Question for #MathSky: What is your favorite result, trick, or technique involving generating functions? Whenever I ask a question like this I always learn something new.

I've added an update to reflect some of what we are learning, which is basically that the rule may be applied on a more limited basis than first announced and that higher ed may be partly exempted. But we still don't know how this will work and it is causing chaos.

Here's what a Mississippi judge wrote in 1979 about school vaccine mandates. Things have changed. www.gravityisgone.com/mississippi-...

I'm 6'1" and 222 lbs. So if I gain 5 lbs before my next physical, I'll have a BMI index of 30 and will thus be eligible for a COVID vaccine. Or I could just not exercise for a few months and claim high risk due to "inactivity." Which should I shoot for? Make America Healthy Again! 🙄

Hey #MathSky, have any of you read this book? "An engrossing saga of a young mathematician caught between two countries, two cultures, two eras, and two loves. Set against the violent turmoil of the Chinese Cultural Revolution..." www.penguinrandomhouse.com/books/690668...

The pawpaws are ripe! The only temperate soursop in the world.

If you could get a crib in any five cities (five cribs) of your choice in the world, which would you choose? - NYC - Cape Town - Santa Barbara - Tokyo - Reykjavik

When you unexpectedly run into colleagues because two workshops at the same institute happen to be scheduled during the same week. @mathprofcarrie.bsky.social @icerm.bsky.social

Excited to be heading up to Rhode Island for the Illustrating Mathematics workshop at ICERM! Looking forward to seeing @mathzorro.bsky.social, @msmathcomp.bsky.social, @mathgrrl.com, @stevejtrettel.bsky.social, ‪@peterkagey.com, @henryseg.bsky.social. Did I miss anyone?

Same energy

ChatGPT 5.0 was released today. I was curious to see how it would handle a few visual algebra questions. Answer: not good. I'm safe for at least a few years! This was its attempt at constructing the subgroup lattice of D₄, with the group D₄ at the top. (It's in the middle.) It's also missing 2.

Four types of figs from my trees: Celeste, Brown Turkey, LSU Gold, and Chicago Hardy (the purple ones).

I picked nearly 11 pounds of figs from my trees this evening.

Vaccination schedules on the CDC website have already started changing under RFK Jr. So we published a guide to the evidence-based vaccine recommendations in place *before* all 17 members of the advisory panel were abruptly dismissed by the new admin. www.scientificamerican.com/article/see-... 🧪

Question for #MathSky: what are some fundamental results in ring theory that fail w/o the assumption of unity? Here are 3 examples: #1. {r₁x₁+⋯ +rₙxₙ : xᵢ∈X} = ∩ ideals that contain X Ex: X={2} in the ring R=2Z[x], b/c 2∉LHS but 2∈RHS #2. maximal ideal => prime ideal Ex: I=4Z in R=2Z 1/2

I will definitely be using this example the next time I teach abstract algebra to warn students of using AI. The claim that 2x ∈ (2,x) but 2 ∉ (2,x) and x ∉ (2,x). is gold! What are your favorite examples of things like this?

I’m celebrating the 4th of July this year by working all day in the office and drinking tea with a cricket match in the background. ‘Merica! 🇺🇸🇺🇸🇺🇸

NEW: NSF will be kicked out of their building. Announcement will be made tomorrow by HUD Sec. and Governor of VA. HUD will take over the NSF building over the next two years. NSF staffer: "There is no planning for NSF, no identified future location, appropriation for a new building or a move."

I submitted finalish drafts of Chapters 1-6 of "Visual Algebra" to the AMS, and have stable drafts of the other chapters. Is anyone interesting in reviewing it? Either formally or informally. I'm sure the AMS offers something for such a service, like book credit. 1/2

Seriously?!? [Yes, I've Googled this issue, and it's convinced me to switch from using mdframed to tcolorbox.]

Stephen A Smith at ESPN is apparently a topologist as well! #MathSky

If you had to pick a math word to put in the Scripps National Spelling Bee, what would it be? The first one that comes to mind for me is “Nullstellensatz”, but I’m sure there are better ones. #MathSky

Read the replies! 😂😂😂

Fascinating lecture by Rudin—“Set Theory: An Offspring of Analysis” www.youtube.com/watch?v=hBcW... In brief, it describes how studying the wave equation led to trigonometric series, which eventually led to Cantor’s introduction of limit points and the notion of countable sets.

Graduate Student, Jonah Botvinick-Greenhouse, Cornell University, who recently competed in the 2024 World Juggling Federation Ultimate Championship, discusses the mathematics of juggling. Watch the full video here: www.youtube.com/watch?v=r2iO... Read more: www.ams.org/publicoutrea...

I’ve been making #WaterKefir with the elderflower that’s growing in my backyard orchard, with some lemon and honey. It’s really good!

Presidential budget is out. Here's NSF. Biggest cut, by amount, is $1 billion, or 66.8%, from MPS (Physics & Math directorate). nsf-gov-resources.nsf.gov/files/00-NSF...

Hi Blue Sky! I edit the Journal of Humanistic Mathematics. We publish articles, essays, #fiction & #poetry on doing, teaching & living of #mathematics. So far we had more than 700K full-text downloads of our content - why not check us out? scholarship.claremont.edu/jhm/ #math #openaccess #mathart

Get Ready for a Summer of Playful Math ALL my math game books are on sale now at the Playful Math Store. What a great way to prepare for a summer of mathematical play! Check it out!

Here's my explanation. Feel free to discuss! Descending subnormal series are MUCH more natural than ascending ones. Consider the chief series SL₂(ℤ₃)⊵Q₈⊵C₂⊵C₁. We can say: SL₂(ℤ₃) is an extension of C₃ by Q₈... ...which is an extension of V₄ by C₂... ...which is an extension of C₂ by C₁. 1/6

This morning, my 6-year-old daughter said: "I love you ℵ_{Tree(googolplex)} much!" Quick reference: googolplex = 10^{10^{100}} Tree(1)=1, Tree(2)=3, and Tree(3) is absolutely bonkers [see www.chrisliss.com/p/tree3 ]

A portrait of an Alexander Horned Sphere I drew for a professor’s birthday

Question for #MathSky: Given an exact sequence 1→ N→G→Q→1 of groups (or whatever), we say that "G is an extension of Q by N." Why isn't it "G is an extension of N by Q"? [I have an explanation, but I'd like to hear yours. I suspect I'll learn something new...]

Want to dissuade your advanced math students from using AI for their homework because it can get even the most basic things embarrassingly wrong? Show them this, from May 2025. #MathSky

Mussolini’s Italy expelled university professors who opposed fascism. Franco’s Spain replaced university academics with regime loyalists Nazi Germany removed Jewish professors & left-leaning scholars. Academia is a threat to unified ideology. It’s why fascist regimes always target it.

Incredibly bad (changes to N.S.F. funding for math):

NSF Physics was cut by 85%, basically wiping out most of its capacity for supporting research. NSF Astronomy was cut by 53% Undergrad education was cut by 71% and research on learning by 79% Graduate education was cut by 100% to ZERO. #GiftLink ⚛️🔭 www.nytimes.com/interactive/...

Harvard today, your institution tomorrow. It's all part of the Project 2025 plan to destroy high education in America. All leading US universities depend on federal funding and tuition dollars from international students. They severely curtailed the former. Now they're eliminating the latter.

For the past like two weeks I have been working on this three-post set about what I am calling pqr-groups. Post #1 is a pair of results that feel "weird" in the Ben Blum-Smith sense, both of which I have discussed On Here before: rhinopotamus.github.io/2025/05/20/w...

👊 🇷🇴 🔥

I’m seeing a lot of misinformation and disinformation on here about the new Pope. Just to clear things up: he’s not the first mathematician to hold to the title!

The votes are in, and our next takeover will be..."The Catholic Church"! What should our first step be?

Fellow mathematicians, we did it! Kill screen reached! 🎉🍻🍾 We can now shut down the Premier League. There is no need for it to continue anymore. What should we go after next? #MathSky

The Vatican has the chance to do the funniest thing…

Today is the last day of the #Masters, and among the top 3 on the leaderboard are a former math major (Conners) and physics major (DeChambeau). Let’s go nerds!

This alone should be an impeachable offense.

I'm not sure which convention I dislike the most of these two...

At the age of 44, you'd think I'd know better than to regularly stay up until 2am, wake up at 6:45am to take my daughter to school, not exercise (at least so far in 2025), and skip breakfast in lieu of a large thermos of strong coffee, and yet... ⚰️

Question for #MathSky: do you have a favorite exercise involving the Sylow theorems? These are "show G can't be simple": 1. |G|=84: show n₇=1 2. |G|=12: show n₂=1 or n₃=1 (not enough elts for both) 3. |G|=24: let G act on cosets of the index-3 subgroup, take kernel of G→ S₃ 1/2

Homemade #WaterKefir, at t=0, 24, and 36 hours in the fermentation process. I love how the buoyancy of the fruit changes. Every 2 days, I get a new fresh batch.