Videos

Mathematics

• A brief history of mathematics. A one-hour crash course on the historical development of mathematics by John Dersch.

• Of triangles, gases, prices and men. A superb talk by Cedric Villani that describes the connections between seemingly very different fields of mathematics.

• An introduction to general relativity. A series of incredible lectures by Frederic Schuller, specifically aimed at mathematicians.

• The history of mathematics. A fascinating lecture course by Norman Wildberger that starts with Greek mathematics and ends with the development of non-Euclidean geometry.

Physics

• The Character of Physical Law. A series of lectures by Richard Feynman.

• Boltzmann and the Arrow of Time. A lecture by Leonard Susskind.

Popular Science

• A fascinating Feynman interview. Some real gems here.

• COSMOS by Carl Sagan. Compulsory popular science viewing.

Articles and Lecture Notes

• Functional Analysis lecture notes by Michael Struwe. The best introduction to Functional Analysis I've had the pleasure to read. In German unfortunately....

• The Feynman Lectures. Self-explanatory. Definitive introduction to college-level physics.

• How to write Mathematics, a short guide by Paul Halmos. Extremely valuable for researchers who are just starting to write mathematical articles.

• Here and here are some musings by the late Gian-Carlo Rota who was a Professor of `Applied Mathematics and Philosophy' at MIT. He has some interesting thoughts on the teaching and philosophy of mathematics.