I am languid & bedeviled & hate nonassociative algebra

If my history of mathematics class were automatically closed captioned, then today we are going to discuss Day Cart and Firm Ah.

I remember when my very-out-of-touch-with-reality undergraduate differential geometry professor was baffled that no one in the class had ever heard the phrase "differential form". I guess he thought the prerequisite to his class was having already had the class.

It's funny how whenever I read that so-and-so has a very influential substack, my brain immediately tunes out.

*sigh* Sometimes being unable to have incorrect opinions is a real curse.

Eating M&Ms for lunch and pretending I can tell the difference between the tastes of the different colors.

Thanks to everyone who played along.

The first and second options are definitely the most common.

The third is still used in parts of central Europe. I have a colleague who uses it, much to his students' confusion.

The fourth is there just to mess with you all. 😁

The set of all x such that P

1️⃣ <a href="https://poll.blue/p/grBlDn/1" class="hover:underline text-blue-600 dark:text-sky-400 no-card-link" target="_blank" rel="noopener" data-link="bsky">{ x | P }
2️⃣ <a href="https://poll.blue/p/grBlDn/2" class="hover:underline text-blue-600 dark:text-sky-400 no-card-link" target="_blank" rel="noopener" data-link="bsky">{ x : P }
3️⃣ <a href="https://poll.blue/p/grBlDn/3" class="hover:underline text-blue-600 dark:text-sky-400 no-card-link" target="_blank" rel="noopener" data-link="bsky">{ x ; P }
4️⃣ <a href="https://poll.blue/p/grBlDn/4" class="hover:underline text-blue-600 dark:text-sky-400 no-card-link" target="_blank" rel="noopener" data-link="bsky">{ x s.t. P }

📊 Show results

While it's nice that we honor 18th century Swedish astronomer Anders Celsius, I can't help but wonder how Joe Centigrade felt about it.

Me to students: It's fine to use the rotated A, rotated E and other symbols for taking notes, but please write in complete unabbreviated sentences in your homework. For clarity, I'll try to do the same when I write on the board.

The board, 20 minutes later:

Thm: G cyc gp, H ≤ G => H cyc.
Pf:...

Reading over my old slides from my history of mathematics course and I found this gem:

"We will avoid the debate over whether the Renaissance was real or just an invention of 19th century historians. We will use the term as a marker for the period from roughly 1350-1550."

Nah

Wishing we could revive the word "sursolid". It's a wonderful word.

I'm not going to post or link to it, but I just read an email addressed to Epstein where the writer, a neuroscientist, wrote: "Jeffrey, I remembered that you are an extraordinary mathematician...." 🤮

Right! Time to grade this homework assignment the students turned in two weeks ago!

*continues to scroll bsky*

How to humanize a proof found by an automated theorem prover that worked on it for several days:
1) Look at the last line. The prover proved "for all x,y, x=y".
2) Go to the beginning. There is a typo in one of the hypotheses.
3) Stare at a blank wall. Regret your life choices.
4) Repeat ad nauseum.

"...Aristarchus has brought out a book consisting of certain hypotheses... His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit..." -- Archimedes, _The Sand Reckoner_

The associate dean just sent around a message asking if anyone still uses clickers in classrooms. My brain immediately went to one particular kind of clicker, briefly wondering how anyone would use one in a mathematics class.

Quick explanation of what it feels like to learn more advanced #mathematics. Specifically, how do you answer the question

"How many intersections do two algebraic varieties have?"

You could probably do this with any math subject tbh...

#mathsky #maths #scisky

When my advisor taught calculus, he used the Stieltjes integral whenever possible. For "substitution" or integration by parts, he refused to introduce new variables, he'd just move stuff past the d, e.g.,

\int x cos(x) dx = \int x d(sin(x)) = x sin(x) - \int sin(x) dx = x sin(x) + cos(x) + C

Let p(n) denote the partition function, the number of ways of writing n as the sum of positive integers.

Heffernan-MacHale Conjecture: If p(n) divides n!, then
n ∈ { 1,2,3,7,9,10,11,12,14,15,16,17,18,19,20,21,24,28,32,33,39 }.

Verified for n ≤ 2x10^6. See oeis.org/A046668

I'll let someone else write verses for analysis, topology, etc.

Neugebauer on the purpose of historical studies

To all who teach matrices/linear algebra, I highly recommend vol. 24, issue 1 (Jan. 1993) of The College Mathematics Journal, a special issue dedicated to the teaching of linear algebra. Different ways of interpreting matrix multiplication is one of the themes of the issue.