Generalizing Circles and Ellipses

[Reading and thinking about: n-Ellipses and the Minimum Distance Sum Problem, a paper that I was able to stick pretty well with until about the last third.] 1. Generalizing Circle Definitions There often comes a point in my geometry classes where I ask students to come up with a definition that describes a circle. It’s […]

The toilet is going to eat my pee

“I’m going to tell you that the toilet is going to eat my pee,” he said. It was my son, nearly three, standing with his pants over his ankles. He held himself, umm, firmly. “I’m going to tell you that the toilet is going to eat my pee,” he repeated. “OK.” “The toilet is going […]

“A liquid moon”

Winter Trees – William Carlos Williams All the complicated details of the attiring and the disattiring are completed! A liquid moon moves gently among the long branches. Thus having prepared their buds against a sure winter the wise trees stand sleeping in the cold.                          […]

Mathematical and Scientific Crises

[This post is wildly speculative. File under ‘playing with ideas.’] On the continuing and fascinating saga of the ABC conjecture and Mochizuki’s befuddling proof: Five years ago, Cathy O’Neil laid out a perfectly cogent case for why the (at that point recent) claims by Shinichi Mochizuki should not (yet) be regarded as constituting a proof of the […]

The piranha problem

A fundamental tenet of social psychology, behavioral economics, at least how it is presented in the news media, and taught and practiced in many business schools, is that small “nudges,” often the sorts of things that we might not think would affect us at all, can have big effects on behavior. Thus the claims that […]

When I say people, I mean mathematicians

On the wave equation and the beginnings of Fourier analysis: “Very soon after that, people began…when I say people, I mean mathematicians.” I only know Rudin from his analysis books, but come on, man! What, are you worried that someone will think mere people would be interested in this? Another not great moment comes a few […]