Analysis
Topics about functions, either complex or real valued
Visualizing the Riemann zeta function and analytic continuationWhat is the Riemann zeta function? What is analytic continuation? This video lays out the complex analysis needed to answer these questions.
But what is the Fourier Transform? A visual introduction.An animated introduction to the Fourier Transform, winding graphs around circles.
The more general uncertainty principle, beyond quantumThe general uncertainty principle, about the concentration of a wave vs the concentration of its fourier transform, applied to two non-quantum examples before showing what it means for the Heisenberg uncertainty principle.
But what is a Fourier series? From heat flow to circle drawingsHow Fourier series arose from studying heat flow, and how they can be thought of as decomposing any drawing in 2d into a sum of rotations.
Researchers thought this was a bug (Borwein integrals)A curious pattern of integrals that all equal pi...until they don't.
But what is a convolution?From probability to image processing and FFTs, an overview of discrete convolutions
Winding numbers and domain coloringAn algorithm for solving continuous 2d equations using winding numbers.
What does it feel like to invent math?A journey through infinite sums, p-adic numbers, and what it feels like to invent new math.
Music And Measure TheoryHow one of the introductory ideas in a field called "measure theory" can be thought of in terms of musical harnomy and dissonance.