We are continuing our conversations with mathematician colleagues at the University of Cambridge, part of the podcast we produce for the Maths Faculty here. Today we meet Julian Sahasrabudhe, Professor of Mathematics, and one of the invited speakers at the International Congress of Mathematicians (ICM) in July this year.

The ICM is one of the biggest events in the mathematics world and is the host of several prizes, including the prestigious Fields Medal. Only mathematicians at the very forefront of research are invited to speak, so we were very excited to learn more about Julian's work.

We spoke to him about his path into mathematics, from his childhood dreams to his early career as a drummer, before he finally settled on maths. Julian also gave us a brief introduction to his work in the field of combinatorics and how it offers partnerships with other areas of maths.

The podcast mentions Maryna Viazovska, who won a Fields Medal in 2022. Julian discusses the link between Ramsey theory and her work on sphere packing, as in the image below (courtesy Greg A L, CC BY-SA 3.0).

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Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.

We are very lucky to be based at the Centre for Mathematical Sciences at the University of Cambridge. To start our latest podcast season we bring you a series of conversations with our mathematician colleagues, part of the podcast we produce for the Maths Faculty here.

In our first podcast we meet Richard Samworth, Professor of Statistical Science and Director of the Statistical Laboratory. We spoke to him in the run up to the International Congress of Mathematicians (ICM), one of the biggest dates in the mathematical calendar, where the most prestigious prizes in maths, including the Fields Medals, are awarded. Held every four years, the ICM features the world's leaders in the field and celebrates the diversity of today’s mathematics. Only mathematicians whose work is of the highest international standard are invited to speak at the week-long event, and Richard is one of the invited speakers at the ICM this July!

Richard's contributions to statistics have been recognised with numerous honours and awards. In 2025, he won two prestigious prizes in the space of 24 hours – the David Cox Medal for Statistics and the Guy Medal in Silver.

We talked to Richard to find out more about the work he will be speaking about at the ICM, how his field of statistics is simultaneously very theoretical and very applied, and what he most values about being part of the mathematical community here in Cambridge.

Find out more about:

Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.

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:

This content was produced as part of our collaborations with the Isaac Newton Institute for Mathematical Sciences (INI) and the Newton Gateway to Mathematics.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. The Newton Gateway is the impact initiative of the INI, which engages with users of mathematics. You can find all the content from the collaboration here.

"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.

In this episode of Living Proof we talk to Céline and Frank about the book, what it was like writing it, and what their different backgrounds brought to the 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.

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.

This content forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration 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. Visit www.newton.ac.uk to find out more.

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 of Jess Enright's 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 of Erica Thompson in her book, Escape from Model Land: how mathematical models can lead us astray and what we can do about it. 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 geoscientist Chris Skinner 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 Tarrus, 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:

This podcast is part of our collaboration with 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 JUNIPER here.

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 involves 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 of Living proof we meet 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 called Big Proof at the Isaac Newton Institute for Mathematical Sciences (INI) in Cambridge. This programme, which attracted some of the best minds in modern mathematics, followed on from a pioneering workshop on the same topic which took place at the INI in 2017.

To find out more about the topics mentioned in this podcast, see the following articles:

This content forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration 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. Visit www.newton.ac.uk to find out more.

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.

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 Maths on the Move 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:

Dye Diffusion in Water by Henrique Biasi. Find out more here.

A microcosm of milk by Christian Casaljay. Find out more here.

Work by Lilia Bakanova, which which won the category for textile, sculpture and other medium. Find out more here.

The mathematical area of topology 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. Topological data analysis (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 of Maths on the Move we talk to algebraic topologist Michael Hill 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 brilliant Rothschild lecture at the Isaac Newton Institute for Mathematical Sciences (INI) in Cambridge. He was at the INI to attend the research programme Equivariant homotopy theory in context.

To find out more about the topics mentioned in this podcast see:

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.

This podcast forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration 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. Visit www.newton.ac.uk to find out more.

Welcome to the new season of the Maths on the Move podcast! 

We start the season with theoretical physicist David Tong of the University of Cambridge looking at an important milestone in the history of physics: the 100th birthday of quantum mechanics which we celebrate this year. David tells us why a new theory was needed, which of the many strange aspects of quantum mechanics is, in his opinion, the most significant, and that Erwin Schrödinger had a tendency to be grumpy.

David also tells us how quantum mechanics links to quantum field theory, the language in which all of modern physics is formulated, and reveals some mysterious connections between very different areas of physics — such as the theory of black holes and fluid mechanics. Join us in a wavy dance from the very small to the very large!

For some background and further reading and viewing see: