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 could we ever make anything useful with them?
Are we ready to just let go of our intellectual faculties and give them to a giant supercomputer nobody understands? How do we tell truth from fiction?
> 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”.
Math is an incredibly broad field. I mean, you don't expect a traffic engineer to understand anything about nuclear reactors, do you? Yet, they are all 'career engineers'.
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.
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?
Nah, people are vibe coding lots of apps that no one cares about, but this is more like going through Stack Overflow and answering the most upvoted issues that don't have answers. These are published problems that have prior interest, for decades usually, and a few snarky internet comments don't undo that.
One of the most famous mathematicians of all time studied number theory. He wrote an apology to humanity for all of the very smart and capable people wasting time studying number theory, since these things are clearly unless old puzzles with no practical use whatsoever. Now, 100 years later, these results underpin all of modern public key cryptography.
So a good fraction of famous old math puzzles with no practical use are famous because they are in some way similar to problems people actually care about. If you can solve the toy problem that is in some way simpler, maybe you can use the same methods to solve the "real" problem.
One open question is whether these machine solutions to these problems will act as springboards to future research, either when given to human mathematicians, or when used to train future machine models.
It's just really hard to affirm that something has "no practical use whatsoever". Maybe it doesn't have use "now", maybe it doesn't have "direct" use but can be used for another finding that is useful, Math has a long story of finding out stuff that turns useful later on.
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.
> 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”.
Huh?
Mathematics is an extremely wide subject, it's perfectly normal even for two professional mathematicians not to understand each other's work. Have you considered that maybe they just don't work in that area?
Are you implying OpenAI's paper (which was, by the way, edited by humans and provided Lean certificates for most of the proofs) is actually gibberish? That's flat-earth levels of conspiracy.
I have the same questions about human mathematicians!
I can't tell if xkcd #435 is still true, or if math is just as mushy as everything else seems to be. When a math proof can only be understood by a handful of people, what does that mean about that proof? I think the LLMs are pushing a problem that existed already and pushing it further.
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 (or disprove) them, with the discovered arguments then being used as training for refined models. This will require autoformalization to check the results as there will be too many for manual verification.
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 HN wouldn't lead to meaningful discoveries in CS.
I often see comments that some of the users here long to "make a computer do neat tricks all day", and I can't help but think meager sponsorship could go a long way in this area. Existing grant structures, being much more traditional, are constrained by their cost.
> I wonder if national, institutional, or otherwise "eccentric" sponsorships (encouraging a similar migrant-madman approach to academic cultivation) of some of the folks on HN wouldn't lead to meaningful discoveries in CS.
The problem is that Paul Erdos was eccentric but he was also Paul Erdos. I'm not saying you're implying that, but I feel it's a similar line of thinking to how popular culture often romanticizes autism and Asperger's because some very smart people are (allegedly) affected. The same group includes people who need 24/7 care.
Computer science at the frontier is as specialized and hard as mathematics, you need years of study to truly understand a field well enough to make meaningful contributions. You can try sponsoring me if you really want, but I don't think you'd be spending your money wisely in expectation.
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.
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.
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 either way, but it'd be nice to actually understand more of what is happening.
One of the recent problems was actually proven with elementary results. It did use a technique not usually applied to the problem space, but it wasn’t a hyper specialized result.
There is no such thing as the Renaissance Fund. Quanta receives funds from the Simons Foundation... I also don't know where you get it from that Renaissance Technologies is heavily invested in AI. Any sources to back up your claims because I suspect you made all that up?
We have now passed the point where the AI bots were annoying. Now it is the reactionary “everything even possibly slightly remotely tangentially connected to AI must be deplatformed” rants everywhere that are even worse.
It would be tempting to assume the commenter here has no idea what Renaissance is or how they made so much money.
> The company is widely considered one of the most profitable hedge funds in history, generating an estimated $7 billion to $8 billion in annual revenue solely from management and performance fees
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 could we ever make anything useful with them?
Are we ready to just let go of our intellectual faculties and give them to a giant supercomputer nobody understands? How do we tell truth from fiction?
Math is an incredibly broad field. I mean, you don't expect a traffic engineer to understand anything about nuclear reactors, do you? Yet, they are all 'career engineers'.
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?
One open question is whether these machine solutions to these problems will act as springboards to future research, either when given to human mathematicians, or when used to train future machine models.
P.S. Couldn't resist :p
Huh?
Mathematics is an extremely wide subject, it's perfectly normal even for two professional mathematicians not to understand each other's work. Have you considered that maybe they just don't work in that area?
Are you implying OpenAI's paper (which was, by the way, edited by humans and provided Lean certificates for most of the proofs) is actually gibberish? That's flat-earth levels of conspiracy.
I can't tell if xkcd #435 is still true, or if math is just as mushy as everything else seems to be. When a math proof can only be understood by a handful of people, what does that mean about that proof? I think the LLMs are pushing a problem that existed already and pushing it further.
[0] https://xkcd.com/435/
The process is very, very faintly similar to running a typechecker over your software sources.
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 (or disprove) them, with the discovered arguments then being used as training for refined models. This will require autoformalization to check the results as there will be too many for manual verification.
I wonder if national, institutional, or otherwise "eccentric" sponsorships (encouraging a similar migrant-madman approach to academic cultivation) of some of the folks on HN wouldn't lead to meaningful discoveries in CS.
I often see comments that some of the users here long to "make a computer do neat tricks all day", and I can't help but think meager sponsorship could go a long way in this area. Existing grant structures, being much more traditional, are constrained by their cost.
The problem is that Paul Erdos was eccentric but he was also Paul Erdos. I'm not saying you're implying that, but I feel it's a similar line of thinking to how popular culture often romanticizes autism and Asperger's because some very smart people are (allegedly) affected. The same group includes people who need 24/7 care.
Computer science at the frontier is as specialized and hard as mathematics, you need years of study to truly understand a field well enough to make meaningful contributions. You can try sponsoring me if you really want, but I don't think you'd be spending your money wisely in expectation.
I'm afraid you only know that after the fact.
You might also like TempleOS, or at least the context and history behind it.
He died aged 83...
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.
The whole article is an ad that covertly or overtly inserts how websites are built with ChatGPT, how humans say that AI is better than them etc.
This is incidentally the future of chatbots. I could not have written this comment without Illy Espresso. Would you like to find a cafe near you?
Except it's not? It's owned by a private foundation where the only link is both were founded by the same dude who hasn't run either in like 15 years.
That seems like a pretty big thing to just gloss over like it's just set-dressing.
https://www.simonsfoundation.org/about/our-history/
It would be tempting to assume the commenter here has no idea what Renaissance is or how they made so much money.
> The company is widely considered one of the most profitable hedge funds in history, generating an estimated $7 billion to $8 billion in annual revenue solely from management and performance fees
If you don't know Ren you should!