I am super pumped to be hosting the 138th Carnival of Mathematics, a monthly round-up of great stuff on the internet that has to do with math. Last month it was hosted over on the AMS Blog on Math Blogs by Anna Haensch (who also has a lovely podcast called The Other Half ) and Evelyn Lamb (my fairy blogmother who also writes for Scientific American, Slate, etc.). Curiously, the first thing that came up when I looked up “138” was a 1978 song by the horror punk band The Misfits: https://www.youtube.com/watch?v=SOqVs-K1eEo

A little bit catchy, but not quite my cup of tea. What is my cup of tea? An integer sequence that does not appear in the amazing OEIS! 138 is the smallest product of three primes such that the third is the concatenation of the first two: so 138 is , 777 is , and 4642 and 10263 are the next in this sequence (I applied for an account to OEIS to submit this, so if you find a smaller one or the next several in the sequence let me know). So off we go, to venture into the great unknown (aka the internet)! This month we have a fun mix of grammar, history/sociology, math, and games!

- First,
**grammar:**Manun Shah over at Math Misery [which hosted CoM#136] posted Does 11=8 + 3? to chat about linguistics and mathematics. If you love those memes about the Oxford comma, this post might be right up your alley. My favorite sentence: “I bought orange juice and dishwasher detergent and drank it for breakfast.” He argues we should think more about linguistics when teaching math, and the implicit biases that language might have on students as they learn mathematical reasoning. - Also in grammar, Thomas Oléron Evans of Mathistophiles posted Understanding an Abused Unit: The Kilometre-Hour, which delves deeper into a specific example of how common language can hurt mathematical understanding, and he uses a DELIGHTFUL example of turtles. Favorite sentence here: “Unless they sidestep across the beach, of course, like some sort of synchronised reptilian dressage.” Here’s an amazing graph from his example:

- Keeping up with his fun theme, Thomas submitted a SUPER FUN
**game**by David Peter called cube composer which is all about functions. Do please do go play it! It’s so fun! It’s an intuitive individual puzzle game, and you can fly through the levels. It also remembers your progress, but you can skip levels if you want too. Here’s a screenshot of me picking random functions and not solving the puzzle:

- A high school math teacher friend texted me about another game called Square It on a website for math educators supported by the University of Cambridge. We proceeded to lose, lose, lose, and continue to lose against the computer. I played against my spouse a few times, and he won his first time. Those darn programmers and their algorithm-minds! For the record I did eventually win. This one is faster and lighter than cube composer, and it offers different mathematical questions to think about in different size grids.

Square It! is also great to play with kids. Two more submissions are also **kid-friendly. **

- Brent Yorgey of Math Less Traveled submitted his post about Making Tesselations, which delves into the math behind the delightful new children’s book Tessalation! that I will definitely be reading to my toddler. In his post he also talks about ants on a doughnut, and y’all know how we mathematicians love our analogies to lean toward the absurd. Here’s a wonderful joke Brent nonchalantly sneaks into his post: “The ant is so small that it can’t tell that the surface it lives on is curved. To the ant, it just looks flat. (You may know some tiny creatures in a similar situation who live on a sphere.)” So fun.
- Matthew Scroggs submitted a post dear to my heart, written by Belgin Seymenoglu over at Chalkdust Magazine: an ode to the delightful half hour film Donald in Mathemagic Land. The post includes a link to the 1959 cartoon, which I’ve watched many times since I first saw it when I was 15. I guess this is a fun month, because I really really recommend watching this cute and funny cartoon that includes actual math in it.

Now for a sort of random assortment of history/sociology/whatever posts that have to do with math:

- Paul Plowman wrote a 2 minute 20 second guitar song using the number
*e,*and posted about it over on his blog as Transcendental Music. Sort of a silly but fun little exercise like memorizing digits of , and the riff sounds nice. - Poppy Brady submitted a story she wrote for The Voice about Nira Chamberlain, titled Teachers said I could be a boxer, but Never a Mathematician, one of those feel-good stories about mathematicians. One fun quote by Chamberlain: “I also like what British mathematician Sir John Kingman once said that ‘mathematicians are better if they stay a bit childish and play the game as a game.’” I think that keeps in line with our theme this month!
- Over in
*Nature,*Davide Castelvecchi wrote a news story about how the Majority of mathematicians hail from just 24 scientific ‘families’, a result by Floriana Gargiulo who analyzed the Mathematics Genealogy Project. Every grad student has used the MGP to stalk their advisor/potential advisor to see their lineage, and you can print out a tree and give it to your advisor as a defense present! So it was fun to read about someone actually analyzing this trove of data. - Finally, saving the best for last, the brilliant Evelyn Lamb, explainer extraordinaire, wrote a post on Roots of Unity at Scientific American about How Converting Between Addition and Multiplication makes Math Easier. If you don’t follow/read everything that Evelyn writes, you really should. So approachable and so lucid. She also wrote a fun piece about using different bases for your birthday candles, so you should read these two articles, follow her on Twitter, and tell her happy birthday!

If you run into anything interesting on the math-internet from now until October 15th, submit them to the Carnival of Mathematics site; the Carnival will be hosted next month at the online magazine Gonit Sora. Hope you had as much fun as I did with the submissions this month!

In your prime sequence, is it necessary that the first prime be less than the second? You include 138 = 2*3*23 and 777 = 3*7*37, but not 795 = 5*3*53.

In a few cases, both orders work: 113 and 311 are both prime.

With that requirement I get 138, 777, 4642, 10258, 10263, 12207, 13282, 16167, 19762, 30793, …

Without it, there are a lot more numbers: 138, 777, 795, 1533, 3729, 4642, 8823, 10258, 10263, 11001, 12207, 12467, 13282, 16077, 16167, 19762, 25491, 26201, 29109, 30783, …

I’ll leave finding the primes that produce each of these as an exercise for your readers.

This is great, John! My sequence is not well defined as written. Thanks for the sequence!