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A Fields medalist walked into an Oxford room in 2020 and taught first-year students what a determinant is.
The lecturer is James Maynard. He was 32 at the time and had already broken open a problem the field had been stuck on for 2,000 years.
The subject is Linear Algebra II. He is defining a function that eats a square matrix and returns 1 number.
The number is a volume. Feed a matrix the unit cube and the determinant tells you how much the transformation stretched or squashed it.
A determinant of 0 means the shape got flattened into a lower dimension. Nothing can unflatten it, which is exactly when a matrix has no inverse.
A negative determinant means the space got turned inside out.
Every graphics engine, every physics simulation, every solver checks that 1 number before doing anything else.
Maynard won the Fields Medal in 2022 for work on gaps between primes, sharpening the bound Yitang Zhang had produced from nothing.
Oxford films these and puts them up for free, tutorials and problem sheets included.
The best number theorist of his generation spent an hour on the volume of a box.
A BBC interviewer asked a Nobel physicist the simplest question in the world: why do two magnets push each other apart. He refused to answer it. What he did instead is the best seven minutes on thinking ever filmed.
The man is Richard Feynman, at home in 1983, no blackboard, no notes, sitting in an armchair.
He does not dodge because he cannot answer. He dodges because he wants you to see what the question is actually asking. So he takes an ordinary sentence, that a woman slipped on the ice and broke her hip, and starts asking why, and every answer opens another why, until the ground gives way.
Then he turns it around on the interviewer with a question about ice that sounds trivial and is not.
The point he arrives at is the uncomfortable one. Every explanation is only a translation into something you already accept without explanation. Magnets have no such translation. There is nothing more familiar than magnetism to reduce magnetism to, which is why every answer you were given at school was a picture, not a reason.
It matters more now than it did in 1983. Any tool will hand you a fluent answer in a second. Knowing which questions actually have a bottom is the part that is still yours.
One question. Seven minutes. It is in the video.