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3Blue1Brown builds intuition for Euler's formula, e^(pi i) = -1, using the core ideas of group theory. It treats exponentiation geometrically as rotation and scaling instead of repeated multiplication.

3Blue1Brown's first chapter on deep learning explains what neurons and layers are and the math underlying a basic neural network, using handwritten digit recognition with visual animations.

Kurzgesagt explains how the European Union is governed, how its officials are elected or appointed, and whether a citizen's vote actually matters.

A short CGP Grey explainer on the overlapping and inconsistent membership arrangements of European countries across the EU, Schengen, the euro and the EEA. It shows why "the EU" is full of exceptions.

An animated map showing the borders and populations of European countries for every year since 400 BC. Vassal states and colonies are excluded from population counts.

A short 3Blue1Brown video explaining Euler's formula e^(i*pi) = -1 through dynamics, treating velocity as the thing that moves a point to a new position. It builds geometric intuition for why an exponent with i produces rotation.

3Blue1Brown's second neural network chapter explains cost functions and gradient descent, showing how a network learns by minimizing error during training.

Two Minute Papers covers a paper on speeding up fluid and smoke simulation with convolutional networks. It contrasts the approach with earlier regression forest methods.

CGP Grey's six-minute explainer of the relationships the UK could have with the EU, based on Barnier's slide, shown as orbits of different closeness. It explains why the UK's red lines ruled out the closer options.

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.

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.

A Two Minute Papers episode on NVIDIA's recurrent denoising autoencoder, which cleans up noisy Monte Carlo path-traced image sequences. It shows how a neural network can produce usable renders from very few samples.

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.

CGP Grey explains split-brain patients, where severing the corpus callosum lets the two hemispheres act independently. He uses this to explore the idea of two minds in one head.

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.

An RSA Animate summary of Iain McGilchrist's lecture on the divided brain, arguing the brain's two hemispheres attend to the world differently and that this has shaped culture and society.

A video arguing that exercise matters for the brain as much as the body, linking movement, the nervous system and BDNF to learning and memory. It draws on research connecting complex movement to brain development.

A short TED-Ed animated lesson by Anita Collins on what happens in the brain when people play a musical instrument. It argues that playing engages many brain areas at once, like a full-body workout, with long-term benefits.

Mentour Pilot, a 737 instructor, explains the approach-to-stall and escape manoeuvre and why the 737 MAX needs MCAS while the 737NG did not. He covers the jackscrew and pitch behavior in terms a general viewer can follow.

Tom Scott explains why hold music sounds worse than it used to, tracing it to old telephone exchanges and the audio compression applied by modern switches. It is a short visit to the Milton Keynes Museum.

3kliksphilip summarizes Valve's GDC talk on VACNet, a deep-learning system that flags CS:GO cheaters and feeds the Overwatch review queue. It covers Trust Factor, VAC, and how the data is collected and analyzed.

Verge Science's pilot of its Trial & Error series follows amateur scientist Jon Larsen on a hunt for micrometeorites. It shows how tiny space rocks can be found on rooftops and confirmed under a microscope.

CGP Grey asks whether Star Trek-style teleportation would kill you and recreate a copy, working through the philosophy of identity and the Ship of Theseus. It is a short animated explainer.

Chubbyemu narrates the true case of a professor who spilled two drops of dimethylmercury on her hand and suffered fatal neurological damage.

Numberphile talks with Grant Sanderson of 3Blue1Brown about a darts puzzle with a shrinking bullseye. Solving it takes the volumes of high-dimensional spheres, and the answer turns up Euler's number.

3Blue1Brown's animated visual introduction to the Fourier Transform, showing how a signal breaks into frequency components.

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

A 10-minute 3Blue1Brown chapter explaining the determinant as the factor by which a linear transformation scales area or volume. It builds the idea geometrically with animations before any formulas.

A short animated simulation comparing how Multics and Unix were developed, showing why Unix's small composable programs and pipes gave it a efficiency advantage. It frames Unix as a moonshot achievable by a small team.

3Blue1Brown explains fractal dimension and shows why many fractals are not strictly self-similar. Self-similarity turns out to be a special case of the broader idea of fractional dimension.

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 visualizes high-dimensional spheres to explain a surprising puzzle about how a sphere fits in a box as dimensions grow. It builds geometric intuition for counterintuitive properties of high-dimensional space.

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 short How to ADHD explainer, featuring Brendan Mahan, on why simple tasks can feel impossible for people with ADHD. It introduces the 'wall of awful', a pile of past failures, shame and anxiety that builds up in front of a task and blocks starting it.

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.

Matt Parker talks Numberphile through the different kinds of numbers: algebraic, transcendental, computable, normal, and beyond. It shows how few numbers we can actually name or describe.

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.

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.

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.

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