Huge shout-out to authors who put humour, even very mild humour, in their papers. You keep me awake.

New paper published today! "A hierarchy of eigencomputations for polynomial optimization on the sphere", with Benjamin Lovitz: link.springer.com/article/10.1...

New paper published today! "The factor width rank of a matrix", with Shirin Moein and Sarah Plosker: www.sciencedirect.com/science/arti...

Happy belated pi day! Had a midterm in my Vector Calculus class yesterday, so I asked my students to compute some vector line integrals along pi: www.desmos.com/calculator/u... #ITeachMath #MathsToday

Now, two months later, Musk says that "Grok 3 is becoming superhuman" because Grok 3 obtained just as good as solution (i.e., an absolutely terrible non-solution) to this Putnam problem. Unreal.

I'm teaching Vector Calculus this semester (for the first time, somehow!) and making lecture videos to accompany the course. The first video is now up, with about 3 per week planned (35 to 40 total): www.youtube.com/watch?v=VbDE... The videos make huge use of @desmos.com #ITeachMath #EduSky

Happy New Year! Just like every year, there were tons of fantastic discoveries and theorems proved in Conway's Game of Life in 2024. This is a thread for my three favourites (and the context behind them to try to convince you that they're interesting). 🧵 #MathSky

There's been a bunch of claims (mostly on X) that ChatGPT did great on this year's Putnam math competition. Let's do a thread to talk about it! 🧵 #MathSky

It seems like a tradition is emerging here, and it is out duty to maintain it. So here is my part announcing the publication of our review in semidefinite programming for characterizing quantum correlations @dulwichquantum.bsky.social journals.aps.org/rmp/abstract...

The Putnam math competition happened this past weekend! Made a video of how to work through question A1, which (not surprisingly) was the most "rote" of the bunch. I thought questions A6 and B1 were really neat too. #ITeachMath www.youtube.com/watch?v=ccu-...

It looks like Overleaf's new AI writing tools don't like the notes that I make to myself while writing papers.

Had a recent research project where we had to evaluate this hideous sum. Convolution to the rescue! Made a video to talk about how it works (or at least how some similar but simpler sums work): www.youtube.com/watch?v=aIj6...

Overleaf's down, so I'm cancelling research for the day. Everyone go home and play Slay the Spire.

Me, a moron: I don't need a local TeX installation, Overleaf works so well and is so easy! Overleaf: like every online service that exists, goes down from time to time. Me: shocked Pikachu.

There are lots of standard examples of binary operations that are associative but not commutative (e.g., matrix multiplication). But I don’t know of a better example of the opposite (i.e., commutative but not associative) than Infinite Craft: neal.fun/infinite-cra...

Having links to relevant lecture videos included in the margin of the lecture notes is one of the cooler things I’ve seen. Those are gorgeous.

The On-Line Encyclopedia of Integer Sequences (OEIS) is hiring someone to manage the crazy number of sequences that it has to review. If you're a US resident with a math PhD, give it a look! Applications due Jan. 25, 2025. neilsloane.com/doc/OEIS.ME....

I wrote a review of Jane Hawkins' new book "The Mathematics of Cellular Automata", which is now online. tl;dr: It would be fun to teach a CA course from this book to students who have already taken Real Analysis. www.tandfonline.com/doi/full/10....

Fun fact: my advanced linear algebra textbook has a page about exactly this! Screenshot attached.

Back making math videos! #ITeachMath #EduSky I'm teaching calculus this semester, so I'm filling in some of the gaps in my calculus playlist. Animations made with #Manim. www.youtube.com/watch?v=Afc4...

Little known fact: the Bloch Sphere is named after a famous Swedish physicist Felix Sphere.

What are everyone's favourite instructional and/or weird examples to illustrate how much weirder functions of 2 variables can be than functions of 1 variable? ♾️ I'll start with two of my favourites (1/3).

Does anyone on #MathSky / #ITeachMath have a favourite way to illustrate and/or motivate mixed 2nd partial derivatives of 2-variable functions?

Recent paper with Sarah Plosker about Laplacian integral graphs is now published! Open access: www.sciencedirect.com/science/arti...