Category: Topology

Stone-Weierstrass on a disk

A couple weeks ago I wrote about a sort of paradox, that Weierstrass’ approximation theorem could seem to contradict Morera’s theorem. Weierstrass says that the uniform limit of polynomials can be an arbitrary continuous function, and so may have sharp creases. But Morera’s theorem says that the uniform limit of polynomials is analytic and thus […]

Putting topological data analysis in context

I got a review copy of The Mathematics of Data recently. Five of the six chapters are relatively conventional, a mixture of topics in numerical linear algebra, optimization, and probability. The final chapter, written by Robert Ghrist, is entitled Homological Algebra and Data. Those who grew up with Sesame Street may recall the song “Which […]

A genius can admit finding things difficult

Karen Uhlenbeck has just received the Abel Prize. Many say that the Fields Medal is the analog of the Nobel Prize for mathematics, but others say that the Abel Prize is a better analog. The Abel prize is a recognition of achievement over a career whereas the Fields Medal is only awarded for work done […]