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3Blue1Brown walks through a very hard Putnam competition problem and its elegant solution, emphasizing the visual intuition and the thought process behind solving it.

3Blue1Brown explains why plotting primes in polar coordinates produces spiral patterns, using modular arithmetic, Dirichlet's theorem and rational approximations of pi.

3Blue1Brown's third deep learning chapter gives a visual, intuitive account of backpropagation and what happens to a neural network as it learns. A follow-up video covers the underlying calculus.

Zack Freedman gives advice on why makers fail to finish projects, including scrapping bad ideas, showing work publicly and writing a plan that keeps projects fun. It is aimed at hardware DIY but generalizes.

Tom Scott argues that grammatical gender is a silly concept and that the singular 'they' is an established gender-neutral pronoun. The description carries later corrections and reflections he added in 2019.

Kurzgesagt's animated explainer on CRISPR gene editing, covering how the technology works and what it could mean for curing disease, designer babies and aging. It frames genetic engineering as an irreversible change coming to humanity.

Real Engineering explains the materials science behind metal 3D printing, including crystal structure, laser sintering, and why printed parts develop fatigue cracks. It shows how process imperfections limit the strength of printed metal.

A Computerphile video in which Mark Jago of the University of Nottingham explains Turing's halting problem and how it led to the blueprint for the modern computer.

minutephysics, in collaboration with the US Census Bureau, explains differential privacy and why the 2020 census adds noise to protect individuals' data. It walks through how statistics can leak private information.

3Blue1Brown's chapter 4 on deep learning gives a more formal, symbol-based account of backpropagation calculus, connecting the intuition from the previous chapter to the math found in textbooks and code.

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 shows how the uncertainty principle arises from Fourier transforms. A wave packet cannot be narrow in both position and frequency, so the principle is a property of waves rather than of measurement.

David and Ben Crystal introduce the Original Pronunciation production of Shakespeare and show what it reveals about the history of English, including puns and rhymes lost in modern speech.

Numberphile with Daniel Erman on the Josephus problem, where people in a circle are eliminated in turn. It shows how the survivor's position follows a neat pattern tied to powers of two and binary.

Wendover Productions explains how UK rail privatization worked and why it failed. It covers the fragmented operator and infrastructure structure and why market forces apply poorly to rail.

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

Tech Ingredients explains the principles of magnetohydrodynamics and builds several demonstrations, including propelling liquid metal and electrolytes with magnets and a railgun-style setup.

A Vox explainer on why California's high-speed rail project is years late and far over budget, with only a few concrete structures built by 2022. It covers the political, legal and routing challenges behind the delays.

Destin of Smarter Every Day goes behind the scenes at the 23andMe lab to show how genotyping works. He also discusses DNA testing and privacy.

A Veritasium video touring Relativity Space and explaining why 3D printing whole rockets cuts tooling costs, allows rapid iteration, reduces part count and enables new designs. It includes an interview with Scott Manley on aerospace engineering.

A short video on the US Sprint anti-ballistic missile, which accelerated to around Mach 10 in seconds under extreme g-forces and heat. It includes striking launch footage and a brief development history.

An illustrated 23-minute summary of David Friedman's talk based on The Machinery of Freedom. It describes how law, police and courts could work as market services in a stateless society, covering private law, polycentric law and objections.

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.

The Map Men explain why British place names are so hard to pronounce, tracing it to layers of Viking, Anglo-Saxon, Celtic and Norman influence, with a pronunciation guide.

Breaking Taps explains how the cryogenic mirror actuators on the James Webb Space Telescope achieve nanometer precision using flexures. It shows a 3D-printed replica and how one motor handles both coarse and fine motion.

A Blender-animated explanation of the Toyota Hybrid Synergy Drive, showing how the engine, two motor-generators, planetary gearset and battery work together as an eCVT.

Tom Scott explains why confetti and snow wreck video quality, using interframe compression and bitrate. He demonstrates it live by changing the quality on screen.

A PBS Space Time episode explaining the holographic principle: the idea that our 3+1 dimensional universe may be described by information on a lower-dimensional boundary. It walks through black hole entropy and the AdS/CFT correspondence.

David Spiegelhalter, Professor of the Public Understanding of Risk, uses statistics to weigh everyday risks such as bacon sandwiches and cycling. The six-minute piece introduces micromorts as a way to compare the risk of dying.

Tom Scott explains phatic expressions such as hello, thank you and how are you, which carry social meaning rather than information, and why replies like no problem can seem rude to some people.

Tom Scott visits Penistone to explain the Scunthorpe problem, showing why naive web and profanity filters block innocent words.

An episode of Coding Secrets by Jon Burton on retro copy protection, in particular physically damaging a disk with a laser so copies fail. It explains how this defeated hackers and pirates.

Veritasium explains Bayes' theorem with examples and introduces the 'Bayesian trap', where repeated events get mistaken for inevitable ones. It discusses how priors shape our expectations and behavior.

Chuck Marohn of Strong Towns explains how a land value tax differs from an ordinary property tax, why it makes economic sense, and why it is rarely used. It is a short six-minute explainer.

Numberphile's James Grime discusses highly composite numbers, nicknamed anti-primes, which have more factors than any smaller number, using 5040 as the central example. It touches on Plato and Ramanujan.

A Veritasium video on how a feud between Russian mathematicians led to Markov chains and the modern prediction algorithms built on them. It covers the history and the math behind them.

A Vox reporter tries to learn what his son's birth would cost before it happens and fails, showing how opaque US hospital pricing is even for the most common procedure.

Technology Connections spends 22 minutes on the humble can opener and what its design shows about products and why people don't know what to look for. It uses an everyday tool to draw broader lessons.

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.

Wendover Productions examines why carbon offsets so often fail to reduce emissions, covering specific examples and the perverse incentives in offset schemes.