ℝolliℵg M∀th Thr∑a∂

That's how it is for most people. I chose my grad institution knowing that it was really only good in the one area I wanted to study, so it's a good pedigree even if I'd studied, like, number theory it would have been a trash place to be. (Or any other discipline except philo & theology, it's not a very good place to do grad work in general, but it's a wealthy place so it worked out.) The big advantage of my well-established advisors was that they taught me, from my 2nd year on, how to talk to big shots, the senior faculty at other universities that I'd meet at conferences. I.e. networking, still the most important skill I learned aside from first-order "here's how you solve a problem" etc.

ILX - COVID-77

Woke up in the middle of the night and thought about R. L. Moore for a second. Ugh.

Now thinking about Paul Garabedian, a more pleasant memory.

what's wrong with Moore?

I had at least one undergrad prof who'd been a doctoral student of his. He told us a story of how, when Moore taught courses to engineers, he'd bring a loaded gun to class, and told the engineers that if any of them asked a question in class, he'd shoot them.

Heard a similar story from that son of a Nobelist I mentioned. Applied mathematician is hired at UT Austin. Shows up for first semester of work, is greeted by R. L. Moore sitting there with a shotgun his lap. “What are you doing here, son?”
“I came to teach <insert applied math subject here>.”
“Oh no you aren’t.”

haha

what's wrong with Moore?

I had at least one undergrad prof who'd been a doctoral student of his. He told us a story of how, when Moore taught courses to engineers, he'd bring a loaded gun to class, and told the engineers that if any of them asked a question in class, he'd shoot them.

Posts Whose Second Paragraph Answers The Question Raised In Their First Paragraph

;)

RFI: best way to express a half open range in a non-or-quasi-mathematical setting.

maybe...

integers: "x, x+1 ... y-1"
reals: "from x up to but not including y"

but if "quasi-mathematical" is like programmers or physicists then [x, y) is understood or quickly understandable for both integers and reals, and certainly a <= x < b is fine.

not exactly what you're looking for but maybe useful

https://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.html

Thanks, already went with your last suggestion.

HI DERE!

Does anyone read the Cantor’s Paradise section of Medium?

never heard of it before, but just read this nice post on concentration bounds https://medium.com/cantors-paradise/concentration-of-measure-the-glorious-chernoff-bound-1e96777cc29d

The few things I’ve read have been pretty good so far.

Twitter programming language enthusiasts are the absolute worst promoters of category theory applicability.

Who's the picture at the top of this thread a picture of?

https://www.youtube.com/watch?v=sdlWiDgvjAY

sometimes things work out well:

I taught a course in computational algebraic geometry this summer.

To high school students.

Here's how it went.https://t.co/fCASlEoExx

— Bill Shillito (@solidangles) August 3, 2021

Good stuff, especially leading up to this:

In short, we need to stop conflating logical foundation with pedagogical foundation.

I think this is good but I also think it is super unclear to me that "pedagogical strategies that work well in a small group of student selected specifically as self-motivated high math achievers" has THAT much to say about what K-12 should be doing generally. And of course the idea that school math should involve playing around, discovery, "why do we do it this way? what if we did it this other way? if that doesn't work, what went wrong?" rather than "follow these rules to get the answer" is exactly the aspect of Common Core that was hated by legislators and parents and to be frank lots of kids (though I still can't help feeling there has to be a way to do it right.)

Fair enough.

I want to look at his divide by zero thing later.

never divide by zero, it always ends badly

and yes, it absolutely depends on this being a schoolroom of the self-selectedly curious in a territory where the outcome stakes aren't especially high yet (in a bridge-will-fall-down car-will-catch-fire sense)

never divide by zero, it always ends badly

trying to vibe at the pole of a reimann sphere, just not happening man

I was trying to work out myself how to prove that pi is a constant, that all circles have the same ratio between diameter and circumference. I got stuck -- I couldn't figure out a way to prove that if there exists the same angle-side-angle values for two triangles, they are congruent. I looked it up in Euclid's Elements, but Euclid's proof only works when that applies for ANY given side. Is there a simple proof of this without going into the law of sines?

Found it, Book I Proposition 26 in Elements.

To me the definition of a circle implies that all circles are similar to each other so pi has to be constant.

I suppose using Euclidean methods you could use dilation and then superposition.

here’s one way to prove it using integral calculus

take any circle x^2 + y^2 = r^2

circumference is the arc length of the curve, which is equal to 2r times an integral not involving t (as here https://math.stackexchange.com/a/1049390)

not involving r*

Okay, someone take the Terence Tao masterclass and tell me what he says.

I never heard the term The Martians before.

I'm laughing so hard at this slide a friend sent me from one of Geoff Hinton's courses;

"To deal with hyper-planes in a 14-dimensional space, visualize a 3-D space and say 'fourteen' to yourself very loudly. Everyone does it." pic.twitter.com/nTakZArbsD

— Robbie Barrat (@videodrome) June 10, 2018

Lol

Old enough to remember when the thing was to watch Tom Banchoff rotate a tesseract to help see the fourth dimension.

https://www.youtube.com/watch?v=90olwwLdEYg

Hinton's a real one

who knows how to visualize a complex or even quaternionic one

Anyway I see what he is saying.

Category theorists are always wilding out on my timeline

I have just learned that it may not be related to category theory and is likely a byproduct of Twitter’s new recommendation features (I assume it’s inferring an interest based on following math people and following computer science people).

pic.twitter.com/maySTJd1wA

— depths of wikipedia (@depthsofwiki) April 18, 2022

What does Snopes have to say?

Surely there is a Medium article or two addressing this. I believe I may have gotten an email alert about one this morning iirc.

https://www.newyorker.com/magazine/2022/05/16/the-mysterious-disappearance-of-a-revolutionary-mathematician

https://www.youtube.com/watch?v=uqwC41RDPyg