arithmetic

Matt Parker of Stand-up Maths explains why people keep making the same mistake with millions and billions, using a Bloomberg cash calculator example. He looks at the unit slip behind the repeated arithmetic error.

3Blue1Brown explains why plotting primes in polar coordinates produces spiral patterns, using modular arithmetic, Dirichlet's theorem and rational approximations of pi.

MinutePhysics explains Shor's algorithm, showing how a quantum computer factors large integers by finding the period of a number modulo N. It walks through the modular arithmetic and number theory that give the exponential speedup over classical factoring, and why this threatens encryption.

Numberphile's James Grime makes the case for base 12 (dozenal) over base 10, showing how twelve's many divisors make arithmetic and everyday fractions easier.

Mathologer shows how times table diagrams on a circle produce cardioids and other curves connected to the Mandelbrot set. He explains the patterns and links to a tool for making your own diagrams.

Tom Scott-style absurdist tour by Tom7 of SIGBOVIK chess projects: a tournament of 30 weird chess algorithms used to rate a color- and piece-blind chess program. Topics include mirrors, arithmetic encoding, perverted game tree search and a diluted Stockfish.

jan Misali presents an humorous but earnest case for counting in base 6 (seximal) instead of base 10 or 12, comparing the arithmetic advantages of each.

Matt Parker explains the history behind NTSC television running at 29.97 frames per second rather than 30, tracing it to the backward-compatible addition of color. He walks through the arithmetic behind the odd ratio.

A short CGP Grey animation showing how the US electoral college lets a candidate win the presidency with as little as about 22 percent of the popular vote. It lays out the arithmetic of winning states by narrow margins.

A short Art of the Problem clip explaining Diffie-Hellman key exchange, using a paint mixing analogy for one-way functions and touching on modular arithmetic and discrete logarithms.

Rob Miles discusses GPT-3 on Computerphile, covering how scaling parameters kept improving results over GPT-2 and how the model nearly learned arithmetic without anyone knowing exactly how.