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pegasus • yesterday at 1:34 PM • 2 replies • view on HN

But math is not formalizable (ask Goedel why). And no, computers have not decisively beat humans at maths, that's a laughable assertion. Sure, laymen always imagined math as being about proving theorems, but there's a saying among mathematicians: good mathematicians prove theorems, great mathematicians make conjunctures, the greatest mathematicians write definitions. But maybe you already thought they've solved math when they were able to calculate a zillion digits of pi, lol.

It sounds like you're a bit like that AI stuck in the datacenter, confirming their hypothesis without needing to actually check whether it's true or not in the real world. Then proceeding to imagine how the rest of the world is wondering at your imagined magical capacity of prediction.


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cousin_it • yesterday at 1:50 PM

(Sighs)

Goedel's theorems don't stop AI from finding and formalizing math results. They certainly don't stop AI from making conjectures or writing definitions. They have nothing to do with any of that.

The theorems are about inability of formal theories to prove certain sentences involving provability (the first is about "this sentence is not provable", the second is about "this theory is consistent"). Most mathematicians never touch any such sentences in their entire career. All the life's work of someone like Gauss, an all-time great, can be formalized just fine.

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