tim-kt

Well, I meant that I would rather have the "old" Tao blog with less guest posts and people who want both can also subscribe to the separate blog.

I also feel like many of the current guest posts have overlapping ideas and arguments and so I get less out of each one of them. Maybe a separate blog for endorsed opinion pieces would be appropriate.

You raise good points. I don't have answers for them. We will see how this plays out in the next few months.

I'm about to start a PhD in mathematics. The idea of puzzling out what an AI did to prove something sounds quite boring and unappealing. But yes, maybe it's a viable career path.

I'm just not happy with the presentation of OpenAIs result. Maybe they could have gotten into contact with the people of the research areas of the problems that they solved and worked with them to create a better exposition. Sure, it's a slow process and requires lots of staff. But I believe that they can afford it.

The point is that so far the AI is not doing a good job at explaining the "trick", so we (humans) have to do it. And the way these results are published at the moment (that is, dumping a load of proofs with badly written explanations) is not cooperative to enable this distillation (for example, presenting results at conferences and engaging with mathematicians). I recall Tao working through the disproof of the Jacobian conjecture, stating some steps as "miracles" for lack of better terms. If a human solves a problem in an unexpected way, at least there is some reason why they chose this path, which can help in understanding. This is not available to the same extent with AI generated proofs.

I'm a somewhat ambitious climber (mostly indoor, however) and am in general very active. Factorio is an effective way to keep my brain busy as sometimes I get overwhelmed with my thoughts. But of course it is not the only thing that I enjoy and the remark about autumn was an exaggeration. I'm also very much against considering days "wasted". Sometimes I just need to take a day off and spend it at home, as long as there is a balance.

Factorio is to me what Minecraft is to Mike Tomlin. I give it a full recommendation. Oh, is it autumn already?

They said that a customer would have paid around 15 million for the required compute. I can't imagine that this was not a significant internal spending even with "free" tokens.

I mean, yes. But "it doesn't hold that <anything>" is equivalent to "it holds that <not anything>" and since not anything is also anything... Ah, I see.

If mathematicians aren't solving problems people are having (which your comment seems to imply), then putting them out of their job with AI is not a bad thing. Of course mathematicians are solving problems, just in a very different way than other professions.

It's true precisely because it's vacuous. If you quantify over the empty set, anything is true.

In other words, the statement "for every x in {} it holds that <anything>" is always true.

You can also think of conditional convergence as convergence under the condition of a specific order. It then turns out that unconditional convergence (that is, convergence where it doesn't matter what order you choose) is equivalent to absolute convergence (that is, the sum over the absolute values converges).

But this defeats the point of having open access and usually a DOI points to a journal. Why have a journal that reviews journal articles?

I'm in math, so I can't give you an answer on tech journals unfortunately. And for math, I don't really read any specific journal. It's so much work to read and get something out of a research paper in math that I pretty much only read papers that are directly related to my work or have been recommended to me.