This page contains list of mathematical Theorems which are at the same time great, easy to understand, and published in the 21st century.
Here, by “great” is meant that a theorem is proved in a paper which is:
- either published in a top journal (Annals of Mathematics, Journal of the AMS, Acta Mathematica, Inventiones Mathematicae, Publications Mathématiques de l’IHES, Forum of Mathematics Pi),
- or is one of the most cited papers on Mathscinet in the corresponding year and subject category,
- or won a prestigious prize given for a specific paper/theorem (Millenium prize problem, Fulkerson prize, Godel prize, etc.),
- or solves an important long-standing open problem,
- or is a recent preprint which, in my opinion, has a potential to satisfy the criteria above (e.g. be accepted to a top journal) in the future.
By “understandable” I mean that a good undergraduate student should be able to understand the theorem formulation (possibly after looking online for background definitions) with not too much efforts.
By “published in the 21st century” I mean that the last, final version of the paper (which is usually but not always a journal version), should be dated in 2001 or later. In particular, papers submitted (to arxiv or journal) at the end of 20th century but published in the 21st century are included.
Theorems of the 21st century 