The notion of symmetric programming grew out of a gradual realization that symmetric structures – as defined in this book – provide the means for a wide ranging unification of economic problems. A conjecture immediately and naturally followed: symmetric structures are more general than asymmetric ones as long as the right approach to symmetry is embraced. There are, in fact, two ways to symmetrize asymmetric problems: a reductionist and an embedding approach. The reductionist strategy eliminates, by assumption, those elements that make the original problem asymmetric. This is the least interesting of the two approaches but one that is followed by the majority of researchers. The alternative strategy seeks to embed the original asymmetric problem into a larger symmetric structure. The way to execute this research program is never obvious but is always rewarding. This book is entirely devoted to the illustration of this second approach.

With the unification of problems there comes also the unification of methodologies. Rather than associating different algorithms to different problems, symmetric programming allows for the application of the same algorithm to a large family of problems.

Unification has always been one of the principal objectives of science. When different problems are unified under a new encompassing theory, a better understanding of those problems and of the theory itself is achieved. Paradoxically, unification leads to simplicity, albeit a kind of rarefied simplicity whose understanding requires long years of schooling.