661–670 of 1001 posts
I like how everyone laughed when OpenAI said their models will have "PhD-Level Intelligence" and now the goalpost has been moved to if AI can create new math (i.e., not PhD-Level, but Leibniz/Euler/Galois level.)
PhDs used to mean publishing a novel mathematical result: when has that changed?
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Well yes, but there is a choice being made here and I would love to believe we can do better. The rational response to being afraid about your livelihood isn’t to spend time filling every HN thread on LLMs with embittered negativity. Not to mention all the flat denials that LLMs can do mathematics and write decent code, which is almost a self-contradictory position if you are worried they are going to replace you. Th…
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Speaking as a postdoc in math, I must say that this is rather exciting. This is outside of my field, but the companion remarks document is quite digestible. It appears as though the proof here fairly inspired by results in literature, but the tweaks are non-trivial. Or, at least to me, they appear to be substantial to where I would consider the entire publication novel and exciting. Many of my colleagues and I have b…
Why would it excite you, rather than terrifying you? The better LLMs get at math, the closer the expertise you spent your whole life building is to being worthless. Along with all the rest of what humans find meaningful and fulfilling.
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> Every day, it grows harder and harder to contain a mental map of recent relevant progress by simple virtue of the amount being produced. I cannot help but be very optimistic about the ambition mathematicians of this era will be able to scale to. There still remain lots of problems in current era tools and their usage though. Always, always always, the problem with research and development is leadership, not insuffi…
I think we’re looking at a new class of wonderful machines that can potentially make meaningful contributions to the sciences and maybe even humanity as a whole, in addition to far more insidious and destructive capabilities. You are right to point out that the ones who fully own and pilot the machines all belong to the “fuck science and humanity as a whole” group. So the likely outcomes don’t look good. Echoes the e…
That's true. But. Maybe you've seen the Oppenheimer movie, there is a moment where Oppenheimer shakes Teller's hand, basically after the guy ruins Oppenheimer's life in a completely immature betrayal. That's what people are angry about, the academy community is Oppenheimer's wife asking, why the fuck did you shake his hand?
At least regarding leadership and funding, I don't know if it's a matter of likely or unlikely outcomes. It's just facts: these guys are collaborators. The commenter might very well have zero graduate students starting next year. What pisses me off is the utter obliviousness that STEM people have about how deeply political their work is.
And perhaps this is the real reckoning for the mathematics community. Not the possibility that AI is going to replace their jobs, it's not going to do that. But that having these intensely myopic and disagreeable personalities mean that basically zero leadership skills have been nurtured in the mathematics community. You cannot name a single politician who is a mathematician. You have to be elected to have power in this country, it's that simple, there are way more billionaires than there are presidents! Leadership is far more scarce. So that's why these disputes matter, and while it's great that people engage on Hacker News about it, it's intensely disappointing that "reduced science funding is really bad" gets downvoted.
That is a result of Hacker News's emphasis on this very 2010s view that it wants to be a place where the math nerds gather (in @dang's words) - he doesn't get that the quality of the discourse was caused by great leadership at many political and academic levels. Nobody credits how much better leaders were during Y Combinator's biggest success stories, or how much we overvalue the intellectual powers of math because it makes money as opposed to enlightening our view of the world.
I like how everyone laughed when OpenAI said their models will have "PhD-Level Intelligence" and now the goalpost has been moved to if AI can create new math (i.e., not PhD-Level, but Leibniz/Euler/Galois level.)
My only complaint is the claims always start spreading 6-12 months before the delivery. A little patience goes a long way in what's possible with AI and we all just have to wait and see what parts actually grow this next cycle or not. Guessing at it based on trend lines only leads to people getting excited when it matches their particular guess and ignoring it when it doesn't.
> My only complaint is the claims always start spreading 6-12 months before the delivery.
If delivering on such promises "always" occurs 6-12 months after the promise, is that pretty good?
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We haven't seen a significant increase in the quality of LMM output since 2023 that hasn't been the result of throwing even more energy and compute at it. AI "reasoning" is just recursive iteration on their output, with diminishing improvement on each pass. It seems to be the reason why Mythos is not generally available, maybe a canary of sorts. If LLMs were improving significantly independent of scaling up compute r…
> We haven't seen a significant increase in the quality of LMM output since 2023 that hasn't been the result of throwing even more energy and compute at it. This is completely false. Most of the dramatic improvements in LLM quality in the last two years were due to the application of new post-training methods, especially RLVR. It’s really interesting to read about (you should!) and it is the whole secret to why LLMs…
I think one interesting thing to point out is that the proof (disproof) was done by finding a counterexample of Erdős' original conjecture. I agree with one of the mathematician's responses in the linked PDF that this is somewhat less interesting than proving the actual conjecture was true. In my eyes proving the conjecture true requires a bit more theory crafting. You have to explain why the conjecture is correct by…
Searching for a proof and disproof are sometimes not so different. In most cases, you nibble the borders to simplify the problem. For example, to prove something is impossible let's say you first prove that there are only 5 families, and 4 of them are impossible. So now 80% of the problem is solved! :) If you are looking for counterexamples, the search is reduced 80% too. In both cases it may be useful In counterexam…
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I'd hope most functional adults understand that the Fields Medal and basically every other annual "prize" out there is awarded to both "recombinant" innovations and "new-dimensional thinking" innovations. Humans aren't going to come up with "new-dimensional" innovations in every field, every single year. I'd say yes, LLMs "just" recombine things. I still don't think if you trained an LLM with every pre-Newton/Liebniz…
I think an LLM trained on pre-calculus material would easily stumble into reinventing at least early calculus. It's already pretty easy for students to stumble into calculus from solid enough fundamentals. We even think that the Babylonian astronomers figured out they could integrate over velocity to predict the position of Jupiter.
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There's an unstated assumption there, which is that you'll have some reason to continue to want your work to be required. In the (probably unlikely) event that AI use results in a post-scarcity economy in which there's no need to work to survive, a lot of people wouldn't regret sentiments like the ones in question. On the contrary, it would mean they could work on whatever they please, including potentially standing…
And how do you see us getting from what we currently have: a working class and capital/ownership class, where a vast majority of society is required to work 40+ hrs/week to sustain their ability to live. To a society that provides a livelihood to all humans, equally? For, I would love to hear how we get from here to there during an era with the largest wealth disparity ever seen in human history. (Yes, it's worse tha…
History is full of examples of situations like this being corrected, at least to an extent. If we learn from those, we can do even better next time around.
Btw, the inequality you mention is far worse in the US than Europe. Here's one source that covers this: https://wid.world/es/news-article/why-is-europe-more-equal-t...
This demonstrates a point that should be obvious, that better societal choices can produce better outcomes.
The proof brings unexpected, sophisticated ideas from algebraic number theory to bear on an elementary geometric question. The more I read about these achievements the more I get a feeling that a lot of the power of these models comes from having prior knowledge on every possible field and having zero problems transferring to new domains. To me the potential beauty of this is that these tools might help us break thro…
What you describe here has always been true in all sciences, but also in medicine. But both modern engineering and education runs completely counter to this. You are encouraged to stay in your niche and never look out. People with vast interested are filtered out by hiring managers. So the crossdomain pollination that used to exist in scientists is not only not encouraged. It's also actively punished by society.