a given situation so that we can better prepare our energy grids and health systems?

We spoke with Dr Ellen Zapata-Webborn, a Senior Research Fellow in Data Science and End Use Energy Demand at the UCL Energy Institute, where she works on the Smart Energy Research Lab (SERL) project. She was also an organiser for the INI's satellite programme on Mathematics for Human Behaviour, which took place from July 20th to August 14th at the University of Nottingham.

In a wide-ranging discussion, we talk about career paths in behaviour modelling, how time in industry can give a fresh perspective, what useful patterns might be hiding in smart meter data, and the potential benefits of interdisciplinary working.

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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

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How have pre-prints and ArXiv changed the landscape of mathematical publishing? And how is AI changing ArXiv?

Plus Magazine editors Rachel Thomas and Marianne Freiberger sat down with Professor Ramin Zabih, one of the leaders of ArXiv, when he came to visit the INI for our AI for Maths and Open Science in April.

Watch the talk he gave here: https://www.youtube.com/watch?v=RyT0Z94kvGU

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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 Marianne Freiberger and Rachel Thomas, from Plus Magazine.

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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.

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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

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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

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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

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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

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**Correction** At 5:26, the date of the earliest numerical tables is the beginning of the second millenium before the Common Era.

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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

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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.

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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 prestigiousRamanujan 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.

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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.

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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.

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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

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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

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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.

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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.

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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 geniusproduced by Plus magazine as part of their collaboration with INI.

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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

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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

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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