Richard Green

2 months ago | quantamagazine.org | Leila Sloman |Richard Green |Solomon Adams

Introduction In 2003, a German graduate student named Britta Späth encountered the McKay conjecture, one of the biggest open problems in the mathematical realm known as group theory. At first her goals were relatively modest: She hoped to prove a theorem or two that would make incremental progress on the problem, as many other mathematicians had done before her. But over the years, she was drawn back to it, again and again.

Nov 9, 2023 | apieceofthepi.substack.com | Richard Green

The picture above shows an approximation to the Gosper curve, which was discovered by Bill Gosper in 1973. The Gosper curve is a space-filling curve, which means that it converges to a curve that completely fills in the interior of a shape. The shape in question (shown below) is called the Gosper island. Despite having a fractal boundary, the Gosper island has a property called “rep-7”, which means that it can be split up into 7 identical smaller copies of itself.

May 24, 2023 | apieceofthepi.substack.com | Richard Green

The comedian Steven Wright once asked: “Why is the alphabet in that order?

May 11, 2023 | tinyurl.com | Richard Green

For the intelligent general reader who likes mathematics. What if I told you: you’re playing tic-tac-toe, but both you and your opponent are playing as X, and you’re trying to lose the game? In that case, you would be playing misère X-only tic-tac-toe, which is an example of a combinatorial game. A combinatorial game is a two-player game with no hidden information and no chance elements.