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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 time: 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 genius produced 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

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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’”

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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