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)?