It's because the cache comes from the prefix. `f(f(f(A,B),C),D)` is quite different from `f(f(A,B),D)`.

Yes, that's my understanding- though I realize that OpenAI has made changes to what you can do with caching over the API recently, so you may be able to do some fancy stuff to get around this.

I disagree. There are things which are very annoying outside of core ideas or otherwise take a lot of time. Too much time and energy to justify normally. Personal example: https://github.com/wiwa/gpu-typing

Typechecking with my own algorithm. Simple enough to specify in Python. Annoying with much boilerplate in CUDA. Similarly annoying to test.

It's too good.

Are you sure whatever the LLM said was actually credible though?

Why would I assume it would be credible? Instead, I simply proposed some designs and had it find out if such hardware existed / was feasible.

Absolutely not… but maybe the LLM was trying to tell them it’s a crazy idea and they are only reporting that a conversation occurred.

Lol, this feels like it would otherwise be a good thing, out of context.

The idea that FFT's decomposition is non-optimal is surprising. What the new bound means is we basically were looking at the problem and its structure incorrectly, and therefore implicates other problems for which we have used recursion to get to our currently-best bounds. Almost no interesting math problems are just sitting there alone in their little corner. Getting a hint like that is a big deal.

Is it surprising though? If you assume constant time when it doesn't exist (in this case arbitrary precision arithmetic), it should be obvious that you will be able to devise algorithms that are faster than the commonly accepted best results.

If you can do arithmetic on arbitrarily large integers in constant time, you can sort lists in linear time.

It depends on what you're doing to the integers. You still cannot comparison-sort arbitrarily large integers in linear time.

Also, consider this: it would have been trivial to get a so-called "better bound" on FFT if such a "cheat" were what people allowed.

I find it highly ironic that many people here seem to believe mathematicians should just accept LLM proofs, but software projects shouldn't accept LLM code.

I really don’t think those are the same people. Goomba fallacy, etc.

Why would anybody need more than `268 435 456 ^ 62` KB of RAM?

Also, the strong force is extremely repulsive at shorter distances.

The good news is that wikipedia has very good (and simple) figures for the shape of the force: https://en.wikipedia.org/wiki/Nuclear_force

*For now. If a company were to degrade something, it shouldn't be so obvious that the "goodwill" was just a reallocation. Just a good strategy. For example, it allows them to claim that they're "just going from 150% to 125% usage allowance, which is still more than 100%".