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 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.

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.

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

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.