Когда мне было около 11 лет, я впервые услышал о последней теореме Ферма. Меня сразу заинтересовал постановка проблемы, а также сопутствующая история, и я предпринял серьезную попытку доказать ее. And while, unsurprisingly, я failed, я многое узнал от попытки. Blissfully ignorant of the fact that the case had been proved by Euler over 200 years earlier, я решил, что это будет хорошее место для начала: once я sorted out that, я был оптимистичным, что смогу приступиться к общему случаю.

Since я еще не мог really увидеть, с чего начать, я решил упростить проблему и сосредоточиться на последовательных разницах кубов, с целью показать, что такая разница не может быть кубом сама по себе. At the time я не knew how to express what я was doing in algebraic language, so я did not explicitly try to prove that the Diophantine equation had no solution. Rather, я worked out some successive differences and stared at them, trying to get some idea of why none of them was a perfect cube. (I should be clear that this story is a reconstruction of what I think probably happened given the few memory traces that remain half a century later rather than a completely reliable account).

At some point, я had the idea of taking the difference sequence of the difference sequence, and discovered that it formed an arithmetic progression. That felt like progress, so я investigated difference sequences a bit more and discovered, purely empirically, the rule that if you start with th powers and keep taking successive differences, then eventually you get to the constant sequence . Somehow я never managed to turn this observation into a proof of Fermat’s Last Theorem, and later on my dream of solving it got replaced by other mathematical dreams.

However, when я reached the point in my mathematical education where я was taught about taking difference sequences and about what happened to polynomials, я understood those topics much better than I would have if я had not discovered difference sequences for myself and spent happy hours playing around with them. I mention this story just as an illustration of the phenomenon that was strongly emphasized in this letter signed by 25 Fields medallists, that one learns a lot from thinking about a problem, regardless of whether one solves it. In the end, however, я felt that я could not sign the letter, despite agreeing with much of what it said.

Instead, it seemed better to do what I did with the Leiden Declaration and set out my own position in a blog post. But it should be understood that by doing that I am not setting myself up as a member of some opposing camp: indeed one of my worries at the moment is that the mathematical community might become bitterly divided, something I would very much like to avoid. Also, я agree on the fundamental point that we are facing a crisis: я just want to offer a slightly different analysis of what that crisis is.

I don’t claim full originality for this analysis, as I know that several other mathematicians have already put forward thoughts that are similar to the ones I have, though (for what it’s worth) I have largely come to these conclusions independently. On the subject of independence, it will perhaps help if я clarify that while я have contacts in the mathematics group at Open AI, and have also been given early access to some of their models (typically only a few days before they have been released), and have been given free access to their Pro models once released, я have never been paid by Open AI. I mention this in the hope, perhaps naive, that what I write will not be dismissed for ad hominem reasons.

Another potential reason for my being regarded as “pro-AI” is that, as I have stated publicly several times, я have a group in Cambridge devoted to automatic theorem proving. However, that is actually more of a reason to be anti-AI, since our group has been tryi...