proof assistants

Veritasium's explainer on Godel's incompleteness theorems and the limits of mathematical proof, tracing set theory, Hilbert's program and the road to Turing and modern computing.

WIRED has UCLA professor Amit Sahai explain zero-knowledge proofs to a child, a teen, a college student, a grad student and an expert. Each round goes deeper into the cryptography and why it matters.

3Blue1Brown explains the math and mechanics behind Bitcoin visually: ledgers, digital signatures, proof of work and the blockchain, building up a decentralized payment system from first principles.

Engineering Explained follows up on Tesla's claim that a Cybertruck towing a Porsche 911 could beat the 911 alone over a quarter mile. He walks through the MotorTrend drag race and explains why the claim did not hold up.

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.

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.

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

Andreas Antonopoulos answers a Bitcoin Q&A question about energy consumption in mining. He argues that mining is arbitrage for the cheapest electricity, drives investment in renewables, and that the traditional financial system has hidden externalities.

Not Just Bikes argues that winter is not what stops Canadians cycling, using Oulu, Finland as proof that safe, well-maintained cycling infrastructure enables year-round biking despite harsh weather.

Techmoan's beginner introduction to the compact cassette, testing metal tapes and Dolby S noise reduction on a Sony TC-S1 deck. He checks whether a cassette can sound close to a CD when good tape and equipment are used.

Big Clive tears down the Dubai lamp, a Philips LED bulb developed with Dubai's ruler for maximum efficiency and long life. He examines its construction and circuitry, including underrun LEDs and many filament strips.

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.

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

Numberphile's Tony Padilla and Matt Parker discuss Graham's number, once the largest number used in a mathematical proof, and how enormous it is.

Technology Connections examines an old feature-rich microwave and shows how it uses a humidity or steam sensor and lookup data to cook food well, arguing it beats many modern ones.

The Slow Mo Guys film a TV and screens with a high-speed camera to show how displays build an image. The footage includes CRT-style scanning and how pixels light up over time.