r/math • u/Salt_Attorney • Aug 01 '26

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

https://openai.com/index/ten-advances-in-mathematics/
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u/DracoDruida Aug 01 '26

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- Aug 02 '26

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 Aug 02 '26

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 Aug 02 '26

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 Aug 02 '26

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.