Mathematics and the computer

Speaker: Kevin Buzzard

Abstract

For decades, mathematicians have been using computers to calculate. More recently there has been some interest in trying to get them to reason.What is the difference? An example of a calculation: compute the first one million prime numbers.An example of reasoning: prove that there are infinitely many prime numbers. Tools like ChatGPT can prove things like this, because they have seen many proofs of it on the internet. But can computers help researchers to come up with new mathematics? Hoping that a computer will automatically prove the Riemann Hypothesis is still science fiction. But new tools and methods are becoming available. I will give an overview of the state of the art.

Bio

Kevin Buzzard got his PhD from the University of Cambridge in 1995, he was a Miller Research Fellow in Berkeley in the late 90s and a visiting professor at Harvard in the early 2000s; he is currently a professor of pure mathematics at Imperial College in London England. In 2022 he gave a plenary lecture at the International Congress of Mathematicians.