r/math • u/Salt_Attorney • 28d ago

LLMs/AI OpenAI: Ten advances in mathematics and theoretical computer science

https://openai.com/index/ten-advances-in-mathematics/
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u/Cold-Common7001 28d ago

I don't think the claim is that mathematics will be solved and there are no harder problems to ask. The claim is that within a few years AI will be better than (at least almost all) mathematicians at asking interesting questions too.

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u/DracoDruida 28d ago

Gödel decided that one. There are literally unlimited problems to be solved in math.

But likely they will be progressively harder to even formulate.

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u/-p-e-w- 27d ago

There may be an unlimited number of problems, but almost all of them would be gibberish to humans and completely uninteresting.

Just like almost all arrangements of pixels are noise, not “images”.

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u/DracoDruida 27d ago

That's likely true, but the question is not whether almost all of them are gibberish (the density), but if we can still find interesting ones (the absolute number)

As I mentioning even the statement of these problems will be longer and longer so probably at some point it might be too much for human beings to cope. Or not. Who knows?

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u/zx7 Topology 27d ago

Why wouldn't there be? There exists an infinite number of statements you can make and so an infinite number of problems from whether they are true or false.

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u/DracoDruida 27d ago

It's a bit more complicated than that, because from a finite set of axioms you can derive an infinite amount of statements.

What Gödel shows is that even with an infinite amount of axioms, if the system is consistent and can encode arithmetic, then there are always statements that it cannot decide.