JPC21

Whilst I agree that AI costs are falling and AIs have practically infinite uptime, I fail to see how/why the current AIs will perform better overall in the work place.

The example of AIs solving mathematics is all fun and games, but it assumes that mastery of mathematics implies that everything else will also be mastered eventually. But instead we're seeing that LLMs exhibit this thing called jagged intelligence, which means that they can be extremely good in one area, but completely fail in another. In theory the LLMs could be improved if data would be available for other areas and if there are good verifiability criteria. Fact is that many fields just don't have those and would not be willing to give up their data.

I think you're misunderstanding what the objective of mathematics is. It is not just about what theorems are true and false, but rather why they are true and false. A highschool sophomore could use these prompts, but I severely doubt whether they'd be able to understand the entire structure. And I think it is exactly this ability to deeply understand structures is what makes a mathematician valuable.

Solving problems is a by-product of the understanding. New techniques are a by-product of the understanding.

But I can understand you're scared that some future version of AI will undermine this as well. I personally pivoted to a field adjacent to mathematics. But that doesn't mean my mathematics education wasn't valuable. To the contrary, I find that it helps me think much more sharply about problems than most of my colleagues.

Second this. What I also wonder about is how closely the TeX write-up and the Lean formalization line-up.

Just don't. If you read the story here carefully, you see that AI was used to work from theory built by others which showed that the Euler equations possesed finite-time blow-ups. But to make that step, actual good understanding for mathematics was needed. My experience with software has been the exact same.

I noticed something similar. Phrases I have noticed that Claude likes using are "... is doing major work ..." and "... worth pulling apart ...". Unfortunately, some of these have subconsciously become part of my own writing style as I noticed recently. English is not my mother tongue, so I'm pretty sure that I inherited these from Claude.

I have played quite a lot of video games in the past yes. But not much anymore.

You say pretty obvious, but it took me 2 years during my PhD to be consciously aware of this. And once I did, I immediately knew I wanted to leave my field as soon as I would finish.

I can only commend this, but people should be aware that not every church is equally welcoming. But usually every town has at least one that is!

I remember having a hard time understanding limsup/liminf and only actually understood the concept after reading this book. I am sure it is not for everyone due to its age, but I think this book is a much better introduction than baby Rudin.

Generating functions are also a great tool in combinatorics (see for example the book Analytic Combinatorics by Flajolet and Sedgewick).