mathematical logic

Technology Connections takes apart the step-by-step electromechanical logic of a 1970s pinball machine. He shows how relays, steppers and switches track state and score without electronics.

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.

Technology Connections takes a long, detailed look at how a 1970s electromechanical pinball machine works, from relays to stepper motors and mechanical logic. It is the first part of a series.

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

Arthur Keller gives a roughly half-hour crash course on environmental collapse, covering exponential growth, carrying capacity and ecological overshoot.

Kyle Hill explains what nuclear waste actually is and how it is stored, arguing that the problem was effectively solved decades ago. It covers solid shielded waste and deep geological storage.

Kurzgesagt asks whether advanced civilizations could have existed on Earth in the deep past and left little evidence. It looks at time as a dimension for searching for alien civilizations and the limits of the geological record.

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.

Kurzgesagt's hour-long animated film that compresses Earth's 4.5 billion year history into one hour, roughly a million years per second. It follows the evolution of life through to humanity's tiny final stretch.

3Blue1Brown presents the Triangle of Power, an alternate notation that unifies powers, logarithms and roots in a single triangular symbol. The video shows how the inverse operations relate and how the notation could help.

A short explainer on the physiological differences between fasting and simply eating less. It covers ketosis, ghrelin and hunger waves, and the hormonal effects of fasting.

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.

Ben Eater gives a detailed look at how an NPN bipolar junction transistor works and what it does. It is an eleven-minute explanation aimed at building real understanding of the device.

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.

A PBS Space Time episode on how the Higgs mechanism gives particles mass, prompted by Fermilab's heavier-than-expected W boson measurement. It goes beyond the usual pop-science treatment without heavy math.

Steve Mould explains homochirality: why biological molecules like sugars and amino acids come in only one handedness. He covers ideas about how this asymmetry might have arisen, touching on meteorite samples and RNA.

A Wendover Productions explainer on how airport security is designed, covering screening layers, x-ray scanning, and the contrast with Israel's profiling-based approach. It walks through the logic behind why security works the way it does.

Technology Connections takes apart a 1970 Wurlitzer 3400 jukebox to show how electromechanical relays and switches automated its behavior without a computer.

A short Art of the Problem clip explaining Diffie-Hellman key exchange, using a paint mixing analogy for one-way functions and touching on modular arithmetic and discrete logarithms.

Curious Droid asks what traces human civilization would leave in the geological record 65 million years from now. It considers how thin the fossil record of humanity might be.

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

3Blue1Brown introduces group theory and abstract groups, then builds toward classification of finite simple groups and the enormous Monster group with its 196,883 dimensions.

Chubbyemu presents a case study of a man who followed AI health advice, replaced salt with sodium bromide and developed bromism with severe neurological effects. It is told as a dramatized medical case by a doctor.

PBS Space Time examines the Silurian hypothesis, the idea that an industrial civilization could have existed on Earth before humans. It looks at what traces such a civilization might leave in the geological record.