Dataflow matrix machines (by Anhinga anhinga)

An Oct 6, 2026 essay, "Mathematics of the Future", by Pavel Etingof and Slava Gerovitch:

www.dropbox.com/scl/fi/zmqzdrneyunkueu1th9iq/futuremath8.pdfrlkey=oarhqm8savaef4umcb60ldb4e&dl=0

The essay "tries to make sense of the AI-induced changes in mathematics and imagine a way forward for mathematicians". I am finding it quite useful.

 scottaaronson.blog/?p=9668

The wise child asks, “what are the main classes of problems that are currently known to admit superpolynomial quantum speedups?” To this child, you can talk about quantum simulation and finding hidden structures in abelian and occasionally nonabelian groups, as well as Forrelation, glued trees, HHL, and DQI—explaining how the central challenge has been to find end-to-end speedups for non-oracular tasks.

The wicked child asks, “so can I buy a quantum computer right now to help me pick stocks and search for oil and turbocharge LLMs, or is this whole thing basically a fraud?” To this child you answer: “the quantum computing people who seek you as their audience are frauds.”

The simple child asks, “what is quantum computing?” You answer: “it’s a strange new way of harnessing nature to do computation, one that dramatically speeds up certain tasks, but doesn’t really help with others.”

And to the child who doesn’t know how to ask—well, to that child you don’t need to bring up quantum computing at all. That child is probably already fascinated to learn classical stuff.

LessWrong organized a blog writing program encouraging people to create 30 relatively long blog posts in Oct-Nov as an exercise (relatively long meant being 500+ words).

I have actually done that, here are the posts (mostly AI-related, although there were some diary-like posts too; 30  posts + 2 auxiliary ones): mishka-discord.dreamwidth.org/

(They are open for commenting, but I don't expect to continue posting new posts there.)

> On when to use coordinates and other concrete constructions in mathematics, and when to use coordinate-free formulations and abstractions:

> 1. If your priority is to perform computations in mathematics, use coordinates and concrete constructions.
> 2. If your priority is to generalize to as broad a range of use cases as possible, use coordinate-free formulations and abstractions.
> 3. If your priority is to actually understand what is going on behind the mathematical formalism, learn how the coordinate-based and coordinate-free approaches are equivalent.

mathstodon.xyz/@tao/114456756661540097

"Narrow AGI" is mostly an AGI-level artificial software engineer, an AGI-level artificial mathematician, an AGI-level artificial AI researcher (and probably a single entity combining these three application areas, because a strong AI researcher has to be a decent software engineer and a decent mathematician).

It seems that at least OpenAI (and, perhaps, other entities) should have this by the middle of 2025, if not earlier, at least for their internal use (assuming no major disasters, that is, assuming that San Fransisco Bay Area is intact, and AI companies continue functioning normally).

What do we know about the technical aspects? We see o1 performance (and can experience it directly), we see the claimed (and partially confirmed) numbers for the demo versions of o3 and o3-mini, in math and in software engineering. We know that the jump from o1 to o3 took about 3 months. Two more jumps like that would probably be sufficient (and one can add "scaffolding" on top of that).

Another thing we know is that Sam Altman sounds much more confident recently. I've come to these conclusions a number of days ago, but now it turns out that Sam's mood has also shifted in a similar fashion. I'll put some links in the comments.

Jan 19 update: Sam Altman will allegedly do a closed-door government briefing on Jan 30 (that's apparently is not a very big secret and has been leaked; the main topic is presumably as follows: many people in the leading AI labs have approximately the same degree of techno-optimism as I have myself, and so their timelines are tentatively quite short). www.axios.com/2025/01/19/ai-superagent-openai-meta  

Dec 31 update: no, we did not get "Narrow AGI" this year. But we had 2 revolutions, one centered in June plus/minus 2 months (o3---GPT5, "mature reasoning"), and one centered on the border of October/November plus/minus 6 weeks (GPT5-Codex---GPT5.2-Codex/Opus 4.5/Gemini 3, "competent programming software agents"). The distance between subsequent revolutions keeps shrinking: 7.5 years - 3 years - 18 months - about 9 months - about 4-5 months, mishka-discord.dreamwidth.org/4806.html (we don't know if this trend of distance between subsequent revolution shrinking continues, but we are watching what happens in January in this sense, in particular, whether we can progress to "trustworthy autonomy" in January; the current generation of agents is competent in software engineering, but there is no expectation of trust, so one has to work really hard to carefully organize security, quality control, and such, the whole lifecycle of software engineering can't be outsourced yet).

This is a non-trivial angle: x.com/StringChaos/status/1869571815548596308 (UC Berkeley)

For some reason, I keep losing this remarkable blog by Grigory Sapunov and finding it again, instead of just reading it regularly:


gonzoml.substack.com/

Говорят, что Денис Гайцгори и его коллеги доказали достаточно общий вариант геометрической гипотезы Ленглендса.

Это вполне эпохальное событие, и надо собрать вместе всякие линки, относящиеся к этому делу. Вместе с тем, это для меня слишком сложно (может быть, ИИ (современный или будущий) сможет мне, со временем объяснить детали всего этого так, чтобы у меня возникло уверенное понимание).

"Enhancement for categories and homotopical algebra", arxiv.org/abs/2409.17489

600 pages

"We develop foundations for abstract homotopy theory based on Grothendieck's idea of a "derivator". The theory is model-independent, and does not depend on model categories, nor on simplicial sets. It is designed to accomodate all the usual potential applications, such as e.g. enhancements for derived categories of coherent sheaves, in a way that is as close as possible to usual category theory."

He also released references [K3] and [K4]:

arxiv.org/abs/2409.18380 and arxiv.org/abs/2409.18378