Call me crazy, but I’m not ready to concede. I’m having a different set of reactions entirely, based around a simple difference: I think the main thing holding back mathematics has been human sociology of mathematicians.
Here’s why I’m excited:
“When will it stop solving problems and build its first original theory?”
“Can it figure out how octonions and exceptional algebra are actually part of the mainstream?”
“At last! A mathematics that won’t be built around a Putnam and Olympiad-style problem-solving fetish.”
Can it at last say “Y’all just wasted a *TREMEDOUS* amount of time and energy on Calabi-Yau phenomenology and Superstrings while calling people closer to the answer, morons, grifters and worse.”? That would be huge!!
“I hope @OpenAI will hurry up so that the machine can at last shake its human prejudice from the training corpus and stop deferring to our ‘leaders’.”
“At last, a non-PhD colleague!”
“Somewhere I have notebooks full of ideas and observations in areas that were too expensive to explore!”
“Does this mean that mathematicians are going to finally drop the bullshit about how they don’t care about credit?! Or that they don’t care about money?? Because @OpenAI is now running them in emulation…sped up! At last: a mature and non-infantile version of mathematics!”
“Shalom Koide, Tits-Freudenthal, Elliptic Cohomology, and Interstellar.”
—-
Let our leaders call for a slow down. Then get those leaders out of the way as there is no telling what the rest of us humans can do with these new tools.
My condolences to the problem solvers. A tough break for you. But know: It’s coming for all of us. I have no illusions about that.
For now at least we humans (e.g. theory builders, great writers) are still top dog. Let’s spend that time wisely and optimistically.
For all our sakes.
@PuckOfAmp I wanted to show you to my team during a meeting yesterday, but I couldn't find a decent video.
Is there a decent video of example usage you would recommend? I remember @beyang showing it not long ago, but wondering if there's anything more recent.
@mathelirium Your focus should be what the focus of programmers has been since the beginning: figure out how to replace yourself with a machine. The good news is this strategy seems to result in you never succeeding, and it always points you at what to work on next, recurrently.
i was completely wrong about this and @thdxr was obviously right btw. turns out i was reasoning via analogy w human ergonomics based on extremely low capability models (opus 4.6), but actually spiky superintelligence prefers to just use python for everything including editing files
going forward there's basically no reason to expect what feels "efficient" or "easier" for us will be the same for entities that have undergone truly intense optimization pressure
The thing I learned this year is that when engineers say they like working on “hard problems”, they actually don't. What they like is puzzle solving, and having a repertoire of patterns that they can pattern match onto traditionally hard problems, usually involving databases or something with scale, etc. And they know that the industry used to pay you a lot for how deep and broad this repertoire was. Unfortunately, in 2026, well, you have a cheat code machine that has infinite breadth and depth for pattern matching. So the question is, do you actually like hard problems? Because there are now hard problems that are a complection of engineering, product, society, culture, politics, and they are fairly intractable, probably unsolvable! Because if you do want to work on those actually hard problems, there is so much money that people will pay you for it. But you’ll have to face that truth about yourself first.
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Opus 5.5 can iteratively build insane “slopgarithms” that outperform anything on speed and quality by a large margin. The aesthetics are awful, and would make any human cringe, but it’s hard to argue with the results. Expect many miracle-performing black slopboxes from here.
Cool eval. Simply ask an LLM “Land or Water?” and give it a latitude and longitude coordinate as text. Ask 16,200 times, plot as image. The models know. From compressing the internet.
[continued]
I say "almost" because there is going to be one way to maintain secrecy. Software as a service with the executable hiding behind a network connection to the cloud. But as of now, we must assume that anything shipped as an executable, or even a firmware image, is as transparent as glass. It won't keep its secrets for any longer than it takes for somebody to be motivated to throw an LLM at it.
I did not see this coming. When I wrote down the theory of open source, 30 years ago now, I thought closed source would be gradually driven towards extinction by cost gradients, but survive indefinitely in certain niches. I did not foresee it being wiped out in a technoapocalypse.
Ironically, I thought one of the application areas in which closed source would persist longest was games.
There are still some obstacles. In US law, decompilation of a binary is a derivative work of the binary that falls under whatever copyright it had. However, it is also settled law that if you decompile binary code to a precise specification of what it does, then generate fresh code from that without looking at the decompiled stuff, you're in the clear. This was the case law that allowed PC clones to exist, after Phoenix Technologies reverse engineered the original IBM PC BIOS.
The two-step process - binary to specification to unencumbered code - will no longer takes a large number of programmers and years of development time. With an LLM, it's now a thing you can do in a day. Ubiquity will make it impractical to prosecute all the people who might skip the specification step.
Source code can also be covered by patents. You can be able to see their source code for a patented technique and not be able to use it without violating the law. Linux has evolved practices for dealing with this problem - one is not shipping patented video codecs, but requiring you to download them as plugins from jurisdictions where U.S. patents can't be enforced. This presents patent holders with the impractical challenge of individually suing millions of end users, assuming it can even figure out who they are. To date, AFAIK, this has not been attempted.
And that's about it. If there are any other ways left to retain software secrecy and lock-in than SaaS or patents, I can't think of any. Well, you could epoxy-pot a firmware ROM, I suppose, but that can be defeated with a heat gun and a dental pick. Device manufacturers will learn not to pay for an assembly step that has become useless.
Forced migration from shipped binaries to tied cloud services will be tried - Adobe pioneered this, and Microsoft is pushing it as hard as they can given that their OS is a binary that has to run locally. Both companies are seeing massive user revolts over this. There is good reason to doubt that it's a strategy that can hold customers in the long term.
Also, a lot of things can't safely be tied to the cloud at all, because they can't tolerate a random network outage. Machine tools, medical devices...
A whole lot of proprietary software business models are going to collapse. Hard. One that I think might survive is tax software; being able to decompile it doesn't necessarily do you a lot of good because its actual value is tracking a ruleset that changes over time and has to be maintained by vendor specialists. But cases like this are unusual.
I think some dirty laundry is going to get aired, too. It has long been rumored that the reason graphics card manufacturers are so stubborn in their secrecy is that they've all been committing massive intellectual-property theft on each other for decades. If this is true, it will be exposed, and the lawsuits will be entertaining.
We're entering a new world, with a lot of ancient comfortable assumptions being blown up. It's going to be fun to watch.
2/2