traes

4 ms·

31.
by traes 1mo ago
There's a substantial gap between "the machine is better than human mathematicians" and "the machine can formalize a solution to any problem immediately." Much of the important mathematical theory behind modern scie
32.
by traes 1mo ago
It's speculative fiction written by a professional mathematician about his idea of the worst case scenario of AI's effect on math.
33.
by traes 1mo ago
Out of curiosity, what is the largest C program you have written pre-LLM, and did you ever try to run it through valgrind*? The "oversights" in C tend to be extremely subtle and dangerous, and of a type that would be impossible to
34.
by traes 1mo ago
Do you really think current LLMs can implement a large application in C as securely as they can in e.g. Go? I will freely admit that I have not tried to do so but I have a hard time imagining it. Perhaps my biases are outdated...
35.
by traes 2mo ago
Changing {} to [] seems like a very strange suggestion to me. {} is used here because it's the way you group things in LaTeX. If you were going to change it for human use, why not just use parenthesis? What's wrong with {} in the
36.
by traes 2mo ago
There is money in this, so of course the closed models are far ahead. The open models will likely catch up a bit at some point, just as Stockfish caught up to AlphaZero. That being said, there are already a couple. It seems Deepseek has a
37.
by traes 2mo ago
There is no evidence that I can find for the claim "a bug in the Lean kernel was discovered last week by way of an LLM tricking itself and its handler into believing it had found a non-constructive proof of the existence of a nontrivia
38.
by traes 2mo ago
If accomplishments can't be distinguished between talented people and untalented people with compute, is there really a point in trying? I suppose one can hope that talented people given compute will be more effective than untalented p
39.
by traes 2mo ago
Presumably it's a rounding error compared to their full output, and they're making sure they have enough compute set aside for research by limiting public models. The more datacenters they build the less they have to limit them.
40.
by traes 2mo ago
"I made this proof myself, but the designer is someone else" is an extremely unconvincing claim to ownership.
41.
by traes 2mo ago
If there was any real money in it Stockfish would not be the best chess engine.
42.
by traes 2mo ago
That's clearly just for the tokens, this doesn't really answer OP's question.
43.
by traes 2mo ago
Given that OpenAI pays their employees with stock surely a breathtaking number, but not a very meaningful number now that the infrastructure is in place and the models are trained. AI could never get better and it would still be incredibly
44.
by traes 2mo ago
A fundamental difference being that no one was actually paid to find good moves in chess and go like they are to solve math problems and write code. You're comparing the digital camera and the automobile.
45.
by traes 2mo ago
It's a very important clarification if it took $2000/problem on 20 problem attempts or on 1,000 problem attempts for each successful one. That may be the deciding factor on whether or not it's economically viable to replace a
46.
by traes 2mo ago
Not much point to pure math being kept secret, in all honesty. There isn't really industrial value, its only purpose (to them) is showing off their model's capabilities. More realistically they'll just stop paying for it. Edi
47.
by traes 2mo ago
That seems to have been more of a sensationalized joke. Even your link has a disclaimer in it now. Read this chat from the researcher who did this: https://leanprover.zulipchat.com/#narrow/channel/270676-lean...
48.
by traes 2mo ago
> Also, have there been examples of researchers not affiliated with OpenAI (or another LLM creator), who have done something similar? A couple small ones that I've seen (example here [0]), but not anything of the magnitude that Open
49.
by traes 2mo ago
This isn't really a productive way to think about these things, IMO. It's quite possible it would take hundreds of years for any specific group of PhDs to solve them. Or one individual PhD could have the correct flash of insight a
50.
by traes 2mo ago
Every time someone makes a comparison to chess I die inside. Chess is a spectator sport primarily funded by a few eccentric billionaires. Players artificially constrain themselves in timed environments knowing that they will never be able t
51.
by traes 2mo ago
I'm not an expert at it myself, but my understanding is there are numerous ways to "cheat" in a Lean proof (via `sorry` and similar). They're taking responsibility for fully verifying that none of these cheats were used
52.
by traes 2mo ago
Perhaps not, but I interpreted it as an intended counterexample to the GP's claim > You'd have a hard time convincing most American families to purchase anything with a >$1000 price tag... Which I am skeptical of.
53.
by traes 2mo ago
Is it really wrong to blame this one on philosophy? The source of the disagreement was inherently philosophical, lead by a philosopher, backed up by other mainstream philosophers, and undeniably held back physics. I don't mean to imply
54.
by traes 2mo ago
I have personally never met someone with a personal robotic lawnmower, and I suspect that if you have you live in a bubble that is severely biasing your view of the average American.
55.
by traes 2mo ago
It was indeed sexism, but it was not sexism from the math department, who very much wanted to hire her. In fact, the Chair of Mathematics David Hilbert (of Hilbert space fame) personally recruited her.
56.
by traes 2mo ago
A very interesting story that's worth reading up on. "Natural philosophers" of the day refused to accept the idea of a particle too small to directly observe on purely philosophical grounds. They essentially bullied him out o
57.
by traes 2mo ago
The author recently published a retranslation of the Odyssey, that has rocketed to the top of best seller lists thanks to the movie. I'm sure her bank account provides her plenty of direct evidence that this is happening.
58.
by traes 2mo ago
Writing a screenplay adaptation of a poem and writing a translation in contemporary language are entirely different endeavors.
59.
by traes 2mo ago
I would guess almost none, less than single digit percent. Only a small fraction of undergraduate math majors who happen to be interested in algebraic geometry would be able to understand this. The average HN user knows far less math than a
60.
by traes 2mo ago
1) How do you know this structure is the correct one a priori 2) You are starting at 10^500 possibilities. "Much" smaller is not enough, the order of magnitude of the order of magnitude needs to be changed. 3) You still need all

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