noether's theorem

PBS Space Time explains Noether's theorem: conservation laws such as energy and momentum are consequences of deeper symmetries. It also covers why those laws hold only under certain conditions.

Veritasium explores why energy is not conserved in general relativity, using Emmy Noether's theorem linking symmetries to conservation laws. Physicists interviewed explain energy loss in an expanding universe.

MinutePhysics, with 3Blue1Brown, explains Bell's theorem using a Venn diagram paradox and polarizing filters. It shows why no local hidden variable theory can reproduce quantum correlations.

3Blue1Brown presents Bayes' theorem through a geometric diagram, showing how evidence should update beliefs. It works through the Kahneman and Tversky style questions and base rates.

Chris Stucchio presents the ethical principles behind algorithmic decision making and shows with examples from lending, criminology and education that they cannot all be satisfied at once. The talk frames AI fairness as a set of quantitative tradeoffs.

The first lecture of N J Wildberger's History of Mathematics course, starting with Pythagoras' theorem and following Stillwell's text. It emphasizes the flow of ideas over proofs.

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

Sabine Hossenfelder explains superdeterminism as an interpretation of quantum mechanics, addressing common objections and misconceptions, including the worry that it kills free will or science. She ties it to Bell's theorem and hidden variables.

Veritasium explains quantum entanglement and spooky action at a distance, walking through Bell's inequality and the experiments that rule out hidden variables, in under ten minutes.

Mathematician Kevin Buzzard explains why he believes the Lean theorem prover will shape the future of mathematics, and describes digitizing his university curriculum in Lean with undergraduates, plus the cultural challenges.

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.

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.

Veritasium explains the Dzhanibekov effect, also called the tennis racket theorem, where a spinning object flips unexpectedly about its intermediate axis. The video gives an intuitive account of the underlying rotational dynamics, drawing on Terry Tao's explanation and the original papers.

A ten-minute explainer from Hypermind on the wisdom of crowds, covering Galton's discovery and the diversity theorem. It argues that collective intelligence comes from diversity, independence and aggregation.

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.

PBS Space Time episode on the black hole information paradox, covering how black holes seem to destroy information, the no-hair conjecture and the proposed role of the event horizon. It is part of a series on black holes.

3Blue1Brown, in collaboration with minutephysics, introduces the math of superposition and quantum states using polarized light. It builds up the quantum behavior of photons as a simple counting and probability problem.

The first video of 3Blue1Brown's Essence of Calculus series, which builds toward integrals, derivatives, and the fundamental theorem of calculus from a simple geometry question. It aims to make viewers feel they could have invented calculus themselves.

Philip Wadler's Strange Loop talk on Propositions as Types, the link between logic and computation (the Curry-Howard correspondence). He traces its history through Church, Godel and Turing and shows how it shaped theorem provers and programming languages.

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.

Vladimir Voevodsky's IAS lecture starts from Godel's second incompleteness theorem to explore whether first-order arithmetic could be inconsistent. It motivates his vision of univalent foundations and computer-checked proofs.

Philip Wadler's Lambda Days talk on propositions as types, the link between logic and computation that underlies theorem provers and programming language design.

Martin Kleppmann's Strange Loop talk on database transactions, covering why they were dropped by NoSQL, their reputation for being slow, and newer algorithms that make serializable transactions perform and scale. It touches on consistency, linearizability and the CAP theorem.

A Danish university math revue music video that parodies Barbra Streisand to explain the Banach-Tarski paradox, with oranges multiplying on stage.