One of the recurring themes of this blog will be descriptions of my favorite theorems of the 21st century. I will begin with a special category, Between the Centuries, devoted to theorems that were proved in the late 20th century but published in the early 21st century. After that, I will proceed year by year—starting with 2001, then 2002, and so on.
For each year, I will select my favorite theorem in the following subject areas:
Number Theory
Combinatorics
Analysis
Algebra
Geometry and Topology
Probability and Statistics
Algorithms and Complexity
In addition, I will choose a single favorite theorem of the year across all of mathematics.
This post will serve as a central index for the series, collecting links to all of my selected theorems in one place as the project develops.
Between the Centuries
Number Theory: The Modularity Theorem https://functor.network/user/3333/entry/1572