My Favorite Theorem: How Mathematics Can Surprise Us
summary
A rapid tour of concrete surprises: the Banach–Tarski paradox shows a ball can be cut into a finite number of pieces and reassembled into two identical balls; Euler's identity literally ties e, π, i and 1 in one equation; the four color theorem proves four colors always suffice on any planar map; set theory gives that the power set of the naturals has the same cardinality as the reals; row rank equals column rank for any matrix; classical straightedge-and-compass angle trisection impossibility holds for arbitrary angles.
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chapters (9)
- 0:00Intro
- 0:48Twitter Research
- 1:14Banach Tarski
- 1:34Euler's identity
- 2:00Four color theorem
- 2:21The Infinities
- 3:14Rank in linear algebra
- 3:47Angle trisection
- 4:12Summary • Studying math is cool
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