AI probably changes the equation to some extent, but I still believe I'd rather maintain a complicated data pipeline like that in Python rather than R.

What polemic? Defining the determinant as the unique multilinear alternating form satisfying certain properties is very normal (and in fact the only way that really makes sense for both finite- and infinite-dimensional vector spaces). There are zero unusual things with this book imo.

Huh?

Mathematics is an extremely wide subject, it's perfectly normal even for two professional mathematicians not to understand each other's work. Have you considered that maybe they just don't work in that area?

Are you implying OpenAI's paper (which was, by the way, edited by humans and provided Lean certificates for most of the proofs) is actually gibberish? That's flat-earth levels of conspiracy.

The problem is that Paul Erdos was eccentric but he was also Paul Erdos. I'm not saying you're implying that, but I feel it's a similar line of thinking to how popular culture often romanticizes autism and Asperger's because some very smart people are (allegedly) affected. The same group includes people who need 24/7 care.

Computer science at the frontier is as specialized and hard as mathematics, you need years of study to truly understand a field well enough to make meaningful contributions. You can try sponsoring me if you really want, but I don't think you'd be spending your money wisely in expectation.

It's a very O-ring problem.

I tend to like simpler/textual interfaces though, admittedly this won't be everyone's cup of tea.

I mean yeah, that's mostly what I'm saying?

The only parts where I would disagree are that capabilities are spiky, and also the fact that they're a bit prone to losing the forest for the trees without guidance (the macro/micro distinction). But yeah, by default I don't write code by hand.

With that said, from the material you show in your homepage, it still seems like you're doing something very similar to OpenAI and Anthropic's first party apps? I think it would help your pitch if you could show some task or workflow where your interface truly makes a difference; loading files and asking questions about them is a staple of most harnesses.

I agree with you that it's a delicate issue, I really do. I'm also tired of taking infinite psychic damage trying to steel-man the arguments of people who are clearly not interested in operating at the level of steel.

Again, I don't think your position is indefensible, but this doesn't strike me as particularly convincing. The usual definition of R is that there exists a unique ordered complete Archimedean field up to isomorphism. We get the kitchen sink from the least upper bound property. As a constructivist you're gonna say that I don't get to define R like that, but you can't pretend it's done for no reason or that it buys nothing.

> I certainly learned about areas in geometry

And how were they defined? In elementary geometry we just sweep the question under the rug, usually...

If you get to say that being able to articulate why the measure of Q is 0 is unimportant and uninteresting, then I get to claim that the supposed problems with the usual definitions are also unimportant!

Saying that the non-constructive world leads to worse problems is a respectable position. Pretending the usual way of doing things is completely arbitrary isn't very honest.

> But when we say things like "the rationals are discrete"

In the usual topology they are not?

> In the practical sense the rational numbers are quite continuous -- between any two rational numbers there are an infinite (unbounded) number of rational numbers -- there's no notion of a "leap" the way there is with the integers.

This characterization captures neither the intuitive nor the formal definition of continuity. You are effectively saying that Q is dense in R, but this is insufficient to prove, for example, the intermediate value theorem.

> measure theory, a theory which yields almost nothing of value except endless paradoxes

Come on now. The usual definition of concepts as basic as areas is tethered to measure theory. We say it's "obvious" that the integral is the area under the curve (and it is: e.g. the Riemann integral is trivially the Peano-Jordan measure) but this only works because we're appealing to it. You can route around it, but let's not pretend we're doing it for no reason.

I can see the elegance of a purely intuitionistic construction, but the "usual" real numbers are much closer to how we intuitively (no pun intended) work with numbers.

I assure you they're not in it for the money, I make more than they do and hardcore math research is definitely harder than whatever the fuck it is that I do.

I don't think that trying to be a little bit more understanding towards people who are obviously struggling would cost us that much.

Honestly you're right, I'm sorry. I'm not having a great day and ended up venting online. Logging off.