fractals

Donald Knuth's 2017 Christmas Tree Lecture at Stanford about a combinatorial geometry problem whose computed numbers matched a striking formula. He tells the story of the conjecture and its sequel.

Mathematician Colin Wright demonstrates juggling and explains the mathematics of juggling patterns, including notation that led to new throwing patterns. It is a public presentation at the Museum of Mathematics aimed at a general audience.

A segment from Carl Sagan's original Cosmos explaining the fourth spatial dimension through analogy with a two-dimensional world and shadow projection.

Timothy Gowers thinks aloud, in real time, as he tries to understand why Pascal's determinant equals 1. He does not fully solve it in this episode, but shows his exploratory process.

Matt Parker's LMS popular lecture on how seemingly incredible results can be meaningless random patterns. He ranges from ancient Woolworths civilisations to shoelaces and DNA.

A 3Blue1Brown live lockdown math episode asking what Euler's formula e^(pi i) is actually saying. It builds intuition through exponentials, rotation and vectors landing on the unit circle.