Hyperbolic Geometry Unlocks Infinite Tilings

ttps://x.com/GreshamCollege Watch the Q&A session here: https://youtu.be/tv554JY9TPU

In 1588, the young Galileo delivered some lectures that were impressive enough to secure him a mathematics professorship at the University of Pisa. His subject? The geometry of Dante’s Inferno. In this lecture we’ll look at some of Galileo’s deductions, and how the questions raised may have influenced his later mathematical research. Using this and other examples of creative work in mathematics that crosses our modern ideas of subject boundaries, I will argue that thinking across disciplines is not only intellectually exciting but academically vital.

This Annual Provost's Lecture was recorded by Sarah Hart on June 18th 2025 at Barnard's Inn Hall, London.

Sarah Hart was the first woman Professor of Geometry at Gresham College, and Acting Provost between March and October 2025. She is also Professor Emerita of Mathematics at Birkbeck, University of London.

Professor Hart 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.

The transcript of the lecture is available from the Gresham College website: https://www.gresham.ac.uk/watch-now/galileos-journey-underworld-case-interdisciplinary-thinking

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