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84 sats \ 3 replies \ @adlai 7h \ on: Mathematics AI Aristotle proves 30 year old Erdos Problem #124 AI
edit: It's doubly unsurprising when you consider how much of what Erdos left mathematics was statements of open problems... his productive time [which was allegedly almost all of his waking hours] was spent either mercilessly roping his friends into coathoring papers with him on his ever-growing list of problems, or brainstorming interesting problems for future papers. So it's much less surprising that an Erdos problem has been attacked successfully, than e.g. a Hilbert problem.
It's not too surprising; lots of the challenges in mathematics are related to comprehensibility, not reachability.
Consider the following thought experiment:
Think of the space of all sequences of all ASCII characters; most of these are noise, right? Not even slop, just noise.
Narrow down the space, radically, to all LaTeX programs; most of these are invalid, or garbage, right? Not even slop, just garbage that you can feed a compiler to heat your computer.
Narrow the space down further, to all LaTeX programs producing renderable documents... still, we're far from anything useful, as this is essentially what the "million monkeys at a million typewriters" produce, although with less animal cruelty.
Now things get interesting: narrow down the space to the LaTeX programs that produce documents beginning with a list of axioms, and continuing with a series of propositions. Most won't be logical, although some tiny vanishing fraction of these will be valid mathematical proofs.
Are any of them proving anything new? Are any of the proofs simpler than the ones found by schoolchildren? Do any of these help us figure out which concepts are worth spending words to name, rather than considering them merely some intermediate noise which lives and dies within the span of one convoluted proof?
Interesting perspective... I guess we'll see where we are a year or two from now.
Appears he recently raised $120M for this startup which seems quite a large sum for a mathematics startup... curious how investors expect to get their money back.
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Appears he recently raised $120M for this startup which seems quite a large sum for a mathematics startup... curious how investors expect to get their money back.
Off the top of my mind, two possible sources for a finite1 valuation are the possibility of getting acquired for the technology, and the possibility of selling a service that is used by customers who value mathematical rigor [e.g. aerospace engineers]. I agree that $120M is a lot, especially given how rapidly any bored undergraduate from almost any STEM field could vibe code a theorem proving agent as a semester project by gluing together open source tools.
Footnotes
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rather than infinitesimal ↩
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@remindme in 1 year
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