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So in the early hours of Monday morning, just after the World Cup final had finished, a mathematician called Levent Alperge posted a tweet which read like this: "Hello there.

The Jacobian conjecture is false.

Thanks to my close friend Akhel for asking about it and my other close friend Fable for working on it during the World Cup final." So Alperge is a junior fellow at Harvard, as well as having a position at Anthropic AI, who have a model called Claude Fable-5.

So this is presumably who he's referring to when he refers to his close friend Fable.

But the best part of the tweet is that in the remaining two-hundred-and-sixteen characters, he proceeds to give a counterexample to this eighty-seven-year-old maths conjecture called the Jacobian conjecture.

Uh, it's considered one of the most important open problems in maths, and for years, mathematicians were going nowhere trying to prove it correct, and then just like that, the conjecture is proved wrong.

It's like a mathematician's mic drop moment.

It's...

I mean, it's, it's astonishing, and I suppose we should say, you know, in a sense, it's easier to prove something wrong than to prove something right.

You just need one counterexample, and this whole thing tumbles.

But equally, no one had done that.

[laughs]

No, exactly.

And actually, this is...

I think this is where a lot of, of, um, AI maths is going at the moment.

In fact, just yesterday, uh, I read about another example of, of, a guy called Dmitry Rabin, who posted on X that he'd used ChatGPT to find a counterexample to a, another long-standing conjecture, and his prompts were absolutely hilarious.

He basically said, "Construct a counterexample to general non-play in the case of this Dinits-Gog-Gurman's conjecture." And he said, "You should do a breakthrough and find a structured counterexample." It's brilliant.

And when it didn't do it after the first prompt, he said, "Please continue, continue the search." And then the last prompt he gave it was, "That's enough of partial results.

Let's finish with a complete unconditional counterexample." And it did it.

It was absolutely astonishing.

Now, there's, there's another bit of-- before we get onto journals, there is another bit of AI news today, which, which could in, in a sense be good for that 'cause it's possible that the AI might actually just end up killing us all before it takes mathematicians' jobs.

Yeah, it might just take u- take us all over and enslave us, perhaps.

So, [laughs] um, yeah, OpenAI, another, uh, AI company, says that during what they call a controlled security exercise, one of its advanced AI agents, AI agents, so it found a weakness in the testing environment, which we often call the sandbox.

You put it in the sandbox, so it can't do too much damage.

So it didn't have access to the internet.

So in the early hours of Monday morning, just after the World Cup final had finished, a mathematician called Levent Alperge posted a tweet which read like this: "Hello there.

The Jacobian conjecture is false.

Thanks to my close friend Akhel for asking about it and my other close friend Fable for working on it during the World Cup final." So Alperge is a junior fellow at Harvard, as well as having a position at Anthropic AI, who have a model called Claude Fable-5.

So this is presumably who he's referring to when he refers to his close friend Fable.

But the best part of the tweet is that in the remaining two-hundred-and-sixteen characters, he proceeds to give a counterexample to this eighty-seven-year-old maths conjecture called the Jacobian conjecture.

Uh, it's considered one of the most important open problems in maths, and for years, mathematicians were going nowhere trying to prove it correct, and then just like that, the conjecture is proved wrong.

It's like a mathematician's mic drop moment.

It's...

I mean, it's, it's astonishing, and I suppose we should say, you know, in a sense, it's easier to prove something wrong than to prove something right.

You just need one counterexample, and this whole thing tumbles.

But equally, no one had done that.

[laughs]

No, exactly.

And actually, this is...

I think this is where a lot of, of, um, AI maths is going at the moment.

In fact, just yesterday, uh, I read about another example of, of, a guy called Dmitry Rabin, who posted on X that he'd used ChatGPT to find a counterexample to a, another long-standing conjecture, and his prompts were absolutely hilarious.

He basically said, "Construct a counterexample to general non-play in the case of this Dinits-Gog-Gurman's conjecture." And he said, "You should do a breakthrough and find a structured counterexample." It's brilliant.

And when it didn't do it after the first prompt, he said, "Please continue, continue the search." And then the last prompt he gave it was, "That's enough of partial results.

Let's finish with a complete unconditional counterexample." And it did it.

It was absolutely astonishing.

Now, there's, there's another bit of-- before we get onto journals, there is another bit of AI news today, which, which could in, in a sense be good for that 'cause it's possible that the AI might actually just end up killing us all before it takes mathematicians' jobs.

Yeah, it might just take u- take us all over and enslave us, perhaps.

So, [laughs] um, yeah, OpenAI, another, uh, AI company, says that during what they call a controlled security exercise, one of its advanced AI agents, AI agents, so it found a weakness in the testing environment, which we often call the sandbox.

You put it in the sandbox, so it can't do too much damage.

So it didn't have access to the internet.