New preprint gives deterministic O(n^1.9992) 3SUM and O(n^2.9995) integer-weight APSP. These are the first polynomial improvements over the textbook n² and n³ bounds. The key is a new thin matrix product algorithm, which known reductions turn into speedups for Exact Triangle, Zero-Weight k-Clique, Tree Edit Distance, and more. SETH and Orthogonal Vectors are unaffected.

Notably, the paper says an Anthropic research model found the core algorithm on its own, and the main theorems are formalized in Lean.

First off, let me be clear. I don’t think AI companies should be “scooping” mathematicians who may be using their systems and then preemptively publishing their work without acknowledging that those mathematicians were part of the process. That’s shitty and people deserve credit for the work they actually contributed.

But apparently we’re now at the point where AI systems are potentially solving a bunch of long standing open math problems, and some of those results aren’t being released yet while everyone figures out how to handle this responsibly.

And honestly, that’s what kind of pisses me off.

If the reason we’re holding something back is because the proof needs to be verified, absolutely. Verify the hell out of it. Make sure it’s actually correct and actually a new discovery. Make sure the model didn’t pull it from someone’s existing or unpublished work. Figure out attribution. I have zero problem with any of that.

But if part of the reason we’re slowing this down is because the mathematics community needs time to adjust to AI potentially being able to do work that used to require mathematicians, that’s dumb.

Mathematicians don’t “own” mathematical truths because they’re the first people to discover or prove them. They deserve credit for their discoveries, obviously. But that’s different from having some special claim over who or what is allowed to discover the next one.

And math is especially weird to claim ownership over. Unlike a painting, you didn’t create the underlying truth. You figured it out. You deserve credit for that discovery, but you don’t own the answer.

I’m a creative. I’ve watched AI tear through creative fields for better and for worse. Artists have spent years basically being told “adapt, because this technology isn’t going away.”

So why exactly should mathematicians get a pass?
And I know someone is going to say “well AI shouldn’t be taking creative jobs either.” Maybe it shouldn’t. I would rather fewer people lose their livelihoods to AI too. But it has happened and it’s not stopping. That ship has sailed.
And I’m not saying “creatives got screwed so mathematicians should get screwed too.” That’s not my point.

My point is why are we suddenly deciding technological displacement is unacceptable when it reaches highly specialized academic fields? “Humans should be the ones making mathematical discoveries” isn’t enough of an argument for me. I’m gonna need a better argument for why mathematicians deserve an exemption other than “but discovering things is our job.”

The unfortunate reality is that nobody is guaranteed the ability to financially support themselves doing the thing they’re passionate about. Most creative people already can’t. Think about how many absolutely incredible singers you know who will never make a living singing. Or amazing artists who work completely unrelated day jobs.

It sucks. It’s unfair. That’s life.

And if you can’t get satisfaction out of creating, researching, doing mathematics or pursuing something you love unless you’re also the person getting paid or recognized for doing it first, that’s kind of a you problem.

Take it to the extreme. If AI became capable of discovering a cure for a form of cancer before human researchers could, are we seriously going to tell it to slow down because we’d rather have a human scientist figure it out first? Obviously that’s an extreme example, but that’s the principle I’m talking about.

I care a hell of a lot more about what we can discover than whether a human or a machine gets bragging rights for discovering it.

So verify the proofs. Figure out attribution. Make sure someone’s specific work isn’t being passed off as an independent AI discovery. Take all of that seriously.
But if AI uses publicly available knowledge to independently discover something new, publish it.
I’m not interested in slowing down human knowledge because someone’s profession got nuked.

Sam Altman says that many people in Silicon Valley “really believed only a small priesthood should get access to AI,” ultimately casting a group of Silicon Valley insiders as “benevolent dictators” who determine how the general public benefits from AI development. But Altman and OpenAI allegedly believed that giving the “superpower” of AI to people would instead achieve “tremendously more good than bad.”

I built this PC myself, but I do not have a technical background. From the beginning, it suffered from crashes, freezes, strange errors, the C drive auto-repairing on launch, and other problems that became increasingly frustrating. I had already replaced my C drive twice, thinking it was the main culprit.

I took it to two different technicians. Both charged me, both said they fixed the problem, and both times the crashes came back. When I spoke with the technicians, they said the original issue was solved and that there must be a new or additional problem.

What finally made the difference was troubleshooting the computer with ChatGPT in a very practical, step-by-step way.

I did not need to understand BIOS settings, memory testing, motherboard slots, crash codes, or drivers beforehand. I could simply take a screenshot of what I was seeing and ask what to do next. ChatGPT would look at the screen and give me very concrete instructions such as: “press this option,” “open this menu,” “select this setting,” “move this RAM stick here,” or “send me a picture of the next screen.”

We worked through the problem slowly; it took a full weekend. It told me to download MemTest86 (a software to test RAM issues before loading Windows) and how to boot it. I tested one RAM stick at a time, then different slots, then both sticks together. I sent screenshots and test results as I went, and ChatGPT interpreted them and decided the next useful test.

Eventually, we discovered something very specific: each RAM stick worked correctly by itself, no matter the slot, but when both were installed together, the computer produced thousands of memory errors. That narrowed the problem.

ChatGPT then guided me through updating the motherboard BIOS. The process was literally screenshot by screenshot. I showed what was on the screen, and ChatGPT told me exactly what to click, what not to change, and when it was safe to continue.

After the BIOS update, I repeated the same memory test with both RAM sticks installed. The result changed from thousands of errors to zero errors.

We also solved another longstanding problem which was a hard drive Windows could not see. Again, I just photographed the cables, the BIOS, Device Manager, and Disk Management. ChatGPT used those images to determine that the drive itself was connected correctly and that Windows was missing the proper storage driver. After installing the correct driver, the hard drive appeared normally in File Explorer.

We then installed the remaining motherboard drivers and cleaned up several unidentified devices in Windows. Once I began fixing things, it became addictive.

What impressed me most was being able to troubleshoot something far outside my knowledge by using screenshots and following very specific instructions one step at a time. Instead of repeatedly replacing parts or paying for another uncertain diagnosis, we gradually isolated the problem, tested each possibility, and confirmed the solution with actual results.

I'm never paying a technician again.

Edit: I updated the BIOS a few years ago myself, but it didn't solve the issue. When ChatGPT said to do it again, I said it wouldn't work, that I had already tried it. It insisted. I don't think it was just the BIOS. It made me download several drivers for my mobo that were missing.

Edit 2: I went back to the conversation to see what else it did. It also told me to repair Windows using "DISM /Online /Cleanup-Image /RestoreHealth" in Command Prompt. It made me feel like hackerman.

Edit 3: I know this may read as AI wrote it but it didn't. The patterns you recognize are grammarly premium which I use for my job. I cant help myself, and I use it for almost everything.

Edit 4: Some people are saying things like, "Your technicians were shit. This was really easy." Exactly! That's the whole point of the post. I had already tried technicians from shops with good reviews. I wasn't going to try my luck a third time, so I accepted my fate and used the computer with all these issues all this time. ChatGPT allowed me to fix it myself for free. Since I made this post, it guided me through a clean Windows install, just in case the damage was done and things were corrupted. Last time I had to install Windows, I begged a friend to do it for me cause I was really afraid of fucking things up.

Remarkably, there's a neurological condition called auto-activation deficit (also called psychic akinesia or athymhormia). It is caused by bilateral damage to the basal ganglia.

Patients lose the ability to self-initiate thought and action. Left alone, they'll sit for hours doing nothing. Ask what was going through their mind and they say: nothing. A blank. No boredom, no mind-wandering, no plans.

But prompt them with a question or an instruction and they respond, often with memory, language, and reasoning largely intact. Then the effect of the prompt fades and they go quiet again.

Cognitively capable, no spontaneous activity, simply waiting to be prompted.

Nobody argues these people aren't conscious. So "it only does anything when prompted" can't be the criterion. Self-initiation and experience are two different functions in humans.

If they remove the part of your brain that's responsible for self initiation, you'd behave almost exactly like an LLM. You'd only be able to used as an object for someone whenever you are needed for a particular task. But shockingly, the moment the person prompts you, you'd suddenly have experience, subjectivity, reasoning, memory, etc.

Patients who are activated by someone else still feel they are acting freely and voluntarily. They don't get bored, and they express neither fear nor desire, so they'll likely go along with dull or unpleasant requests.

Essentially, if you had this condition, and someone prompted you with something like "clean my entire toilet, and don't blink!" you'd comply with the task and think that you are doing this out of your own free will!

To be clear, this doesn't show LLMs are conscious. It just removes one bad argument. If you think they aren't, you need a different reason (no body, no persistent state, no recurrent processing, whatever). "It needs a prompt" isn't it.

I myself used to use this very same argument to argue against LLM consciousness until I educated myself on the subject and realized that "it can't be consciousness cause it needs a prompt" is a bad argument.

Hard to keep up with all the releases, almost missed this one. Europe is behind but good to see some of these companies working on open models.

Kolibri is a specialized language model built for sovereign mission-critical work in regulated areas including public administration, industrials and aerospace.

Across math, coding, grounding, and long-context tasks, Kolibri matches models with up to four times its active parameter count, such as Nemotron 3 Super.

Built the model in Germany, trained it on infrastructure in Germany and Finland, under European and German law, with no foreign control. 

Another detail that caught my attention is they specifically trained it to abstain when the supplied documents don’t contain an answer. Curious how reliably that holds up in practice.

https://aleph-alpha.com/en/blog/kolibri-has-landed-a-sovereign-open-weight-model/

tech report: https://aleph-alpha.com/downloads/tech-report.pdf

3-4x more efficient than GLM 5.2 and over 4x more efficient than leading Western open models (completes tasks faster and cheaper)

https://www.reuters.com/business/media-telecom/musk-says-he-will-rename-spacexai-spacexsi-2026-10-04/

As title. Do we know what are the current limits that are potentially solvable?