Smooth geometry vs (nonsmooth calculus and combinatorics)
I am intrigued by this part of the post from NEW
“The public talk by Cumrun Vafa puts out the classic message that strings have come to the rescue of physics, unifying QM and gravity, and that:
Smooth geometry of strings seems to explain all known interactions (at least in principle)”
Why “smooth”? Probably only because this is in the comfort zone of many.
However, there are two new fields of mathematics which deserve to be taken into consideration by physicists (or not, not my problem in fact):
- Nonsmooth calculus, see for an intro this excellent review by Juha Heinonen .
- Additive combinatorics, see this book by Terence Tao, Van Vu.
That’s the future!
UPDATE: (24.03.2012) Congratulations to Endre Szemeredi, the Abel Prize Laureate 2012, “for his fundamental contributions to discrete mathematics and theoretical computer science, and in recognition of the profound and lasting impact of these contributions on additive number theory and ergodic theory.”
… and modern physics, maybe in 50 years.