I doubt outside of a few exceptional cases that one is going to do better on CPU-bound problems than a well-written LAPACK implementation built for the architecture you intend to run on.

Maybe pedagogy was the point? I didn’t really get that from the article, maybe some intention was lost by filtering it through AI.

LAPACK doesn't do sparse systems.

(On the other hand, I skimmed the article and this might be a banded system, which LAPACK can handle).

Various algebras of dual numbers are used in most automatic derivative routines.

This is treated more rigorously and generically in the subject of synthetic differential geometry.

wanted to say this.

Also conceptually it feels just right to use nilpotents to probe the smooth structure. In a way nilpotents are violently smaller than even non standard analysis infinitesimals, as the laters’ powers are incredibly small but never vanishing.

Another way to see this is that it makes Taylor expansion exact by killing terms above a bound so it works naturally with the ecosystem surrounding it

Finally duals are very similar to complex in a way. i can be defined as root of X^2 + 1 = 0 even if it felt impossible initially, the dual number as a non nul solution of X^2 = 0 even if it is as counterintuitive.

I remember learning about that from Stephenson’s Cryptonomicon, back in the day.

It’s not even a US-specific thing. Many countries recruit foreigners to their militaries.

https://en.wikipedia.org/wiki/List_of_militaries_that_recrui...

I've heard of some people on the lam who wanted to join the French Foreign Legion, a military that gives a no-questions-asked grant of citizenship at the end.

That's not how it works, and I have firsthand experience, and hasn't been for at least three decades. The very first thing that happens when you show up in Fontenay-sous-bois is that they run Interpol checks and other checks in your country of residence or anything notable in your passport.

Gone are the days of accepting any criminal openly.

They do however, if you either complete your contract, or are injured, deem you eligible for French citizenship "by spilled blood".

> Technically a large landmass, but essentially nothing happens in the western half.

Depends what you mean by "western half," I suppose, but China is definitely not a relatively small country. Shanghai to Chongqing is about the same distance as Chicago to Dallas; Beijing to Kunming is about the same as D.C. to Denver.

I hate the dark forest more than just about any scifi trope but reality just keeps proving it right.

I also think the trope is a little overused, but do wonder if there is an interesting analogy for what this will do to research: Massively incentivize keeping results secret, to avoid being scooped by someone willing to throw enormous compute at your partial solution.

So less about hiding civilizations, and more about hiding information. Math is clearly headed in this direction, and I see no reason why the rest of intellectual work shouldn't too.

This is very sad, but I came to the same conclusion with my math blogging a couple years back. There’s little point to publishing any personal effort on the internet anymore. At best you get some spam comments and your work stolen by bot scrapers; at worst you get a doxxed and targeted by a harassment campaign.

My go-to is “It’s the only thing I was good at in school, I was hopeless at everything else,” which is only a slight exaggeration.

> It’s highly nontrivial to verify that a 250k loc Lean program actually represents that which it claims.

Generally you only need to look at 10-100 lines (unless you have a highly novel theorem that essentially invents a new field of math or builds on a field that has never been worked on in Lean before) of the 250k to verify what it claims. This is why there is excitement around formal verification. The rest of it is perhaps useful to read to figure out why the proof works, but is not necessary for checking.

Human verification of the Lean program only requires verifying that the theorem itself is represented correctly. The theorem will only make up a very small part of the entire Lean program.

> do you expect this to remain true? If so, for how long?

For the foreseeable future. Left to their own devices current LLMs kinda wander off into outsider art territory. They aren’t grounded in the real world and they need that feedback loop to stay within the category of relevant ideas. I haven’t seen anyone working on fixing that.

Regarding 1, the same is true of every other scientific field. Verifying some tidbit of knowledge for yourself as an individual isn’t optimally useful in all circumstances.

Regarding 2, if the proof isn’t understandable then it probably isn’t useful. Many people today work in the hypothetical world where the Riemann Hypothesis is true, and many work in the hypothetical world where it is false. If it takes decades to validate that some horrifically complex AI proof of either fork is true, people will probably continue working on the other fork just in case.

> For the foreseeable future. Left to their own devices current LLMs kinda wander off into outsider art territory. They aren’t grounded in the real world and they need that feedback loop to stay within the category of relevant ideas. I haven’t seen anyone working on fixing that.

I have. DataAnnotation and these other AI-training piecework companies are pretty much the backstop now against total navel-gazing model collapse. With the Dead Internet Theory now pretty much reality, it's not like there is, or is going to be, gobs of untainted human-generated data out there ripe for the harvesting so it's going to take active human effort to keep the models grounded. That is, of course, until they start inhabiting robot bodies so they can live and move around in the real world, and thereby achieve their grounding, as in GitS or Ex Machina...