Was watching a Youtube video which looked otherwise interesting about the history of housing in the US. Some footage looked off, never saw the speaker at all, and some facts seemed iffy. Then the voice-over referred a McMansion , pronounced "Em-Cee Mansion." That was the end of that.

On top of this, we also had a counterexample from AI from a major conjecture of Grothendieck that has gotten less attention from the public due to its technica nature xenaproject.wordpress.com/2026/07/20/h... . But Jacobian conjecture is major enough that I discussed it when I taught linear algebra.

„This really is a crucial moment. The firing of Fedorov, if it is allowed to stand along with the keeping of Syrskyi, will not mean that Ukraine will lose the war. However it will mean higher casualties, more corruption, less flexibility and more Soviet style thinking. I can think of nothing worse.“

Now that millions of electric vehicles have been on the road for a decade or more, we have the data to check in on how their batteries are holding up. Quite well, it turns out.

90s X-Men X-97 are depicting roleplaying game where all the players bought in to the worldbuilding where everyone was going to have mutant powers. But Storm's player really wanted to play a weather cleric, and while she agreed to fluff her powers as mutation she's not completely buying into it.

Don't want to speak ill of the dead, so getting this Mitch McConnell take out now. He saw Trump with complete clarity, as a danger to America, but protected him anyway. Perhaps more than anyone, he had the power to end Trumpism, but chose party over country. donmoynihan.substack.com/p/jan-6-and-...

JZ has new paper in the Journal of Integer Sequences: cs.uwaterloo.ca/journals/JIS... where I show that any primitive non-deficient number must have a small component and ask how much that result can be tightened.

If you want to see a tangible example of the shrinking business docket. Here, we have two cases raising identical personal-jurisidction questions against the same defendant on materially identical facts that came out opposite ways where both sides requested review. And the Court denies both.

This made for fascinating reading.

This is a great thing Justin does and it deserves more attention/participation.

Got @zachweinersmith.bsky.social 's book "Sawyer Lee and the Quest to Just Stay Home." We are getting it as a gift for my niece but I wanted to read it first. I was laughing from the first page until the end. On pg 73 I was laughing so hard I dropped the book and just lost it for a good minute.

For once, I'd like to see a crank who claims to have solved a major problem that is genuinely major and also isn't well known to the general public. We need cranks who claim to have solved the Inverse Galois problem or claims to prove that Berkeley cardinal are not consistent.

Trump is so angry that Iran will not give him a deal that he is telling the US military to commit war crimes. Destroying a drinking water facility is not an attack on a target of war, but a mafia-style operation designed to harm the Iranian people. www.nytimes.com/2026/06/10/w...

An additional annoyance from the new Google AI search summaries. Trying to find a copy of a specific paper so I typed in the paper title in quotes. Google gave me a summary calling the paper "seminal." The paper in question had exactly one citation on Mathscinet.

The Trump admin continues to destroy science and academia in the US. It claim to care about illegal immigration but then puts in place rules that make legal immigration more difficult. This is one more way making people visiting to degrees in the US have difficulty www.ams.org/news?news_id... .

I have been informed by one of my incoming debate team captains that she has talked with a lot of students at other schools, and apparently our tournament has developed a reputation for having "deeply unserious" debate topics. Now I feel like for next year's tournament I have a reputation to uphold.

Let P(n) be the largest prime divisor of n. For example, P(30)=5. Erdos asked if for any pair of distinct odd primes p and q is there an n such that P(n)=p and P(n+1)=q?

The claims that current LLM systems are mere "stochastic parrots" (ignoring how this undersells parrot cognition) or are just "plagiarism machines" should be obviously false to anyone paying attention to their usefulness for math research at this point www.quantamagazine.org/the-ai-revol... .

Working on a project with a student. I asked her as a warmup to write a program which finds abundant numbers and find the first few odd abundant numbers. I and my twin wrote a similar thing when we were that age; our program took hours to run. Now, in C on a modern computer it takes milliseconds.

My student made some tricky log equation problems: drive.google.com/file/d/1Xwso... and drive.google.com/file/d/1GyoN... . All of these are tricky problems but with reasonably nice numbers for answers.

Problem I did with my Algebra 2 students today: Simplify (log_2 3)(log_3 4)(log_4 5)(log_5 6)(log_6 7)(log_7 8) .

Trump's comments on Iran are not just morally reprehensible. They are also strategically and tactically bad. This sort of thing is more likely to make the Iranian on the street support the current regime and hate the US. This sort of thing makes the fall of the current Iranian regime less likely.

This Trump message below is getting lots of attention but one element is worth noting that isn't getting a lot of attention: "Open the Fuckin' Strait" reads someone trying to imitate Trump. I'm not aware of him using an apostrophe that way. Staffers trying to write in the style of their Mad King.

**Please share widely!** Announcing CTNT 2026: the Connecticut Summer School in Number Theory, and Research Conference! June 1-7, at UConn. Applications (for the summer school and/or conference) are now open thru our website: ctnt-summer.math.uconn.edu

JZ wrote a short story: "The Ultimate Kitchen Sink: An Oral History of the Last Days of Man." joshuazelinsky.dreamwidth.org/12254.html

This is the Noperthedron. A portmanteau of “nope” and “Rupert,” it is the only known shape that does not have a trait called Rupert’s property. No matter how you bore a straight tunnel through it, a second Noperthedron cannot fit through. www.quantamagazine.org/first-shape-...

Teaching summer enriched precalculus. Midterm is tomorrow. One thing I did today was to do an "Um, Actually" style game with the students where they had to say what was wrong with each statement. Here's my statement list: drive.google.com/file/d/1-8qk... .

My D&D players were going through a dungeon that had a long corridor with a series of different traps each activated by a pressure plate. They had spotted the pressure plates and were carefully walking by. Then the third plate reached out and attacked them. Turns out it was a pressure plate mimic.

Cato has published my comprehensive review of the ~240 Venezuelans the US government renditioned 2 months ago to Salvador’s notorious prison. We identified FIFTY who came legally, never violated any immigration law, but are imprisoned at the US government’s request and at US taxpayer expense.

According to mathematical legend, Peter Sarnak and Noga Alon made a bet about optimal graphs in the late 1980s. They’ve now both been proved wrong. Leila Sloman reports: www.quantamagazine.org/new-proof-se...

arxiv.org/abs/2504.10394 A neat paper by Paula Roba and Karlis Podnieks just came out showing that the digits of pi (and e and some other constants) don't actually seem to follow a lot of statistical tests we might expect if they were genuinely random.

My Algebra II students have been making tricky log system problems that have nice answers. drive.google.com/file/d/1Iu6A... has their problems and answers. They had a lot of fun making these, and some of these are just fiendish.

Challenge problem I'm considering giving to my Accelerated Algebra II students: Can you find all natural numbers a and b such that log_3 a + log_9 b = log_3 (a+2b) ?

The Hebrew word tachash is mentioned in Exodus 26 as some form of animal whose skin was used to make the Tabernacle. The most common translation of Tachash is dolphin although others suggest some other sea creatures. 1/2

A fun problem I just saw today: Find all primes p such that p+1 = 2x^2 and p^2+1=2y^2 where x and y are both integers.

Another PROMYS for Teachers workshop tonight. There were some really fun show-and-tell presentations: * Shapes of various shadows of polyhedra. * How to see every positive integer coprime to 10 has a multiple that consists of all 9s (or 1s?). * The existence of “printer errors” like 2^5 9^2 =2,592.

Let G be a graph. We will say it has property M if every maximal clique of G is the same size. Is there a standard name for property M?

With everything else the Trump administration is doing it is easy for things to get lost in the noise. www.huffingtonpost.co.uk/entry/cdc-wh... is an example that is petty, vindictive, and will like result given authorship ethics rules in the destruction of ongoing nearly finished scientific work.

Republicans who said loudly that Biden wasn't supporting Ukraine enough, maybe we could get your voices again to help Ukraine? Just a thought.

On Friday night, HHS ordered CDC to take down all flu vaccine campaign materials from its website. Materials are starting to come down. For example, a campaign explaining that flu shot can reduce flu severity from "wild to mild" is now offline. Left image is from Friday, right is now Meanwhile...

A review problem I gave my Algebra II Accelerated students in our polynomial unit. Factor 81x^4 +216x^3 +216x^2 +96x + 15. My hint was that this is almost in the form of Pascal's triangle but not quite.

A problem for my Algebra II Accelerated students: Find all x and y such that 1/(x+y) = 6/(1/x + 1/y), 1/x = 1/y +1, and x^2 = 1/(16y +1).

My twin gave an interview www.wypr.org/show/midday/... .

Found out about a neat open problem today: Does there exist a 4th degree polynomial p(x) such that all roots of p(x) are distinct integers, and the same is true for all non-zero derivatives of p(x)?