Most economists believe that markets are efficient, and a lot of our financial
infrastructure is founded on this premise (the EMH).
Most mathematicians believe that P≠NP, and it would be a bombshell in the math
world if it were proved false.
The paper below by Philip Maymin [1] proves these two theories directly
contradict each other, and that only one can be true.
In other words: If P≠NP, then the EMH is not true, and it will always be
possible to make risk-free money. But if the EMH is true, then the capital
markets are the perfect computing fabric, and can efficiently solve any
NP-hard computational problem.
After reading the paper, and a little reflection, it's pretty obvious (almost
intuitive) that the EMH is very unlikely to be true, but the insight is quite
startling.
-Dan
[1] Markets are efficient if and only if P=NP
http://arxiv.org/abs/1002.2284v2
PS: You don't need to be versed in either economics or mathematics to read
and enjoy this paper. It's well-written, and introduces all the necessary
concepts in an accessible, digestible way. Thanks to Raul for bringing this
to my attention on Twitter (by retweeting Charles Stross, @cstross).
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