I’ve been saying for a while that the big problems in computer science (eg, P vs NP; a theory of distributed systems; effective GO-playing machines; etc) need radical new methods, and I have suggested algebraic topology as a likely source of ideas. Joel Friedman has just applied some alg-top to boolean complexity, motivated by the P vs. NP problem, in Cohomology in Grothendieck Topologies and Lower Bounds in Boolean Complexity.

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