7 ms·
The LLM took an entirely different route, using a formula that was well known in related parts of math, but which no one had thought to apply to this type of qu
by userbinator 6mo ago
The LLM took an entirely different route, using a formula that was well known in related parts of math, but which no one had thought to apply to this type of question.
Of course LLMs are still absolutely useless at actual maths computation, but I think this is one area where AI can excel --- the ability to combine many sources of knowledge and synthesise, may sometimes yield very useful results.
Also reminds me of the old saying, "a broken clock is right twice a day."
- karlgkk 6mo agoAlso just the sheer value of brute force. 80 hours! 80 hours of just trying shit!
- FrasiertheLion 6mo agoIt's 80 minutes, not 80 hours.
- ChrisGreenHeur 6mo ago80 minutes! 80 minutes of just trying shit!
- peteforde 6mo ago... shit that solved an apparently significant Erdős problem. That is not nothing, no matter how much you hate AI.
- userbinator 6mo agoIt shows that AI is apparently very good at brute-forcing.
- alex_sf 6mo agoThis isn't brute force.
- userbinator 6mo agoIt is in the same way that educated guessing is.
- userbinator 6mo agoCare to actually refute? Interesting that even an LLM would give an attempt at it, but apparently those who only bother to hit the downvote button aren't even meeting that level of "intelligence".
- alex_sf 6mo ago> It is in the same way that educated guessing is. I guess (heh) it depends on your definition of 'educated guessing'? Looking at the problem, considering a solution, discarding it, trying another and testing, iteratively, is how most people would approach any tricky problem. Brute force is substantially different. It would be saying that, other than maybe setting some basic bounds and heuristics, I'm going to try literally everything and test each. That's not at all what the LLM did here.
- TOMDM 6mo agoAre the human mathematicians who wanted to solve this problem just too stupid to brute force for 80 minutes?
- jasonfarnon 6mo agoand you can be sure mathematicians spent way more than 80 hrs on it
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- brokencode 6mo agoHow long do you figure it’d take to solve the problem yourself?
- jaggederest 6mo ago> Every Mathematician Has Only a Few Tricks > > A long time ago an older and well-known number theorist made some disparaging remarks about Paul Erdös’s work. > You admire Erdös’s contributions to mathematics as much as I do, > and I felt annoyed when the older mathematician flatly and definitively stated > that all of Erdös’s work could be “reduced” to a few tricks which Erdös repeatedly relied on in his proofs. > What the number theorist did not realize is that other mathematicians, even the very best, > also rely on a few tricks which they use over and over. > Take Hilbert. The second volume of Hilbert’s collected papers contains Hilbert’s papers in invariant theory. > I have made a point of reading some of these papers with care. > It is sad to note that some of Hilbert’s beautiful results have been completely forgotten. > But on reading the proofs of Hilbert’s striking and deep theorems in invariant theory, > it was surprising to verify that Hilbert’s proofs relied on the same few tricks. > Even Hilbert had only a few tricks! > > - Gian-Carlo Rota - "Ten Lessons I Wish I Had Been Taught" https://www.ams.org/notices/199701/comm-rota.pdf https://www.ams.org/notices/199701/comm-rota.pdf
- yayachiken 6mo agoI think when thinking about progress as a society, people need to internalize better that we all without exception are on this world for the first time. We may have collectively filled libraries full of books, and created yottabytes of digital data, but in the end to create something novel somebody has to read and understand all of this stuff. Obviously this is not possible. Read one book per day from birth to death and you still only get to consume like 80*365=29200 books in the best case, from the millions upon millions of books that have been written. So these "few tricks" are the accumulation of a lifetime of mathematical training, the culmination of the slice of knowledge that the respective mathematician immersed themselves into. To discover new math and become famous you need both the talent and skill to apply your knowledge in novel ways, but also be lucky that you picked a field of math that has novel things with interesting applications to discover plus you picked up the right tools and right mental model that allows you to discover these things. This does not go for math only, but also for pretty much all other non-trivial fields. There is a reason why history repeats. And it's actually a compelling argument why AI is still a big deal even though it's at its core a parrot. It's a parrot yes, but compared to a human, it actually was able to ingest the entirety of human knowledge.
- tptacek 6mo agoWait, what do you mean "LLMs are still absolutely useless at actual maths computation"? I rely on them constantly for maths (linear algebra, multivariable calc, stat) --- literally thousands of problems run through GPT5 over the last 12 months, and to my recollection zero failures. But maybe you're thinking of something more specific?
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- schneems 6mo agoThey are bad at math. But they are good at writing code and as an optimization some providers have it secretly write code to answer the problem, run it and give you the answer without telling you what it did in the middle part.
- avaer 6mo agoSomeone should tell the mathematicians if they use a calculator or a whiteboard or heavens forbid a computer they are "bad at math".
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- schneems 6mo ago1) That's not related to chain of thought I was replying to. Someone asked about the "bad at math" and pointed out "but it seems good to me" so I added the color of why that might be the case. Your retort seems to imply I'm making an argument that because something uses tools for a job it cannot be good at the thing it's using a tool for. Which is not the case. 2) If you have something to say, just say it. Don't put words in my mouth and then argue with a thing I didn't say.
- tptacek 6mo agoRight, but your narrative was incorrect and based on faulty premises, which you haven't acknowledged. That's fine, except you're still pressing the argument. Can you please present a reasonable maths problem that I can bounce off GPT so we can see it fail? I can give you many hundreds of relatively complex problems, none of which have appeared in a textbook, that GPT has not only solved, but critiqued my own crappy solutions for. I'm only asking you for one counterpoint.
- y0eswddl 6mo agoYeah, they're great at interpolation - they'll just never be worth much at extrapolation.
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- SR2Z 6mo agoLuckily for us, whole fortunes can be made by filling in the blanks between what we know and what we realize.
- javawizard 6mo agoThat deserves to be on a plaque somewhere. I've been using LLMs for much the same purpose: solving problems within my field of expertise where the limiting factor is not intelligence per se, but the ability to connect the right dots from among a vast corpus of knowledge that I would never realistically be able to imbibe and remember over the course of a lifetime. Once the dots are connected, I can verify the solutions and/or extend them in creative ways with comparatively little effort. It really is incredible what otherwise intractable problems have become solvable as a result.
- dalyons 6mo agoWhat’s your field
- speed_spread 6mo agoPaint by numbers
- jedmeyers 6mo agoAnd by having more of those blanks filled humans might be able to come up with much better extrapolations than what we have right now.
- drdeca 6mo ago
- keyle 6mo agoThe ultimate generalist
- nopinsight 6mo ago> "a broken clock is right twice a day." The combinatorial nature of trying things randomly means that it would take millennia or longer for light-speed monkeys typing at a keyboard, or GPUs, to solve such a problem without direction. By now, people should stop dismissing RL-trained reasoning LLMs as stupid, aimless text predictors or combiners. They wouldn’t say the same thing about high-achieving, but non-creative, college students who can only solve hard conventional problems. Yes, current LLMs likely still lack some major aspects of intelligence. They probably wouldn’t be able to come up with general relativity on their own with only training data up to 1905. Neither did the vast majority of physicists back then.
- amazingman 6mo ago> Yes, current LLMs likely still lack some major aspects of intelligence. Indeed, and so do current humans! And just like LLMs, humans are bad at keeping this fact in view. On a more serious note, we're going to have a hard time until we can psychologically decouple the concepts of intelligence and consciousness. Like, an existentially hard time.
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- nandomrumber 6mo agoA stopped clock. A broken clock can be broken in ways which result in it never being correct.
- fragmede 6mo agoThose are just analog. If it's a broken digital clock, then all bets are off.
- heresie-dabord 6mo ago> "a broken clock is right twice a day" and homo sapiens, glancing at the clock when it happens to be right, may conjure an entire zodiac to explain it.
- red75prime 6mo agoAnd homo sapiens, glancing at a system that gets better and better at solving problems, tries to deny it and comes up with the broken-clock analogy.