Georg Cantor set out to solve an arcane problem about trigonometric series and ended up revolutionizing mathematics. Along the way he gave the world new ways to think about infinity. See "On Beyond Omega!" at Mathematical Enchantments: mathenchant.wordpress.com/20…

Here's a more symmetric and satisfying one.

Here's another dynamic Hamiltonian circuit. This one visits 16 moving points on 8 circles; the points form diameters of the 8 incircles of the faces of an octahedron. The circles alternate rotation direction around each vertex. The circuit has constant length!

Here's another constant-length dynamic Hamiltonian path using six circles.

My latest Mathematical Enchantment, "Solving the Flat Cube", describes a new puzzle devised by Oskar van Deventer, Dmitry Andreev, and me, and shows how sometimes you can solve a math problem by adding a dimension OR by throwing a dimension away. mathenchant.wordpress.com/20…

The inspiration for this came from Chuck Hoberman's "Nested Loops" exhibit. I used ChatGPT to search the space of possible solutions in which total length doesn't change (I'm pretty sure that "Nested Loops" lacks this property). youtube.com/watch?v=e4sARevL…

A loop joins eight moving points on four circles in such a way that the length of the loop remains constant.

David Kelly is no longer with us (see mathenchant.wordpress.com/20…) but Yellow Pig Seventeen lives on!

The world's worst way of writing the integer four just dropped. See my latest Mathematical Enchantment, "What Bad Bases Are Good For": mathenchant.wordpress.com/20…

Watch a cancer cell drink itself to death, thanks to Dr. Louise Chow’s work on catastrophic macropinocytosis and my daughter Eliana’s animation. If you like it, please Like it! youtu.be/jC1R8hSzAqs