Hyperclimbing is an intuitive, general-purpose, global optimization heuristic applicable to discrete product spaces with rugged or stochastic cost functions. The strength of this heuristic lies in its insusceptibility to local optima when the cost function is deterministic, and its tolerance for noise when the cost function is stochastic. Hyperclimbing works by decimating a search space, i.e., by iteratively fixing the values of small numbers of variables. The hyperclimbing hypothesis posits that genetic algorithms with uniform crossover (UGAs) perform optimization by implementing efficient hyperclimbing. Proof of concept for the hyperclimbing hypothesis comes from the use of an analytic technique that exploits algorithmic symmetry. By way of validation, we present experimental results showing that a simple tweak inspired by the hyperclimbing hypothesis dramatically improves the performance of a UGA on large, random instances of MAX-3SAT and the Sherrington Kirkpatrick Spin Glasses problem. An exciting corollary of the hyperclimbing hypothesis is that a form of implicit parallelism more powerful than the kind described by Holland underlies optimization in UGAs. The implications of the hyperclimbing hypothesis for Evolutionary Computation and Artificial Intelligence are discussed.