Mathlesstraveled is a blog “dedicated to exploring beautiful mathematics.” The blog is written by Brent Yorgey, an assistant professor in the department of math and computer science at Hendrix College, who lives closer to the computer science end of mathematics. As such his posts are often somewhat computational in nature. He has a whole zoo of good looking graphics and everything is easily digestible by anyone interested in learning a bit of math.
One ongoing series featured in the blog are Posts Without Words. These are just graphics depicting some mathematical idea, sometimes it’s easy to see what the pictures are describing and sometimes it’s more difficult. I really like Post Without Words #5. The explanation is a doozy as it involves Hilbert space filling curves and the Thue-Morse sequence. Although I’ll bet you can come up with a simpler explanation!
As an aside, if you like mathematical ideas in graphic form, you should check out Mathematics in the Eye of the Beholder.
Yorgey also has several other series of posts, including those in which he discusses the irrationality of pi, and more recently, the curious powers of 1+sqrt 2. The later series aims to answer the following question posted on Mathstadon: What is the 99th digit to the right of the decimal point in the decimal expansion of (1 + sqrt 2)500? After stating the problem, Yorgey comes up with a reasonable conjecture (motivated by some computational examples), states a clever solution, and then goes on to explain an alternative approach.
Another great offering on the blog are Yorgey’s factorization diagrams. These are pretty pictures generated using diagrams in Haskell, that give a visual representation of prime factorization. These reminded me of a clever little book my brother gave me recently, You Can Count on Monsters. Yorgey sells the factorization diagrams as a deck of cards along with some fun game ideas for teaching factorization. I’m into it.
Yorgey maintains a second blog, aimed (as he says) at his peers. These posts tend to be slightly less accessible but would probably be of interest to anyone studying type systems, category theory, or combinatorics.