Why Erdős Problems Are Falling to AI
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It seems that AIs are really good at finding counterexamples now.Even if progress by AIs in proving conjectures lags, it seems likely that AIs collectively will, in the next few years, find counterexamples to nearly all the Erdős (and other) conjectures that are actually false and also provably false.That means we will able to assume that nearly…
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I get the impression that the value of unproven conjectures is more in the new math and techniques that may be discovered - by humans - trying to prove/disprove them, rather than much utility in any eventual result.Take something like Fermat's last theorem - I'd be curious to hear of any use of the result itself, but there was a massive amount of…
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The mathematics are above my intellectual capacities, but I still find the man and his lifestyle fascinating. Though I admit his heart attack probably wasn't a coincidence, sadly.I wonder if national, institutional, or otherwise "eccentric" sponsorships (encouraging a similar migrant-madman approach to academic cultivation) of some of the folks on…
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Non-Erdős problems are also falling.The AIs seem to have some combination of very broad familiarity with math (enabling relevant things from other subfields to be brought in to the proof) as well as patience and "sitzfleisch" (stamina in working through details even if they aren't immediately obviously promising.)An obvious area for improvement…
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When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”.Are we missing the forest for the trees here? If a math problem falls in the forest but nobody is around to understand it does it make a sound?How can we possibly…
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Disappointing lack of "Why" in an article that starts with it.Are they actually doing something new and novel, or are they just absorbing that "a=b as was proven in transcendental hyper-circular group theory; and b=c was proven in universal quantum superposition"; and they're the first to find the connection that a=c? And several of the problems…
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something i've just realized : today long-standing maths problems are falling. It's great intellectually but won't probably have an immediate impact on our lives.Now, what will happen once long-standing physics ( and chemistry and biology) problems will start to fall and at the same rate ?Then we're going to enter a totally different world.
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I think it's the scientist version of "I vibecoded ten apps this weekend (at one point I'll have real users too)".Because it's math, it's all mysterious and genuinely impressive, but in the end, if no human cares about it (apart from attention grabbing "it's so over" tweets and articles), does it really matter?
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This seems like an extreme exaggeration from a few people claiming to not understand a very recent result. This cycle of a new result being discovered, and reaearchers needing some time to truly digest and disassemble it, is normal.
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Because pattern recognition and deduction is automatable and LLMs are superhuman at low depth high depth problems. Next