finite fields

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.

PBS Infinite Series explains how Shor's algorithm lets a quantum computer break RSA encryption, building on earlier episodes about cryptography and the math of quantum computers. It works through the idea step by step.

Veritasium argues that electric energy is carried by fields around the wires rather than by electrons moving through them, using a thought experiment with a large circuit.

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.

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.

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.

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.

Veritasium explains how Penrose tilings and quasicrystals overturned the belief that 5-fold symmetry and non-periodic crystals were impossible, including an interview with Paul Steinhardt.

Veritasium explores how electrical energy actually travels in a circuit, arguing that it flows through electromagnetic fields around the wires rather than through the electrons. It builds a long-cable experiment with Caltech to test when a distant bulb lights.

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.

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

A Numberphile video in which physicists Tony Padilla and Ed Copeland show a seemingly astounding result that 1+2+3+4+... equals -1/12. The argument is informal and has drawn criticism for glossing over what the result actually means.

ScienceClic gives a 15-minute animated introduction to quantum field theory, covering fields, spin, conserved quantities, the standard model and interactions.

Veritasium explains magnetism as a consequence of special relativity. Length contraction of moving charges makes a current in a wire attract or repel a nearby moving charge.

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.

A PBS clip in which Richard Feynman explains the strange nature of light and electromagnetic radiation. He conveys how little of it we actually see and how radio waves are present everywhere.

Veritasium explains why many real-world systems follow power laws rather than normal distributions. It covers self-organized criticality, with simulations of sandpiles, magnetism and forest fires.

Kurzgesagt explains why, even with science-fiction technology, most of the universe is permanently out of reach because of cosmic expansion and finite resources.

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.

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.

Veritasium visits the National High Magnetic Field Laboratory to see the world's strongest magnets and demonstrate effects like eddy currents. It covers what intense magnetic fields do to materials and objects.