new math

An animated 11-minute tour of the whole field of mathematics as a single map, showing how pure and applied math and their sub-fields relate to each other.

Real Engineering looks at the numbers for running California on renewables, focusing on the large energy storage needed. It argues about the cost of batteries and the role of other sources.

Owen Maitzen's animated hour-long introduction to Hackenbush, a simple combinatorial game, and how its strategy leads to surreal numbers and the roots of the number system.

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.

Mathologer shows how times table diagrams on a circle produce cardioids and other curves connected to the Mandelbrot set. He explains the patterns and links to a tool for making your own diagrams.

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.

A long Technology Connections video arguing that public understanding of renewable energy is distorted. It covers solar economics, land use compared with ethanol corn, and battery myths such as cobalt.

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 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.

Vsauce explores math through card tricks and big numbers, including an animation of how enormous 52 factorial, the number of deck orderings, really is.

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 Just Have a Think video on the proposed 16 billion pound Xlinks project to build solar, wind and battery capacity in southern Morocco. It would send around 3.6GW to the UK by subsea HVDC cable as near-baseload power.

Matt Parker of Stand-up Maths explains why people keep making the same mistake with millions and billions, using a Bloomberg cash calculator example. He looks at the unit slip behind the repeated arithmetic error.

Matt Parker of Stand-up Maths explains single-pile Nim and the trick that wins it, using Dr NIM, a 1960s mechanical plastic computer that plays perfectly. He teaches the strategy so viewers can beat friends.

Matt Parker of Stand-up Maths examines the Texas Supreme Court filing claiming Biden's 2020 win had a one-in-a-quadrillion chance. He walks through why the statistical argument is flawed.

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

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.

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.

Matt Parker of Stand-up Maths asks whether a country's reported land area accounts for hills and mountains, working through how surface area depends on the resolution of elevation data. It follows up on a question from a viewer and work by researchers who measured it.

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

Mathologer explains epicycles and complex Fourier series, inspired by an animation of Homer Simpson drawn with epicycles. It covers the shape of the Moon's orbit around the Sun and how to make your own epicycle drawings.

CGP Grey argues for picking a theme for the year or season instead of setting goals or new year's resolutions. He explains how a theme gives direction without a pass/fail target.

ScienceClic explains why the rubber sheet analogy for general relativity is misleading and offers a new visualization that includes the curvature of time and shows gravity as motion through curved spacetime.

Mick West explains the three Navy UFO videos (FLIR, GIMBAL and GOFAST) released in 2020, giving mundane explanations such as a distant plane and camera artifacts. He notes the videos were not new and had been circulating since 2017.

Bill Hammack of engineerguy explains how medieval engineers designed stone cathedrals using rules of thumb, with no science, mathematics or literacy. He uses it to define the engineering method.

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.

A mini-documentary by a Canadian living in Japan explaining how an average family can afford a new detached house in Tokyo. It covers how houses are treated as depreciating assets and how Japanese zoning and building practices keep prices low.

Matthias Wandel tests old and new code on a range of PCs, including a new mini PC, to measure how much faster modern hardware really is. He also shows optimization techniques such as branchless code, with benchmark programs on GitHub.

PBS Space Time examines Roger Penrose's idea that consciousness arises from quantum processes in the brain, and reviews new evidence about microtubules. It ends with an estimate of what replicating consciousness would demand.

Mick West shows new night-vision reference footage indicating the Navy's supposed flying pyramid UFO is just an out-of-focus light, likely a plane near LAX, rendered triangular by bokeh. He identifies other lights as Jupiter and stars.

A Business Insider World Wide Waste episode on H&M's garment recycling machines, which turn used clothing into new apparel. It asks whether a fast fashion company can solve the waste problem it helped create.

Vsauce asks whether music will ever run out of new melodies. It counts the possible note combinations and discusses how common chord progressions and remixing affect originality.

Matt Parker explains the history behind NTSC television running at 29.97 frames per second rather than 30, tracing it to the backward-compatible addition of color. He walks through the arithmetic behind the odd ratio.

Freya Holmer explains how Bezier curves work, from the helper-line construction to their uses in animation, text rendering and shapes. It uses visuals from her Unity Shapes plugin and was a SoME1 contest winner.

Practical Engineering explains why connecting solar and other inverter-based generation to the grid is hard. It covers grid stability, load balancing and the behind-the-scenes engineering challenges of renewables.

Mick West analyzes the Navy's Gimbal UFO video and gives four checkable observations suggesting it is an infrared glare that appears to rotate because the camera rotates while tracking. He argues the object is likely a hot craft hidden behind the glare.

Not Just Bikes explains, using Urban3's property-tax analysis, why car-dependent suburbs generate less tax revenue than they cost to maintain, so dense urban cores effectively subsidize them. It is part of a Strong Towns series.

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.

Real Engineering's Brian McManus explains Helion's approach to nuclear fusion: colliding two plasma rings, compressing them magnetically, and capturing energy directly from the changing magnetic flux rather than boiling water. It covers why this pulsed design sidesteps problems of tokamaks and laser fusion.

Veritasium tells the history of how imaginary numbers arose from the quest for a general solution to the cubic equation, including the duels and secrecy among Renaissance mathematicians. It argues math had to give up the requirement that it mirror reality.