init systems

Vsauce's Michael Stevens takes viewers past infinity using transfinite numbers, ordinals and cardinals, with input from mathematician Hugh Woodin. It is a fast-paced, mind-bending tour of different sizes of infinity.

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.

Veritasium shows how Hilbert's infinite hotel can still run out of room, using infinite buses of guests. It explains the surprising answer in a short animated segment.

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.

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.

Primer uses simulations to compare voting systems such as first-past-the-post, approval, ranked choice and others. It shows how each system behaves and can be manipulated, with links to further voting theory resources.

Anders Puck Nielsen clears up common misunderstandings about what legally counts as genocide, then compares the situation in Gaza with the genocide case against Putin. The chapters cover the definition, individual intent, and the two case comparisons.

Numberphile with Tadashi Tokieda on the Trinity Hall Prime, a prime number whose digits form a picture of the college's coat of arms, left as a gift by a departing mathematician.

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.

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 explains space-filling curves and the Hilbert curve, and how infinite mathematical constructions connect to finite, practical approximations. It touches on mapping between dimensions and sensory ideas.

Adam Neely tests the claims for tuning to A=432 Hz by trying the unusual tuning systems that its proponents' numerology requires. He compares how they sound against standard tuning and temperaments.

Musician Adam Neely examines whether certain keys sound sadder than others, looking at the history of tuning systems and temperaments and at how instrument timbre shapes the emotional character we hear. It draws on historical aesthetics writing and audio examples.

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.

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.

Veritasium explains the effort to redefine the kilogram, which was still defined by a physical artifact, and how a near-perfect silicon sphere from the Avogadro project helps. It also covers the history of the unit's odd naming.

An animated simulation comparing single-winner voting methods such as plurality, instant runoff and STAR. Colored regions show which candidate wins as a randomized electorate shifts across a two-dimensional political space, building on Ka-Ping Yee's earlier diagrams.

Veritasium explains how Penrose tilings and quasicrystals overturned the belief that 5-fold symmetry and non-periodic crystals were impossible, including an interview with Paul Steinhardt.

A Vox Borders episode with Johnny Harris explaining how China is gradually erasing the line between mainland China and Hong Kong since the 1997 handover. It describes the one country, two systems arrangement and its expiration date.

Veritasium explains why the kilogram is being redefined in terms of Planck's constant rather than a physical metal artifact. It visits NIST to show the Kibble balance and why measuring mass precisely is hard.

Mathologer uses continued fractions to show why the golden ratio is the most irrational number, comparing it with root 2, e and pi and pointing to where this shows up in nature.

Historia Civilis explains the origins and governing system of the Iroquois (Haudenosaunee) Confederacy. It covers the Great Law and the league's surprisingly intricate legal and political structure.

A six-minute explainer from Undefined Behavior on range (score) voting. It follows an earlier video on Arrow's Theorem and shows how range voting seems to satisfy the criteria Arrow's Theorem says no ranked system can.

Yuta, a Japanese YouTuber, explains whether Japanese speakers can read Chinese text. He shows how shared kanji let people guess meanings while the two languages remain completely different.

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

Veritasium explains why no voting system can be perfectly fair, drawing on Arrow's theorem and the work of Eric Maskin. It looks at problems with systems like first-past-the-post and ranked-choice voting.

CGP Grey explains the Single Transferable Vote, a proportional ranked-ballot system, and why politicians have little incentive to adopt it. It is a short animated explainer of how multi-winner ranked voting works.

CGP Grey explains Mixed-Member Proportional representation, the system used in New Zealand where voters get two votes. It covers how it differs from first-past-the-post.

A Smarter Every Day episode from aboard a nuclear submarine on how the crew makes breathable air. It covers oxygen generation from seawater, oxygen candles and CO2 scrubbing with amine.

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.

The Center for Election Science explains favorite betrayal in instant-runoff voting: in some elections, ranking your favorite first can cause your least favorite to win. It contrasts this with plurality voting's spoiler problem.

Technology Connections explains that US household power is split-phase, with two 120V legs that combine to 240V for large appliances. It covers the breaker panel and how the system works.

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.

CGP Grey explains how the 2015 UK general election showed the flaws of first-past-the-post voting, with parties like UKIP winning many votes but few seats.

jan Misali traces the history of the letter W, including why it is called double u. The video is part of a series of deep dives into individual letters.

A short narrated video describing how reintroducing wolves to Yellowstone triggered a trophic cascade that changed wildlife, vegetation and even river courses. This is a remastered HD version of George Monbiot's viral piece.

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.

Brian Douglas introduces Braitenberg vehicles, simple robots whose sensors are wired directly to motors yet show surprisingly lifelike behavior. He draws on Valentino Braitenberg's book Vehicles.

A short explainer from 2swap on the chaotic behavior of double pendulums. It examines how predictable the system is for some starting conditions and whether closed-form solutions exist.

Yuta asks whether native Japanese speakers can actually write kanji by hand, showing that many struggle to recall characters from memory.