# Diagonalizing the Psalms

This post first appeared on scientificamerican.com.
As I was drifting off to sleep one night, I had one of those brilliant ideas that only comes along when you’re drifting off to sleep: diagonalizing the psalms. Earlier that day I had noticed that Psalm 119 was very long—longer than 119 verses, in fact—and wondered how many psalms from the Bo [...]

# Parallels and Perpendiculars in the L...

This post first appeared at scientificamerican.com.
André Weil. Credit: Konrad Jacobs Wikimedia (CC BY-SA 2.0 DE)
A friend who recently defended his dissertation in comparative literature mentioned Simone Weil’s writing on the Iliad in his defense. Afterwards, I told him her brother André was a famous mathematician. (In my former field of re [...]

# A Thousand Years of Congruent Numbers

This post originally appeared at scientificamerican.com.
On our most recent episode of My Favorite Theorem, my cohost Kevin Knudson and I talked with University of Montreal math professor Matilde Lalín about her favorite bit of math, the congruent number problem. (You can listen to the episode or read a transcript at kpknudson.com.)
A congrue [...]

# A Feat of Mathematical Eponymy

This post first appeared at scientificamerican.com.
Last month, I wrote about the Euclid–Mullin sequence, a sequence of prime numbers generated when you apply the algorithm from Euclid’s proof that there are infinitely many primes. The sequence is named for Alexandrian mathematician Euclid, about whom we know almost nothing but who lived arou [...]

# Happy Numbers Have No Density

This post first appeared at scientificamerican.com.
If you’re feeling a little down today, maybe a happy number will cheer you up. To see if an integer is happy, start by squaring its digits (in base ten, though happiness is defined analogously in other bases as well) and adding them together. So the number 23 would become 13 because 22+32=4+ [...]

# The Funniest Math Joke

No disrespect to “why was six afraid of seven,” but “base 10″ is the funniest math joke.
I have made the mistake of unironically writing the phrase “base 10″ before, and I recently cringed and also laughed at an old post of mine that used the phrase “base 60” over and over again. I almost caught myself writ [...]

# Inka History in Knots (Book Review)

This post originally appeared at scientificamerican.com.
Imagine that in a few hundred years, archaeologists stumble on some of your old files. Maybe they find spreadsheets of tax information, medical bills, or bank statements, or maybe text files with old emails or drafts of your novel. These archaeologists cannot read Latin script, and no o [...]

# A Curious Sequence of Prime Numbers

This post originally appeared on scientificamerican.com.
Prime numbers are often described as the “atoms” of mathematics, or at least of numbers. A prime has exactly two distinct factors: itself and 1. (Hence 1 is not considered a prime number.) All whole numbers greater than 1 are either primes or products of primes.
One of the first questio [...]

# Moon Duchin’s Favorite Theorem

This post originally appeared at scientificamerican.com.
On this episode of our podcast My Favorite Theorem, Kevin Knudson and I were pleased to have the opportunity to talk with Moon Duchin, a mathematician at Tufts University. You can listen to the episode at kpknudson.com, where there is also a transcript.
Dr. Duchin has appointments not o [...]

# The Serendipity of Swiss Cheese

This post first appeared on scientificamerican.com.
Approximation is a recurring theme in mathematics. Sometimes it seems like all of mathematics is saying, “Well, I know how to solve the problem in this domain. Is there a way I can approximate other domains with this domain?” A lot of calculus boils down to approximating arbitrary functions [...]

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