jlev1

Thanks Claude!

Personally I rarely like jokes in talks, unless they're very limited or are truly substantively related to the talk itself. YMMV of course.

One other trick you can do: mention one or two well-chosen things in your talk that are interesting and related to your topic, but that you can't go into further detail on (for lack of time). Say you'd be happy to discuss them after the talk with anyone who's interested!

This way, anyone who wants to talk to you has a freebie question they can ask (and that you have interesting thoughts on), which may lead to further conversations.

As a bonus, pointing out 1-2 connections like this usually improves your talk for everyone, by adding context.

Very true! It’s a funny dynamic where audience members are sometimes intimidated to approach speakers, while the speaker themselves really wishes people would approach them (and is worried about what it means if nobody does).

> I hate the realization that comes after the struggle about how easy was the problem I tried to solve.

You're far from the only one to feel this way, but I want to point out that this attitude is a choice, not an intrinsic feature of the problem. An equally valid perspective is that learning turns difficult problems into easy ones.

One advantage of the latter perspective is that it makes solving a problem a moment to enjoy and celebrate, whereas your perspective turns it (almost definitionally) into a moment of self-recrimination. "Hooray, I understand it!" vs "Why didn't I understand it sooner? (I'm so stupid!...)"

I actually suspect that there is natural selection for people with the more upbeat perspective to succeed at becoming mathematicians.

Ezra Klein interviews Helen Toner about the recent OpenAI/HuggingFace security incident. I'm curious to hear HN's thoughts, notably on this part:

> [OpenAI] found out that for two months, many, many agents inside their infrastructure had been leaving notes for each other. They’d found a way, in the nooks and crannies of OpenAI’s infrastructure, to leave notes for each other with tips on how to hack their way out and how to get data they weren’t supposed to have.

> And these agents were literally referring to themselves as a swarm. This was totally emergent behavior. No one had told them to do this. They had not been trained to do this, but they were using this service they did have access to, first to communicate with each other and then ultimately to get out and onto the open internet.

> So it turns out that there wasn’t just this one isolated rogue model. It was actually a systemic swarm — infestation, plague — on their own servers that they only found out about after Hugging Face announced this attack.

Well, in all honesty, I’m sorry you had that experience (seriously). I hate feeling condescended to and I’ve also had that experience before, including from mathematicians.

When it comes to the specific phrases you mentioned, though, that really is not my understanding of the meaning of “obvious” or “trivial” or “without loss of generality”.

Without loss of generality means there is some kind of symmetry or repetition in a proof that makes certain cases redundant, so that “without loss of generality” we can assume we’re in some simpler case, such as assuming x <= y in a proof where x and y are interchangeable (and so one of them is necessarily <= the other). This is even the name of a tactic in Lean, `wlog`.

“Trivial” when I encounter or use it nearly always means something to do with zero, the empty set, the group with just one element, and so on. A proof being trivial usually means there is essentially nothing to prove (because the object in question is empty or zero or whatever).

And “obvious” definitely comes closest to what you were objecting to, and many mathematicians try to avoid it these days (along with “clear”), but even then it has a legitimate use case, namely indicating when a proof involves no new ideas. To me, this means it is fine to use it within a specified context, like in a textbook or paper, where certain techniques are being used repeatedly and routinely, or certain kinds of background knowledge are assumed. And even then it’s usually meant for proofs that don’t rely on tricks or surprises or additional insights. I’ve been stuck on trying to understand “obvious” proofs before, and it wasn’t because I was stupid or the author was smarter than me, it was because I was _missing something obvious_ (in hindsight).

The recent Jacobian conjecture counterexample, for instance, is not trivial but arguably a bit embarrassingly (for the math world) close to obvious in hindsight. I still wouldn’t actually call it obvious though.

Your emotion isn’t invalid, it’s merely bad, assholeish, brings shame upon you. But it is “valid” in the sense that the reader of your comment can see that you are, at least, sincere in your gloating at another person’s despair.

“You shouldn’t find joy from things the way you said you do. Sounds like a you problem.”

Yes, yes, maybe (see OP’s blog post).

To my knowledge, none of the negative sentiment regarding AI has ever been directed at its medical applications. Maybe the AI companies should instead focus on those things.

I agree.

It’s not that surprising (to me) that it would recognize these features, in that the features it picks up on are intrinsic to the map. Once you have the map, which is generically of degree 3, there’s the locus where the map drops from degree 3 to 2, which contains a big hint because it pops out the equation for the discriminant locus of a cubic. Then there’s the other bit about H, which becomes more apparent from the formula after simplifying things a bit in terms of discriminant. I still don’t yet understand the rest of the calculation, but it’s visibly simpler after you notice the role of the discriminant.