function composition

3Blue1Brown visualizes the Riemann zeta function and the analytic continuation that extends it beyond where its series converges, building toward the Riemann hypothesis.

Mathologer examines the infamous Numberphile claim that 1+2+3+... equals -1/12, explaining what is wrong with the calculation and how it connects to real math like the zeta function and analytic continuation.

A step-by-step animated explanation of how SHA-256 works, from padding and message schedule to the compression function and final hash, with source code for the animations.

Kaze Emanuar searches for the best sine approximation for the Nintendo 64, comparing the lookup tables in Mario 64 and Ocarina of Time with polynomial alternatives. It walks through numerics and 3rd, 4th and 5th order approximations.

3Blue1Brown's second neural network chapter explains cost functions and gradient descent, showing how a network learns by minimizing error during training.

Mathologer examines how identities like 1+2+3+... = -1/12 arise in Ramanujan's work, starting from his 1913 letter to Hardy. The video explains the rules for summing infinite series and why such results are meaningful but not naive sums.

Tom 7 (suckerpinch) delivers a long, comedic digression on gradient descent and floating-point imprecision. He shows how rounding behavior can supply the nonlinearity needed to build a neural network.

Veritasium explains the many-worlds interpretation of quantum mechanics, drawing heavily on Sean Carroll's book. It walks through the Schrodinger equation and why wave collapse may be unnecessary if the universe keeps splitting.

Vsauce's roughly 24 minute explainer on the Banach-Tarski paradox, building from infinity and set theory to the decomposition of a sphere into pieces that form two spheres.

3Blue1Brown introduces Fourier series, from the heat equation to drawing arbitrary shapes with rotating circles. It builds a visual intuition for decomposing functions into sine waves.

Huygens Optics explores the idea that space is a non-linear elastic medium, and uses simulations to show how wave energy might be confined locally into particle-like objects. It touches on inertia, the Schwinger limit and the vacuum as a medium.