What is the current thought on AI creating new emergent forms of mathematics? Even the most stunning results like the proof of the quasi-RH are a clever combination of known mathematics. Humans have created (discovered?) stunning new ideas (e.g. complex numbers) that have opened wide new horizons -- do we think AI will be capable of creting / discovering novel new things like this?

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stephbook a day ago | parent [-]

Are humans going to be able to recognize the things AI discovers?

It took us a while to make the planets line up neatly in a heliocentric system. Just last month I read that a whale mother "might" grief while carrying her stillborn child.

The limiting factor is human imagination and comprehension. No offense, but see your comment.

I think AI has already invented new math, but the guys haven't looked for it because they didn't think it possible. And even under their noses, they wouldn't understand what they see.

> It's not what you look at that matters, it's what you see. —Thoreau

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waynecochran a day ago | parent | next [-]

LEAN and other tools verify from what do know -- at least stepwise. Anything that deviates from these things should stick out. I suppose some million line LEAN program may have embedded within it something that is novel and not readily apparent, but I imagine truly novel approaches should stick out like a sore thumb.

Could AI create a novel set of axioms (a new math) from which things like RH become a by product? I think that would be hard to miss.

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stephbook a day ago | parent [-]

Dozens of agents probably already invented it, but they were given ephemeral containers where noone ever looked or they only wrote it in direct CPU instructions.

	▲	waynecochran a day ago \| parent [-]
		I would really like to see an AI invent a new set of (consistent) axioms from which a whole slew of new problems and solutions arise. Something akin to Euclidean geometry, but for a whole new landscape of theorems.

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pfdietz a day ago | parent | prev [-]

> Are humans going to be able to recognize the things AI discovers?

They have been so far.

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stephbook a day ago | parent [-]

That's like saying that all serial killers make a mistake that gets them caught, which is true only of those that were caught (and studied.)

	▲	pfdietz a day ago \| parent [-]
		That analogy makes no sense to me. Wouldn't OpenAI have the incentive to release results that are incomprehensible, to showcase how beyond humans their models are?