When I was in high school, they put on lots of plays, but I don't actually remember the theater department putting on any musicals. But now it seems like high schools and middle schools put on mostly musicals! I don't understand why there's been this shift. (At Heebie University, I never attend anything but I have the impression that they put on mostly plays.)

Is this an actual trend, or just a weird sample of school districts? (I'm personally a little bummed about it, because Hawaii likes to act but does not like to sing.)

I think this would be an interesting survey question: "What's the minimum amount of money would you need to get paid to be happy at your job for a long, long time?"

I imagine that answers would sort into three categories:
- "I basically like my job, so for [amount that feels UMC to the individual] I'd happily do it forever."
- "My job is fairly shitty, but I'd do it indefinitely for [amount that feels very wealthy to the individual]."
- "My job is so awful that it would take Scrooge McDuck money to keep me here forever."

What I'd be curious is to how this falls out by profession.
- which jobs are well-sorted, ie most people are in category 1?
- which jobs are semi-well sorted, ie there's a bimodal distribution of people who love it and people who are there by circumstance?
- which jobs are roundly loathed (obv some are obvious, but maybe some aren't)
- what happens when you ask this question to people in professions that are generally just driven by greed and not much else?

I assume there are plenty of econ papers out there answering this question, but it's easier to scratch my belly and pretend I've thought of something novel than to go check.

Also, I suspect Unfogged answers won't be so interesting, because I suspect we're all mostly in category 1. (Or category 4, "I'd also be happy retiring and puttering about and entertaining myself on a shoestring budget.")

*It kind of bugs me that "threshold" only has one h. I almost kept my misspelled version in just to troll you all.

I kinda regret not posting about Greta Gerwig and Margot Robbie getting snubbed by the Oscar nominations yesterday, when it was new news. I'm seeing lots of jokes about how Ryan Gosling getting nominated for Best Actor while those two get passed by is basically the plot of the Barbie movie.

My parents finally got Covid for the first time, and so far they're fine, have access to Paxlovid, etc. Four years is a pretty good run!

I think of four years as being a unit of measurement in my life, partly because it's the traditional length of high school and college, and partly because of the spacing of our kids - #1 and #3 are four years (and three days) apart, #2 and #4 are four years (and eight days) apart. So the world melted down just about 1 Life Unit ago. Around this time of the spring, Italy was mid-crisis or maybe still descending, but it wasn't yet in the US in major numbers?

Sure was a surreal time. Happy anniversary!

Also, I forgot to note last year that it was the 20th anniversary of the blog. HAPPY THAT, TOO!

Nick S. writes: This is impressive:

A system developed by Google's DeepMind has set a new record for AI performance on geometry problems. DeepMind's AlphaGeometry managed to solve 25 of the 30 geometry problems drawn from the International Mathematical Olympiad between 2000 and 2022.

...

Evan Chen, a former Olympiad gold medalist who evaluated some of AlphaGeometry's output, praised it as "impressive because it's both verifiable and clean." Whereas some earlier software generated complex geometry proofs that were hard for human reviewers to understand, the output of AlphaGeometry is similar to what a human mathematician would write.

For many years we've had software that can generate lists of valid conclusions that can be drawn from a set of starting assumptions. Simple geometry problems can be solved by "brute force": mechanically listing every possible fact that can be inferred from the given assumption, then listing every possible inference from those facts, and so on until you reach the desired conclusion.

But this kind of brute-force search isn't feasible for an IMO-level geometry problem because the search space is too large. Not only do harder problems require longer proofs, but sophisticated proofs often require the introduction of new elements to the initial figure--as with point D in the above proof. Once you allow for these kinds of "auxiliary points," the space of possible proofs explodes and brute-force methods become impractical.

[T]he DeepMind team developed a hybrid architecture. There's a symbolic deduction engine that mechanically derives conclusions that logically follow from the given premises. But periodically control will pass to a language model that will take a more "creative" step like adding a new point to the figure.

Heebie's take: Wow, this is pretty wild.

At the level of teaching, I believe that you teach calculus, etc, in order to train rigorous thinkers. The content is just grist for the mill (aside from a few who will go on to grad school). But research mathematicians aren't proving theorems in order to train their brains - they're trying to cover new ground and make new connections. It hadn't really occurred to me that AI could do this better someday. What happens to research mathematicians if AI becomes better and more creative at proving new things?

If I were a research mathematician (which I'm not), I'd find it really dreary to contemplate a career shift from problem-solving to trying to verify wild proofs that AI comes up with. I suppose you could focus on the clever programming to generate such proofs, but that also doesn't feel like regular old math to me.