The Hardest "What Comes Next?" - Euler's Pentagonal Formula

Dive into a 54-minute exploration of one of mathematics' most fascinating theorems: Euler's pentagonal number theorem. Uncover its unexpected connection to prime number detection and the intricate refinement of the Fibonacci growth rule for partition numbers. Journey through various mathematical concepts, including triangular, square, and pentagonal numbers, while encountering contributions from mathematical luminaries like Ramanujan, Hardy, and Rademacher. Follow along as the video breaks down complex proofs, offers visual explanations, and provides insights into the historical development of these mathematical ideas. Gain a deeper understanding of integer partitions, generating functions, and the beauty of mathematical patterns through this comprehensive and engaging presentation.

Intro.
Chapter 1: Warmup.
Chapter 2: Partition numbers can be deceiving.
Chapter 3: Euler's twisted machine.
Chapter 4: Triangular, square and pentagonal numbers.
Chapter 5: The Ramanujan-Hardy-Rademacher formula.
Chapter 6: Euler's pentagonal number theorem (proof part 1).
Chapter 7: Euler's machine (proof part 2).
Credits.