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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