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What is your favorite theorem of the 20th century and why?
The rule is a proof must have been published some time in the 20th century. Theorems that were conjectures in the 20th century and but not proven until the 21st century don't count; theorems that were conjectures before the 20th century and proven in the 20th century do.
My personal favorite is the Atiyah-Singer Index Theorem, which is good because it's pretty much my job to think about that theorem. But I have a soft spot for the Jordan Curve Theorem (not proven rigorously until 1905!), and I really wish I understood Deligne's proof of the Weil conjectures.
My least favorite theorems are the four color theorem and the classification of finite simple groups. In the words of Hardy, "There is no permanent place in the world for ugly mathematics".
3 Answers
- spoon737Lv 61 decade agoFavorite Answer
My favorite is one of your least favorites, the classification of the finite simple groups (aka The Enormous Theorem). I understand what you mean when you refer to it as "ugly mathematics" as I would hardly call a proof which spans more than 10,000 pages elegant. However, the theorem itself had such a profound impact on group theory, that it is easily one of the most important mathematical results of the 20th century. I hate to contradict the words of our good friend Hardy, but this theorem definitely has a permanent place in the mathematical world.
- pabstLv 45 years ago
a million) Stravinsky, Denisov, Webern, Schnittke, Varese, Shostakovich, and the occasional Copland piece. 2) Stravinsky - ceremony of Spring; Denisov - solar of the Incas, Peinture; Webern - op. 18, 21, 24, 28, Schnittke - Requiem; Varese - Octandre, Integrales; Shostakovich - Symphony #8, 10, 24 Preludes and Fugues; Copland - Symphony #3 (i'm a sucker) 3) Bruckner wrote great choral song yet would desire to have by no ability written something for orchestra. Ugh. BQ) especially stable, thank you.
- GibsonEssGeeLv 71 decade ago
"Your accumulated clutter moves out to fill the space made available to it". Which is a dead handy excuse when you get asked to clean your room.
