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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.