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An interview with Kevin Buzzard

18 January 2023
  • Quantitative Research

Kevin Buzzard is a British mathematician and professor of Pure Mathematics at Imperial College London.

As part of the G-Research Distinguished Speaker Series, Kevin Buzzard was one of three speakers at the 2022 Computer Guided Mathematics Symposium, speaking alongside Sir Timothy Gowers (Professeur titulaire of the Combinatorics chair at the Collège de France) and Alex Davies (DeepMind).

His expertise lies in algebraic number theory and the Langlands program. Recently, Kevin has started to work in the area of formal proof verification.

His current focus is on teaching computers about modern research mathematics, thereby developing their potential to assist mathematicians.

Mathematics and the Computer

In his talk, Kevin contemplates new uses of computers in mathematics, an area that has been overlooked for decades.

“We have established ways of using computers in mathematics, but there are other new ways which are appearing…there is a chance that they will really change the way that mathematics is done in the future,” Kevin explains.

“Recently, things like AI and interactive theorem provers mean that mathematicians might be able to use computers in new ways. I do feel these systems have got something to offer the modern mathematician.”

An interview with Alex Davies
  • Quantitative Research
  • 18 Jan 2023

Alex Davies is a machine learning researcher at DeepMind, leading efforts to understand how machine learning can be used to solve fundamental problems and make new discoveries in mathematics.

Watch the interview
Why mathematics in some sense, the only subject I could make real sense of because I could, you could explain everything that was happening. So right now I'm interested in teaching computers about modern research, mathematics. So this is computer theory. Improvers have existed for decades, but it's only relatively recently that they've started to understand what humans are doing, uh, in 2022. And that's what I'm interested in today. I am gonna be talking about new uses of computers in mathematics. So mathematicians have been using computers for or for centuries, if you can, pre-digital computers. More recently, uh, things like AI and or interactive theory, improvers and, and other recent tools mean that mathematicians might be able to use computers in new ways. And, and that's the kind of thing I'll be talking about today. I started formalizing number theory and commuter to algebra. And actually I found that they were very amenable to formalization. However, uh, it's not good enough just to do parts of mathematics. One has to formalize all of it. One, one needs a, a big machine that understands all of it. And so recently there has been a push to formalize more geometric, the more geometric side of things. Uh, it's, it's more slow going, but it's certainly possible. It's just harder work. So this whole area of, of using computers in this, in this new way, this area of using computers to prove theorems in mathematics and to verify theorems is existed for decades. But the sort of the, the mainstream mathematician community have really not engaged with it in any way. And I do feel that the systems have got something to offer mathematics. I'm not entirely clear as to what it is, but I, I do feel that these systems have got something to offer the modern mathematician. And so it's important to spread the word. This is one of the reasons I, I speak just to, just to bring greater awareness to the area. 'cause it's been ignored for decades. People Just need to remember that we have established ways of using computers and mathematics, but there are other new ways which repairing and those new ways, there is a chance that they will really change the way mathematics is done in the future.
Open video transcript

G-Research Distinguished Speaker Series

Throughout the year, we host a number of speakers as part of G-Research’s Distinguished Speaker Series.

We pride ourselves on our learning environment, which gives people the opportunity to develop personally and professionally within their roles, and our Distinguished Speaker Series is central to that.

We invite global experts in their fields to discuss their cutting-edge work with an audience of G-Research employees and guests, giving attendees the chance to learn from the best.

Want to watch the talks, panel discussion and interviews from our Computer Guided Mathematics Symposium? Watch here

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