Will AI complete mathematics?

Tom Whipple (0:00)

Hello, welcome to Inside Science from the BBC World Service with me, Tom Whipple.

On Wednesday morning, the world's mathematicians arrived into work. They poured themselves a cup of black coffee. They wiped the blackboard clean. They sat down in the common room and started another day thinking about theorems. Then they learnt that half of those theorems, ish, had just been apparently solved. This week, there was a mathaclysm, quite possibly the biggest day in the 10,000 year history of maths.

On Inside Science this week, we're looking at that, but we're also celebrating human achievement too. It's Nobel week. From mice with blue lights in their brain to massive ice cubes with blue lights underground. What do you need to know? Someone who likes maths, but maybe, I presume, not mice, is Caroline Steel. Caroline has been looking through the other science news. What have you got for us?

Caroline Steel (0:54)

Well, did you know that this week is World Space Week?

Tom Whipple (0:57)

I did not.

Caroline Steel (0:58)

Well, it is. And I've got some space news for you.

Tom Whipple (1:01)

Excellent. Excellent. There's always space news and I'm always excited to hear it.

But first of all, let's do some maths news. Now, in 2023, CHAT GPT arrived and the mathematicians laughed. Give it a simple sum and it would get it wrong. It was less mathematically skilled than my Spaniel Wellington. Then this week, overnight, OpenAI dropped hundreds of mathematical papers on the internet. Decades of maths progress overnight. PhDs of work done in hours.

Jan Kuihei (1:33)

My name is Jan Kuihei and I am a mathematician here at the London Institute for Mathematical Sciences. I suppose I see this coming, but it is still surprising to me how fast this has come. So within about nine years or so, I've now finally see the point where LLMs are doing very, very serious mathematics.

Sophie McLean (1:54)

My name is Sophie McLean and I am a final year maths PhD student at King's College London.

One of the things that I love most about maths is the humanity, and the need to know the answers, and the love of the puzzles, and working together to find a solution.

And all of these things are lost. This isn't to say that AI is an entirely bad thing for maths, I think it will get rid of some of the things that matter to me most about maths.

Tom Whipple (2:20)

What does all this mean? Well, as we heard, some mathmos are feeling apocalyptic. Others, though, are dazzled by the possibilities.

We spoke to Kevin Buzzard, Professor of Pure Mathematics at Imperial College London.

Kevin Buzzard (2:32)

I'm an expert in number theory. I don't know all of mathematics, but about 30 of these papers were in algebraic number theory. And of those, about six or seven of them look quite impressive. On the other hand, I would say those papers were really theorems that it wouldn't have surprised me if a human had come along and said they could do it. The vast majority of what's happening here is stuff that you would expect a serious researcher to have produced. A lot of mathematicians are just now beginning to wake up to AI, but some people in the field have been watching it for the last five years. When CHAT GPT came out, it was roundly mocked by mathematicians of being terrible at mathematics. It couldn't multiply together four-digit numbers reliably.

We just happen to be at the point now where it's zooming past us. The real question is, what's going to happen in a year's time? Because you have to understand these machines are going to get better and better and better. At some point, things will start to tail off, but we don't really know when.

The future looks very interesting for mathematics, I think, right now.

Tom Whipple (3:37)

Interesting, or if you are one of those decent researchers, or indeed one of those PhD students who might be feeling rather crushed that you've described this work as rather minor, what does this mean?

Kevin Buzzard (3:49)

I think that these new tools are going to accelerate the field, just like the computer. The computer accelerated parts of mathematics, so these new tools will also accelerate parts of mathematics. But they're certainly not doing everything that humans do right now.

Intelligence is not a linear thing, right? We can't say, I'm more intelligent than you, or you're more intelligent than me. It doesn't work like that, right? For example, I'm much better than my daughter at mathematics, but she's much more emotionally intelligent than I am. Intelligence is multidimensional, and these language models, they're just a new dimension of intelligence. When the chaos dies down a bit, I think we'll just understand that we're now able to move faster.