The unit distance problem

[ny_quant]

https://www.scientificamerican.com/article/ai-just-solved-an-80-year-old-erdos-problem-and-mathematicians-are-amazed/

Правда, как я понял, ИИ не решило проблему, а всего лишь показало, что Эрдош был неправ. Но все равно круто!

Comments

[tropicalizator]

>Но ни у кого из знающих теорию чисел руки до такого не дошли

Пожалуй это преувеличение. Товарищ Цимерман, например, написал следующее:

I actually briefly worked on this problem and tried to make a counterexample, but failed to make progress.

On Boris Alexeev’s suggestion, I thought about this problem with the idea of making a counterexample stemming from a varying family of bounded degree number fields. Increasing degree occured to me, but is a very scary dynamic and often doesn’t work out. Moreover, it is hard to think through the analytic regimes and retain guiding intuition - it consumes much time and frequently doesn’t work out. While it’s true in the final solution that nothing is all that surprising, there are many ways to attempt to set this construction up (how big are the primes? How big is the ball? Do you take large products? how much splitting does one insist on - this is a tradeoff with how easy it is to make the field). It is definitely an intimidating construction to see through even if you know what is going on, and even harder to go play for yourself. It’s always tempting to look at a completed proof and declare it obvious after the fact.

This may indicate one way that AI systems have an edge: it’s not just that they can try all known methods, but they can play for longer and in more treacherous waters than mathematicians without getting overwhelmed. Of course this is not yet robustly true, but this may be a foreshadowing event.

[lemberger]

Ну то есть у кого-то дошли, но ИИ успел раньше. Или люди не настолько массово этим занимались. В любом случае факт есть факт.