Philosophy & History of Mathematics
Mathematicians and their ideas — miscellaneous lectures (YouTube) Collected talks from Turing Award recipients, Fields Medalists, and senior mathematicians on the nature of mathematical discovery, the relationship between mathematics and physics, and the history of key results. Covers Gödel’s incompleteness theorems, the Langlands program, and the unreasonable effectiveness of mathematics in the natural sciences. [→ mathematics; philosophy-of-mathematics]
Richard Borcherds (YouTube) https://www.youtube.com/channel/UCIyDqfi_cbkp-RU20aBF-MQ
Fields Medalist Richard Borcherds (known for proving the Moonshine conjecture) teaches algebra, algebraic geometry, and number theory in a refreshingly direct, unpolished style — the lectures feel like sitting in his office. Covers Galois theory, modular forms, representation theory, and algebraic K-theory at a graduate level. [→ mathematics; research; algebra]