diophantine equations

Numberphile with Tim Browning on the sum-of-three-cubes problem and why 33 was the lowest unsolved case. The description notes a later solution for 33.

The first lecture of Gilbert Strang's MIT 18.06 Linear Algebra course, covering the geometry of linear equations. It opens a full 35-lecture university course.

A short conference talk from !!Con 2017 in which Kevin Chen explains the HDR imaging algorithm from a foundational paper, framing it as a system of linear equations, and implements it in a Microsoft Excel spreadsheet. No prior image processing knowledge is needed.

Afrotechmods plays with 2600F ultracapacitors that can dump hundreds of amps, shorting them to vaporize bits of metal. Along the way he explains the three most important capacitor equations. The uploader warns that the capacitors are not designed to be shorted.

A Bell Labs film in which Dr. J.N. Shive uses a mechanical wave machine to demonstrate reflection, standing waves, resonance and impedance matching. He includes some equations but relies mostly on real-world examples a layperson can follow.

An animated visualization of basic quantum mechanics using a free particle, with simulations based on the actual equations. It covers waves, particles, and how measurement collapses the wavefunction.

Leonard Susskind's Santa Fe Institute talk on the arrow of time: why the past differs from the future when physics equations are time-symmetric. He covers entropy, cosmology and Boltzmann brains.

Sixty Symbols interviews Nottingham cosmologist Tony Padilla, who says string theory deserves to be taken seriously. He explains how strings emerged from the equations rather than being invented.

A 1969 BBC Tomorrow's World segment about Nellie, a school computer used by pupils at Forest Grammar School to solve equations and play music. Students learn programming and maintenance, and act out binary arithmetic.