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.

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.

> [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.

Comments URL: https://news.ycombinator.com/item?id=49346192

Points: 7

# Comments: 1

If you look closely, you can find a mention of the n=4 Burau representation in it, and the fact that it "remains an open problem" to find elements of its kernel, i.e. to determine whether it is faithful.

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.

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.

There was a little-known sequel to SimTower called Yoot Tower (named after Yoot Saito). It was a commercial flop, but I played it in the 2000s and again in the 2010s and very much enjoyed it! It had a lot of added customizability (more choices of restaurants and shops, for one thing). I would love to see that game recreated.

https://en.wikipedia.org/wiki/Faltings%27_theorem

The reason for the confusion is that a smooth, projective plane curve of degree d has genus (d-1)(d-2)/2, which is 2 or greater starting at d=4. Hence the phrasing in the article, which is missing the “smooth, projective” hypothesis. The equation y = x^4 doesn’t define a smooth curve when extended to the projective plane, because it has a singularity at infinity.

- rauenes: ravens

- “all that heard him were adrade”: I’m guessing it means “were filled with dread”, maybe “were adread”

- I think deme is actually a conjugation of the archaic verb “to doom”, as in “I doom thee to the death”

- “none shall thy biwepe” would be roughly “none shall beweep thee”

Aside: typing this is hard on my phone, it’s so close to modern English that nearly every word gets autocorrected.

I also very much appreciate that they can natively connect to iPhones (this is also essentially the main reason I have an iPhone). This makes phone calls and music and podcasts very easy. (Whereas up until 2017, I used to dread phone calls.)

I actually tried Phonaks briefly in 2022 and hated them. Lots of controls to fiddle with (some with oddly unintuitive names), but that meant I was constantly trying to adjust it and was rarely able to just exist in the moment. I found them markedly worse in noisy environments - I basically couldn’t have a conversation in a restaurant.