integers

A Numberphile video with Dr James Grime on Sloane's Gap, the observation that integers in the OEIS are not evenly represented and some numbers are underrepresented. It explains the clusters of 'interesting' numbers.

3Blue1Brown shows how pi emerges from prime numbers via complex numbers and sums of squares, culminating in a formula for approximating pi.

Numberphile's James Grime explains Cantor's result that some infinities are bigger than others, including why the reals outnumber the integers. It is a short, accessible introduction to countable and uncountable infinity.

A visualization and sonification of 15 sorting algorithms, from selection sort to bogo sort, run on shuffled integers in six minutes. Each algorithm gets a size and speed scaled to its complexity.

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.

A one-minute clip from Barack Obama's 2008 Google visit in which Eric Schmidt asks him the most efficient way to sort a million 32-bit integers. Obama answers that bubble sort would be the wrong choice.