4 ms·

I think most mathematicians feel the same. (Although as the article points out, Scholze did write a 'for Dummies' version of Harris & Taylor's local Langlands

I think most mathematicians feel the same. (Although as the article points out, Scholze did write a 'for Dummies' version of Harris & Taylor's local Langlands paper.) For perfectoid spaces, the most accessible thing I know of is Jared Weinstein's article in the Bulletin of the AMS. http://www.ams.org/journals/bull/2016-53-01/S0273-0979-2015-01515-6/ http://www.ams.org/journals/bull/2016-53-01/S0273-0979-2015-...

Chris2048 9y ago
> I think most mathematicians feel the same About this in particular, or advanced mathematics? If the latter, why don't those mathematicians do it one they understand!?
- lmm 9y ago
  They do, gradually. Good review articles are respected and people put a lot of effort into them; eventually stuff percolates down to textbooks and so on. The kind of thing that an advanced grad student would struggle with a few decades ago becomes an undergrad exercise today. But meanwhile the frontier keeps advancing.
- dkarl 9y ago
  “You have only some kind of limited capacity in your head, so you can’t do too complicated things.” A Peter Scholze quote from the article that captures for me one of the two common aspects of programming and mathematics, that we make progress by building better and better conceptual machines (the intellectual equivalents of levers, pulleys, inclined planes, etc.) to multiply our limited limited capacity to solve more and more difficult problems. Edit/PS: You can see how highly mathematicians respect simplification by the story in the article about how Peter Scholze first became internationally famous in the mathematical community, by discovering a new solution for an already solved problem. His solution was much shorter (and apparently easier to follow,) and that was taken as a sign of exceptional ability, just as it is in programming.

4 ms·

I think most mathematicians feel the same. (Although as the article points out, Scholze did write a 'for Dummies' version of Harris & Taylor's local Langlands

by auntienomen 9y ago

Chris2048 9y ago
> I think most mathematicians feel the same About this in particular, or advanced mathematics? If the latter, why don't those mathematicians do it one they understand!?
- lmm 9y ago
  They do, gradually. Good review articles are respected and people put a lot of effort into them; eventually stuff percolates down to textbooks and so on. The kind of thing that an advanced grad student would struggle with a few decades ago becomes an undergrad exercise today. But meanwhile the frontier keeps advancing.
- dkarl 9y ago
  “You have only some kind of limited capacity in your head, so you can’t do too complicated things.” A Peter Scholze quote from the article that captures for me one of the two common aspects of programming and mathematics, that we make progress by building better and better conceptual machines (the intellectual equivalents of levers, pulleys, inclined planes, etc.) to multiply our limited limited capacity to solve more and more difficult problems. Edit/PS: You can see how highly mathematicians respect simplification by the story in the article about how Peter Scholze first became internationally famous in the mathematical community, by discovering a new solution for an already solved problem. His solution was much shorter (and apparently easier to follow,) and that was taken as a sign of exceptional ability, just as it is in programming.