The idea of proof is fundamental to mathematics. We could argue that science consists of testable theories, and therefore that it is about what can be disproved, not what can be proved. In law, the test is “beyond reasonable doubt”.
Famous conjectures in mathematics have been tested by computers for trillions of numbers – but we still call them conjectures.
In this lecture Professor Hart talked about what mathematicians mean by proof, and she showed some of her favourites.
https://www.gresham.ac.uk/sites/default/files/transcript/2024-06-04-1300_Hart-T.pdf
Professor Sarah Hart
Professor of Geometry (2020 – )
Sarah Hart is the first woman Professor of Geometry at Gresham College, and was appointed in 2020. She is Professor Emerita of Mathematics at Birkbeck, University of London.
She studied at Oxford and Manchester, gaining her PhD in 2000. Postdoctoral research and teaching followed, including a prestigious Engineering and Physical Sciences Research Council Fellowship, before she was appointed to a lectureship at Birkbeck in 2004. She became Professor of Mathematics there in 2013, and served in various management roles including as Head of Mathematics and Statistics, Assistant Dean, and Programme Director for the MSc Mathematics.
Her academic publications have been mainly in the area of pure mathematics known as group theory, which has many applications both inside and outside of mathematics, for example in coding theory and cryptography. She is actively involved in the British Society for the History of Mathematics, and has served a three-year term as President of the Society from 2021-2023.
Professor Hart is passionate about communicating mathematics and is a sought-after public speaker. She is particularly interested in the links between mathematics, culture and creativity: many of her public lectures and talks in schools relate to these topics. Her book Once Upon a Prime: the Wondrous Connections between Mathematics and Literature, was published in 2023, and has been positively reviewed in the press, including The Sunday Times, The Observer, The Economist, The New York Times, The Washington Post and the Wall Street Journal.
Read more about Professor Hart in Qantat Magazine
helen the hare 