Interesting, dropping this link here for others: https://treecalcul.us/

He really likes working in informal categories (like his “ologs”) but I haven’t taught from it yet so I’m not sure if it is more or less confusing to introduce categories that way.

The Little Schemer/Typer could be used as a preparatory text to gear one up for HoTT.

It also has the advantage of being a bit more applicable to functional programming languages, maybe even more so than Mac Lane’s Categories for the Working Mathematician (which I sometimes see suggested to mathematically-inclined Haskell novices).

The textbooks they use in that course are written in modern notation and are accessible to a knowledgeable reader; neither can be said of the Principia Mathematica. The archaic syntax is a serious issue.

Alas.

> You can only throw up your hands and say "this isn't tractable" if tractability is 0, i.e. the charity doesn't help at all, no matter how much money you spend on it.

Even I don’t believe this. You’ve gone too far in the other direction and made tractability a useless metric.

In practice, it can be used as a fully-general counterargument to supporting most charities, since decisively and completely solving problems in this space is rare. It’s harder to split a problem into component parts than it is to throw up one’s hands and say, “well, this isn’t tractable.”

I think it’s pretty likely. Contrary to all the negative things said about mathematicians in this thread, in my experience they’re mostly not profit-driven (for the ones that are tend to filter out of academia during grad school, it’s a high-effort, low-reward environment).

Tao does not seem particularly threatened by AIs doing math, and I trust his judgment.

For instance, I found insertion sort to be the most effective at sorting papers when I was grading. . . at least, as long as the students bothered writing their names on their homework.

My coworkers holding such degrees would beg to differ.

> And if you are trying to snarkily describe an MS, then most MS programs are too short.

It wasn’t snarky, it was a listing of common points between the two. I don’t see what distinguishes this from a MS.

A year still isn’t enough time to write a doctoral-level thesis, so if the I-PhD is supposed to represent a “longer MS” then it’s still insufficient.

There’s already a 3-4 year advanced degree in the United States with an optional thesis component that companies in relevant industries can intervene in and direct if they so desire.

So why are they calling it a doctorate? I don’t see the point. It’s not like the NSF under this administration is particularly fond of STEM doctorates.

I’m open to any theories about what the real point of this is.

It’s the act of comment warring that is pointless. [X/Y] partisans are not intellectually curious about statements coming from a [Y/X] partisan. Nobody’s minds are going to change either way.

There presumably some third parties who could hypothetically be swayed, but from what I’ve seen they’re few and far between.