We are in a golden age of grift. Where adventurers once flocked to California or the Yukon because “there was gold in them thar hills,” the fastest way to get rich today is by fleecing suckers. We’ve got crypto rug pulls, meme stocks, nutritional supplements, MLMs—anything to make a quick buck.

You might think it’s unlikely for any interesting mathematics to arise from incense appreciation, but that’s only because you’re unfamiliar with the peculiar character of Muromachi (室町) era Japanese nobles. There has never been a group of people, in any time or place, who were so driven to display their sophistication and refinement.

One thing you may have noticed about the trigonometric functions sine and cosine is that they seem to have no agreed upon definition. Or rather, different authors choose different definitions as the starting point, mainly based on convenience. This isn’t problematic or even particularly unusual in mathematics: as long as we can derive any of the other forms from any starting point, it makes little difference which we start from.

Kaprekar’s routine is a simple arithmetic procedure on four digit numbers which rapidly converges to the fixed point 6174, known as the Kaprekar constant. Unlike other famous iterative procedures such as the Collatz function, the ad hoc nature of the Kaprekar routine doesn’t hint at fundamental mathematical discoveries yet to be made.

In 2020, the Zodiac 340 cipher was finally cracked after more than 50 years of trying by amateur code breakers. While the effort to crack it was extremely impressive, the cipher itself was ultimately disappointing. A homophonic substitution cipher with a minor gimmick of writing diagonally, the main factor that prevented it from being solved much earlier was the several errors the Zodiac killer made when encoding it.

Introduction Visualizing the results of a binary classifier is already a challenge, but having more than two classes aggravates the matter considerably. Let’s say we have $k$ classes. Then for each observation, there is one correct prediction and $k-1$ possible incorrect prediction. Instead of a $2 \times 2$ confusion matrix, we have a $k^2$ possibilities.