Imagine a set of many lines as in a dream. The lines intersect at a point and radiate outward. There’s something perfect about the way they’re spaced that you can’t quite put your finger on. You start counting them, but before you can finish you wake up with a question hanging on the fringe of your mind: Just how many were there? Continue reading

## Category: mathematics

I**t’s now ****15 years** since I published my book *A New Kind of Science* — more than 25 since I started writing it, and more than 35 since I started working towards it. But with every passing year I feel I understand more about what the book is really about — and why it’s important. I wrote the book, as its title suggests, to contribute to the progress of science. But as the years have gone by, I’ve realized that the core of what’s in the book actually goes far beyond science — into many areas that will be increasingly important in defining our whole future. Continue reading

Physicist Richard Feynman returned over and over to an idea that drove his groundbreaking discoveries. His approach was documented by his Caltech colleague David Goodstein in the book *Feynman’s Lost Lecture* about physics classes Feynman taught in the 1960s: Continue reading

Powerful new quantitative tools are now available to combat partisan bias in the drawing of voting districts. Continue reading

Ramsey’s theorem predicts a surprising (and useful) consistency in the organization of graphs. Here’s a simple visual proof of how it works. Continue reading

Equiangular lines are an elemental part of geometry. Mathematicians have discovered a tighter limit on the number of such lines that exist in every dimension.

When a German retiree proved a famous long-standing mathematical conjecture, the response was underwhelming. Continue reading

In order to fully understand the quantum world, we may have to develop a new realm of mathematics. Continue reading