documentary series

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.

Mathologer explains epicycles and complex Fourier series, inspired by an animation of Homer Simpson drawn with epicycles. It covers the shape of the Moon's orbit around the Sun and how to make your own epicycle drawings.

A PBS Infinite Series episode explaining the mathematics of quantum computers, including how qubits store complex numbers and how quantum computation differs from classical computation. Hosted by Kelsey Houston-Edwards.

Andrew Huang explains the harmonic series, which he calls the foundation of almost all music. He builds the idea up step by step, with demonstrations of overtones and how harmonies derive from them.

PBS Infinite Series explains how Shor's algorithm lets a quantum computer break RSA encryption, building on earlier episodes about cryptography and the math of quantum computers. It works through the idea step by step.

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.

The first of four short videos from Bill Hammack (engineerguy) introducing and giving the history of a 100-year-old mechanical computer, Michelson's harmonic analyzer. The series goes on to explain Fourier synthesis, analysis and operation of the machine.

A Numberphile video in which physicists Tony Padilla and Ed Copeland show a seemingly astounding result that 1+2+3+4+... equals -1/12. The argument is informal and has drawn criticism for glossing over what the result actually means.

Part 3 of Kirby Ferguson's Everything is a Remix series, using Apple and the iPhone to show how invention builds on copying and combining prior ideas. It argues that creativity and innovation are inseparable from copying.

Stand-up Maths explains why the perimeter of an ellipse has no simple closed-form equation, showing the infinite series and presenting approximation formulas.

The first video in Not Just Bikes' Strong Towns series explains the financial instability of North American cities, based on Strong Towns research. It argues that low-density suburban growth costs more to maintain than it brings in.

3Blue1Brown's chapter on eigenvectors and eigenvalues in the Essence of Linear Algebra series. It builds a visual intuition for what they mean, why an eigenbasis is useful, and ends with a puzzle.

3Blue1Brown explores infinite sums from convergent to divergent, with an introduction to the 2-adic metric, themed on the cycle between discovering and inventing mathematics.

Technology Connections' long closing video in his heat pump series, arguing that adopting heat pumps is well within reach. It explains how they work and what it takes to start using them.

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.

The first video in potholer54's climate series, giving a basic look at how climate scientists infer that man-made carbon gases are changing the climate. It is a short explainer meant to present the scientific evidence plainly.

AVweb's Paul Bertorelli explains in part two of a series why general aviation has not replaced leaded avgas. He covers industry inertia, bureaucratic delays and the exemption that lets the industry keep using lead.

Part 1 of Smarter Every Day's three-part series on manipulating the YouTube algorithm. It features Renee DiResta and examples of how social media platforms can be manipulated.

Technology Connections explains how analog television produced moving images without computers, covering scanning, CRTs and standards like NTSC and PAL. It is part of a series on analog TV.

National Geographic footage showing the cordyceps fungus infecting ants and other insects and steering their behavior so it can reproduce.

CGP Grey explains first-past-the-post voting and why it pushes elections toward two dominant parties. It is the first in his series on electoral systems.

VFX supervisor Jonas Ussing examines what studios mean by "no CGI", showing how much invisible CGI hides behind practical-effects marketing. It is the first part of a multi-part series that includes analysis of doctored behind-the-scenes footage.

A Technology Connections video on how ground-source (geothermal) heat pumps work and why they hold efficiency in winter. It also covers related heat pump information, and the description notes air-source heat pumps have since improved.

Mike Pound explains the discrete cosine transform and how it underpins JPEG compression. It is part two of Computerphile's JPEG series.

3Blue1Brown builds visual intuition for quaternions, showing how to think about this four-dimensional number system using stereographic projection and rotations in 3D space. It is part one of a two-part series with an interactive companion site.

Technology Connections takes a long, detailed look at how a 1970s electromechanical pinball machine works, from relays to stepper motors and mechanical logic. It is the first part of a series.

Potholer54 presents the climate science case and a market-oriented, conservative-friendly approach to addressing global warming, with sources listed. It is part one of a two-part series.

The first episode of Crash Course World History, in which John Green covers the shift from hunting and gathering to agriculture and how it shaped civilization. It is delivered fast and with jokes.

Bill Hammack of engineerguy explains how medieval engineers designed stone cathedrals using rules of thumb, with no science, mathematics or literacy. He uses it to define the engineering method.

The first part of Extra History's animated miniseries on the South Sea Bubble. It explains how England's government debt led Robert Harley to turn to financier John Blunt, whose schemes began inflating artificial demand for shares.

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

Not Just Bikes explains, using Urban3's property-tax analysis, why car-dependent suburbs generate less tax revenue than they cost to maintain, so dense urban cores effectively subsidize them. It is part of a Strong Towns series.

The first episode of a Cities: Skylines series on urban politics and planning, focused on parking. It uses the game to show how parking minimums shape cities, drawing on Donald Shoup's book The High Cost of Free Parking.

3Blue1Brown's visual walkthrough of the attention mechanism inside transformers, covering self-attention, multiple heads and cross-attention. It is chapter 6 of his deep learning series.

CuriousMarc powers up a vintage HP 5061A cesium beam clock and explains both the quantum principle and the HP implementation in detail. It is part of a longer atomic clock series.

A clip from the 1983 BBC series Fun to Imagine in which Richard Feynman explains heat as the jiggling of atoms and how we perceive it as hot and cold.

A short Al Jazeera animation narrated by Amy Goodman presenting Noam Chomsky's five filters of the mass media: ownership, advertising, media elite sourcing, flak and a common enemy. It is part of the MediaTheorised series.

A PBS Space Time episode explaining how space and time swap roles inside a black hole's event horizon. It is part of the channel's black hole series.

A video essay from the Alt-Right Playbook series that explains how extremist movements draw ordinary people in, using deniable rhetoric, bad-faith games, and gradual escalation. It draws on books about the alt-right, male radicalization, and cult-style brainwashing.

Climate Town gives a comedic, fast-paced account of how the plastics industry promoted recycling, including the resin-code recycling symbol, while knowing most plastic could not be economically recycled. It points viewers to the Frontline documentary Plastic Wars for a deeper treatment.