From the point of view of computational complexity, several combinatorial optimization problems (e.g. MAX 3SAT, MAX CUT, SPARSEST CUT) are equivalent, at first sight: all are NP-complete. In certain cases, even approximate versions, where solutions are merely required to achieve a given fraction of the optimum, remain NP-complete. This is the meaning of the PCP Theorem (1992). For MAX CUT, one is now able to conjecture the exact value of the approximation threshold, thanks to progress relying on geometry and discrete harmonic analysis.