Hacker News: ComplexSystems

New comment by ComplexSystems in "Three new discoveries in mathematics, computer science, and physics"

ComplexSystems — Tue, 27 Oct 2026 00:55:29 +0000

I think that it'd be funny if the polynomial time SAT solver was just "send your SAT instance to Astra and have it try to solve it for a few hours."

New comment by ComplexSystems in "Three new discoveries in mathematics, computer science, and physics"

ComplexSystems — Tue, 27 Oct 2026 00:47:58 +0000

I know, it's awful. How do we get OpenAI to stop before they ruin math forever? /s

New comment by ComplexSystems in "Sam Altman: 'I No Longer Think We're Gonna Be Able to Just Patch All the Bugs'"

ComplexSystems — Sat, 24 Oct 2026 17:56:14 +0000

The idea that a US company is allowed to publicly talk about and release these bugs is a very new thing.

New comment by ComplexSystems in "Sam Altman: 'I No Longer Think We're Gonna Be Able to Just Patch All the Bugs'"

ComplexSystems — Sat, 24 Oct 2026 17:41:31 +0000

I agree he wants that, but also don't think it's that far fetched that there exist unpatchable hardware bugs that AI can learn to exploit.

New comment by ComplexSystems in "The recently proposed o(n log n) integer multiplication algorithm [pdf]"

ComplexSystems — Thu, 22 Oct 2026 03:12:46 +0000

Roughly speaking, O(n log n) means "grows no faster than k(n log n) for some k", whereas o(n log n) means grows strictly more slowly* than k(n log n) for all* choices of k.

New comment by ComplexSystems in "The Other Epidemic: Trying to get off benzodiazepines"

ComplexSystems — Wed, 21 Oct 2026 00:30:19 +0000

"The psych had told me nothing of the nightmare that dependence on those meds can create"

I hear this all the time and never get it. Didn't these people go to school? People talk about this every day on the internet. It's right there on Wikipedia, even.

New comment by ComplexSystems in "Vi Hart's Big Navier-Stokes Post"

ComplexSystems — Tue, 13 Oct 2026 20:44:21 +0000

None of it is ridiculous in principle, but where do you draw the line? Is Google an AI company whose products I shouldn't use? What about Microsoft, where Vi worked for many years? Or is it specifically OpenAI and Anthropic? What about open source companies?

New comment by ComplexSystems in "Vi Hart's Big Navier-Stokes Post"

ComplexSystems — Tue, 13 Oct 2026 06:48:04 +0000

> History judges researchers who work with the bad guys ... To them I say: learn from history and get out now. You’ll still be ahead of the curve. The current backlash against AI may seem huge, but it’s nothing compared to what I think the backlash will be in coming years.

> I chose 7 years because I see certain parallels between the situation with researchers and Big AI today and the relationship between researchers and Epstein in 2019.

Look, I absolutely love Vi Hart's stuff. And I mean love love, and I have for almost 20 years.

But do people really believe this? That associating with AI companies, using their product, etc, is similar to taking money from a child sex trafficker?

I thought the original Mathathon sounded like a great idea. They shut that down, and I think the revised one seems like a half decent idea. But if I get involved in it, in 7 years it'll be the same as if I had been involved with Jeffrey Epstein?

I feel like the discourse on this is starting to get way out of control. I say that with no less love for Vi Hart's ideas than I have always had. But surely this technology can be used for some good?

New comment by ComplexSystems in "Auto Research: Integer multiplication below n log n"

ComplexSystems — Tue, 13 Oct 2026 06:27:19 +0000

This is a very loaded blog post. A unit-cost RAM is a fairly standard model of computation when working with algorithms. When we say that comparison sorting of strings takes O(n log n) time, for instance, we are also implicitly assuming a unit cost for comparing two strings. In real life, comparing two strings scales linearly with string length. Maybe that's silly, but it's par for the course. The original FFT is also assuming unit cost multiplication when we say it is O(n log n) time - we mean O(n log n) multiplies.

Similarly, yes, it's a galactic algorithm, but these things are still viewed as meaningful. The fact that it is even possible at all with a unit cost RAM asymptotically is an incredible result that nobody expected.

New comment by ComplexSystems in "OpenAI, the Partition Principle, and Mathematics"

ComplexSystems — Fri, 09 Oct 2026 02:41:26 +0000

There are plenty of mathematicians who think the results are interesting. Not only do they have the "patience" you speak of, some even seem to be enjoying exploring the new results.

New comment by ComplexSystems in "OpenAI, the Partition Principle, and Mathematics"

ComplexSystems — Fri, 09 Oct 2026 00:46:10 +0000

Here's a guy who's made a "beyond n log n" tracker: https://x.com/aurel_pr/status/2108214135179944096

He's tracking the community progress on sub-n log n multiplication. OpenAI started with 1 - 1.63e-55. The result has been now improved on 115 times, and the current record is "rohanarun"'s 1 - 9.87e-5. I'm sure by tomorrow it'll have improved again.

Does this look like people aren't having fun? Does it look like they aren't discovering stuff? It looks like it's spurred a cascade of interesting community activity. It doesn't really seem much different from what happened with the twin primes conjecture. Isn't that supposed to be the point of all this?

New comment by ComplexSystems in "OpenAI, the Partition Principle, and Mathematics"

ComplexSystems — Fri, 09 Oct 2026 00:38:01 +0000

Have you looked around recently? Because there are plenty of mathematicians that are excited to read and learn about all of the new results. They've improved on the sub-n log n result and have even made a web site to track progress on it: https://beyond-n-log-n.netlify.app/

It looks like people are enjoying themselves, having fun with the new results, and generally doing all of the things you say "science" is supposed to be about. So what's the problem?

New comment by ComplexSystems in "OpenAI, the Partition Principle, and Mathematics"

ComplexSystems — Fri, 09 Oct 2026 00:18:29 +0000

Yes, they should. They have invented a magic button that can tell you the long-awaited answers to the burning mathematical questions that you've spent your life researching. The caveat is that the technology is still new, so the explanations "are not fun to read" like set theory papers usually are (lol). If you don't think that's a worthwhile tradeoff, that's your call, but it sure as hell isn't everyone's.

New comment by ComplexSystems in "OpenAI, the Partition Principle, and Mathematics"

ComplexSystems — Fri, 09 Oct 2026 00:11:55 +0000

I can't relate to this at all. AI models will surely get better at writing "enjoyable proofs," but for now the situation is what it is. You're passionate about this problem, right? But you don't want to do the work to understand the result? Fine. There's a new generation of younger, hungry mathematicians that are highly interested in figuring out why the result is true and I am sure they'd be happy to wade through it and spoon-feed you the answer instead. Maybe they should be running things.

New comment by ComplexSystems in "OpenAI withdraws three mathematical results"

ComplexSystems — Thu, 08 Oct 2026 16:19:02 +0000

It would have stayed broken assuming AI models never improve.

New comment by ComplexSystems in "The Mathocalypse"

ComplexSystems — Wed, 07 Oct 2026 21:47:46 +0000

> I think the next step is to demand that proofs either be human-scale or they prove that a human-scale proof is impossible and the machine proof is as good as it gets.

Who do we demand this from? The AI companies? Or the mathematicians who are worried they will have nothing left to do?

New comment by ComplexSystems in "Navier–Stokes Lost in Translation"

ComplexSystems — Wed, 07 Oct 2026 16:59:04 +0000

Aside from the usual squabbling about AI, it seems the bombshell claim is this:

"In particular, we show that the formalised Lean proof does not correspond to the NL proof of blow-up of solutions to the Navier-Stokes equations."

So these authors seem to be claiming that OpenAI has not really proven Navier-Stokes at all. If I get their idea correctly, they are claiming that the LLM has not formalized the original "natural language" idea of Navier-Stokes correctly. If true, it would mean that their purported Lean proof is not actually a proof of Navier-Stokes at all, but something that is an incorrect translation of the original natural language idea. If correct, this is a really bold claim and I would like to see if other researchers agree.

New comment by ComplexSystems in "What's the future for pure math research in the age of AI?"

ComplexSystems — Sun, 04 Oct 2026 21:14:34 +0000

It can still benefit humans, but there are plenty of situations where humans prioritize guarantees of formal correctness over the ease of navigating granular details.

New comment by ComplexSystems in "Responsible Release of AI-Generated Mathematics"

ComplexSystems — Thu, 01 Oct 2026 05:23:00 +0000

It seems that, despite spending decades obsessing over their various niche problems, they have little interest in a magic button that can immediately produce the answer. At best they view this button as a mild nuisance they need to contain somehow.

New comment by ComplexSystems in "Windows 11½"

ComplexSystems — Mon, 28 Sep 2026 20:47:59 +0000

Someday I'd like to see someone do a similar parody of Linux where your job is to get a printer working in Kubuntu. Preferably on a laptop with a HiDPI monitor.