Tom Ritchford
1 min readJul 13, 2024

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It's even a little worse than this.

In mathematics, right now, there are at least two papers out, by renowned, world-class mathematicians, that claim to prove long-standing, extremely important conjectures.

I say, "claim", not because people believe that these mathematicians are cheating or deluded, but because there aren't other mathematicians who are capable of understanding the full proofs and either verifying them, or finding issues with them.

It's a weird impasse, and it's only going to get worse as the mathematical facts with comprehensible proofs all get proven.

AI to the rescue? But not so fast. Unfortunately, AI is significantly less reliable than a mathematician at writing correct proofs, and it just gets worse as the subject gets more obscure.

There is a lot of research now into automated proof assistants - programs which take the drudgery out of writing and verifying proofs - and I think this will get us a few more years, but it might be that we run out of mathematics in my lifetime. Oh, there will always be new little discoveries: what I mean is that there will be major, fairly easy to explain problems that will always remain out of our reach to generate actual proofs.

And that would be a sad end to this great endeavor that has lasted for thousands of years.

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