Are you thinking of the int multiplication result instead? The DFT result uses a computation model with unlimited precision reals.
Quant finance is very different from math research; quant is much more applied math and programming, and the tasks are typically smaller than math research questions. Although it's true there's a huge overlap in the…
As for #2, personally I feel like OpenAI's results are superhuman at this point. I don't think there's enough human talent alive right now to produce these sorts of results within a few years, no matter the budget.…
This is integer multiplication, not matrix multiplication. The OpenAI dump also has a matrix multiplication improvement though. In either case, no practical algorithm is expected to come from it, because the asymptotic…
I think it makes sense to feel sympthy towards people facing disruption in their plans, even if you believe society is better off overall. It's like getting scooped. If you just founded a startup based on tech XYZ,…
This is a legitimate question, and it'll be interesting to see how these constants evolve in the future. In some cases, maybe it's true the AI did the minimum to break the barrier, and the best constants are much lower.…
Many of these latest results are very important to theoretical math. Some are also theoretical physics and CS. Real-world applications are far off, but developing mathematical understanding does tend to leak over into…
It doesn't have to want to kill humans; indifference is sufficient. There's an exact analogy with humans: we have caused extinction and endangerment for many species, not out of malice, but indifference. There are also…
AI vs AI chess, played from the standard opening position, is pointless--it's always a draw. Human vs human chess is doing well but AI is banned from it. The chess-math analogy would imply AI could bring us into a…
Tbh this sounds perfectly normal to me. Companies often don't think it's worth defending themselves if theres no actual financial damage, and certainly don't want random employees to be doing it. It can be very…
IANAL, but yes, I'd assume the license is unenforceable on the AI content.
No, an AI's output can still violate copyright.
LLMs are indeed very special compared to past efforts at automated theorem proving. The search tree for proofs is enormous, even short textbook exercises (i.e. a few dozen lines of Lean) were difficult with GOFAI…
There was recently an announcement that a group trying to formalize it found a gap exactly where other mathematicians were pointing. So to the extent there was any doubt, it should be gone now--the proof was incorrect.…
I believe that "single source of truth" is a principle that should always be followed. If there's duplicated code where it'd be a bug if they diverge, then you should refactor. It creates a long-distance coupling in…
One of the authors said in a reddit comment (and I hope I am summarizing accurately) that it's impossible to show a diagram as the smallest instance of the technique gives like 10^1000000 points.
The problem was pretty well known, and had many human attempts. There's some room to argue that the right humans hadn't attempted it, as the solution used advanced methods from another field of math. But imho, whereas…
This is happening to other forms of competitive programming too. The most recent AIs have problem solving skills rivaling top humans, and so if AI can't be easily banned, the competition is dominated by AI agents. I…
You can't do this for general functions, but it's fine to do in cases where the definition of f naturally embeds into the rationals. For example, a polynomial over Z is also a polynomial over Q or C.
The movement from R to C can be done rigorously. It gets hand-waved away in more application-oriented math courses, but it's done properly in higher level theoretically-focused courses. Lifting from a smaller field (or…
You can go farther and say that you can't even construct real numbers without strong enough axioms. Theories of first order arithmetic, like Peano arithmetic, can talk about computable reals but not reals in general.
Are you thinking of the int multiplication result instead? The DFT result uses a computation model with unlimited precision reals.
Quant finance is very different from math research; quant is much more applied math and programming, and the tasks are typically smaller than math research questions. Although it's true there's a huge overlap in the…
As for #2, personally I feel like OpenAI's results are superhuman at this point. I don't think there's enough human talent alive right now to produce these sorts of results within a few years, no matter the budget.…
This is integer multiplication, not matrix multiplication. The OpenAI dump also has a matrix multiplication improvement though. In either case, no practical algorithm is expected to come from it, because the asymptotic…
I think it makes sense to feel sympthy towards people facing disruption in their plans, even if you believe society is better off overall. It's like getting scooped. If you just founded a startup based on tech XYZ,…
This is a legitimate question, and it'll be interesting to see how these constants evolve in the future. In some cases, maybe it's true the AI did the minimum to break the barrier, and the best constants are much lower.…
Many of these latest results are very important to theoretical math. Some are also theoretical physics and CS. Real-world applications are far off, but developing mathematical understanding does tend to leak over into…
It doesn't have to want to kill humans; indifference is sufficient. There's an exact analogy with humans: we have caused extinction and endangerment for many species, not out of malice, but indifference. There are also…
AI vs AI chess, played from the standard opening position, is pointless--it's always a draw. Human vs human chess is doing well but AI is banned from it. The chess-math analogy would imply AI could bring us into a…
Tbh this sounds perfectly normal to me. Companies often don't think it's worth defending themselves if theres no actual financial damage, and certainly don't want random employees to be doing it. It can be very…
IANAL, but yes, I'd assume the license is unenforceable on the AI content.
No, an AI's output can still violate copyright.
LLMs are indeed very special compared to past efforts at automated theorem proving. The search tree for proofs is enormous, even short textbook exercises (i.e. a few dozen lines of Lean) were difficult with GOFAI…
There was recently an announcement that a group trying to formalize it found a gap exactly where other mathematicians were pointing. So to the extent there was any doubt, it should be gone now--the proof was incorrect.…
I believe that "single source of truth" is a principle that should always be followed. If there's duplicated code where it'd be a bug if they diverge, then you should refactor. It creates a long-distance coupling in…
One of the authors said in a reddit comment (and I hope I am summarizing accurately) that it's impossible to show a diagram as the smallest instance of the technique gives like 10^1000000 points.
The problem was pretty well known, and had many human attempts. There's some room to argue that the right humans hadn't attempted it, as the solution used advanced methods from another field of math. But imho, whereas…
This is happening to other forms of competitive programming too. The most recent AIs have problem solving skills rivaling top humans, and so if AI can't be easily banned, the competition is dominated by AI agents. I…
You can't do this for general functions, but it's fine to do in cases where the definition of f naturally embeds into the rationals. For example, a polynomial over Z is also a polynomial over Q or C.
The movement from R to C can be done rigorously. It gets hand-waved away in more application-oriented math courses, but it's done properly in higher level theoretically-focused courses. Lifting from a smaller field (or…
You can go farther and say that you can't even construct real numbers without strong enough axioms. Theories of first order arithmetic, like Peano arithmetic, can talk about computable reals but not reals in general.