essai57

Hm, but I'm not sure I understand your point. Are you saying that Kafka is a counterexample to the need for external motivation? It's true that some of his best-known work was only published only after his death (which was against his wishes, though Brod had supposedly told him that he would not destroy his works). But he did still have external motivation, e.g. Brod encouraged him, and Kafka read aloud some of his work to his friends. Also, we should be careful about interpreting his wish to destroy his unpublished works in a certain way; much of it was unfinished, and he was kind of a perfectionist.

I know that it was self-deprecating, but that doesn't redeem it much to me. I also still find it pretty contradictory/ironic because he wrote A Course of Pure Mathematics when he was in his early thirties.

> Forgive me if I have no sympathy for current mathematicians who think this way. It's a pretty ugly kind of arrogance.

Thankfully, very few mathematicians share Hardy's opinion, just as very few share his opinion that "mathematics is a young man's game" (and indeed we now have prizes like the Abel Prize with no age limit).

In fact, many of the greatest mathematicians throughout history have taken exposition very seriously, e.g. Euclid, Euler, Lagrange, Cauchy, Dirichlet, Kolmogorov etc. all wrote textbooks. Many mathematicians today carry on that tradition of taking exposition seriously and write books and freely share their lecture notes.

So we should not take Hardy's opinion as representing the opinion of all mathematicians or even most mathematicians. In fact, Hardy's statement is somewhat self-contradictory since he himself wrote several expository books (e.g. "A Course of Pure Mathematics").

> At a minimum a discussion like this should acknowledge the possibility that the current rate of AI progress continues apace.

But the post does do this: "[...] even if their capacity becomes far superior, there will always be a need for mathematicians at all levels to guide research in paths that make sense for humans to walk (not run)."

> Of course it will get better at exposition than humans.

I'm not so sure about this, because I don't know how one would train towards better exposition as it's not easy to check for good or bad exposition at scale.

> it is not as if knowledge once understood remains difficult

What do you mean by this? Once a person has understood something, it may no longer be difficult for them, but it can certainly still be difficult for those who have not understood it yet. And we humans know of no way of transmitting understanding to another person without having that person exert some effort.

I don't know where you get the impression that mathematicians at large are withholding understanding. In fact, many mathematicians share their lecture notes freely online, share their articles freely on arxiv etc.

If your complaint is that these texts are written in the language of the field and thereby not accessible for laymen: This is the case for any advanced knowledge, because it builds on more basic knowledge that a person must first acquire. That is not withholding knowledge.

I was pointing out that your original comment (before you edited it to just say "ok") did not properly represent the claims of this paper.

I am not making any claims about mathematicians as a collective group, because mathematicians have many diverse views on AI and can't be lumped together into a single "they" (as your comment seems to imply that they can). In fact, some academic mathematicians even work for the AI companies. Your comment seems to imply that if a group of mathematicians publish some statement, then that statement must speak for all mathematicians, but that's simply not true.

What do you mean by "the social aspects of math" here? Even some of the earliest known mathematical texts (like the Rhind Papyrus) contain evidence of a social aspect of math. And certainly mathematical discussions occurred among the ancient Greeks. People have been exchanging mathematical ideas for millennia. If you mean to say that the current academic organization of mathematics is a recent phenomenon, that's certainly true. But pretty much all the math history we know has been people communicating with each other, evaluating each other's ideas and developing them further. Given this, I understand why people are worried if the field should suddenly take a non-social form.

I don't think that's an accurate summary of what this paper or its abstract actually claim.

Really nice article, thanks for writing it! I recently dabbled in some of this in connection with modding a game and there encountered the hierarchy you describe of mips, tiles, blocks and texels, so very relatable. Great write-up!