31–40 of 144 posts
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.
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 are counterexamples, not novel proofs of correctness?
Its fascinating either way, but it'd be nice to actually understand more of what is happening.
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 make use of these breakthroughs if we don’t understand them? How coul…
I don't mean to be dismissive, are these just old puzzles with no practical use whatsoever?
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 make use of these breakthroughs if we don’t understand them? How coul…
Mathematics is an unusually dense (if not the most dense...by a few large steps) field. So lots of areas of mathematics are extremely deep and narrow without any real shortcuts, even for seasoned mathematicians.
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 are counterexamples, not novel proofs of correctness? Its fascinating e…
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 would be automated generation of new conjectures and attempts to prove…
Earlier quoted context omitted.
FWIW I've worked in two different academic labs, both of which would have benefited from a runaway worker barreling down random paths, as long as they were being productive in some capacity.
> [...] as long as they were being productive in some capacity. I'm afraid you only know that after the fact. You might also like TempleOS, or at least the context and history behind it.
Earlier quoted context omitted.
Mathematics is an unusually dense (if not the most dense...by a few large steps) field. So lots of areas of mathematics are extremely deep and narrow without any real shortcuts, even for seasoned mathematicians.
Awesome observation. What would you consider denser?
P.S. Couldn't resist :p
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 make use of these breakthroughs if we don’t understand them? How coul…
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?