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Mathematical discoveries are in viting changes in biologists' thinking about the origins of order in evolution. Allliving things are highly ordered systems: they have intri cate structures that are maintained and even duplicated through a precise bal let of chemical and behavioral activi ties. Since D, biologists have seen natural selection as virtually the sole source of that order. But D could not have suspected the existence of self-organization, a re cently discovered, innate property of some complex systems. It is possible that biological order reflects in part a spontaneous order on which selection has acted. Selection has molded, but was not compelled to invent, the na tive coherence of ontogeny, or biologi cal development. Indeed, the capacity to evolve and adapt may itself be an achievement of evolution. The studies supporting these conclu sions remain tentative and incomplete. Nevertheless, on the basis of mathe …