As theoretical physics and chemistry have developed since the great quantum revolution of the 1920s, there has been an explosive speciation of subfields, perhaps comparable to the late Precambrian period in biological evolution. The result is that these life-forms not only fail to interbreed, but can fail to find common ground even when placed in proximity on a university campus. And yet, the underlying intellectual DNA remains remarkably similar, in analogy to the findings of recent research in biology. The purpose of this present text is to identify common strands in the substrate of variational theory and to express them in a form that is intelligible to participants in these subfields. The goal is to make hard-won insights from each line of development accessible to others, across the barriers that separate these specialized intellectual niches.

Another great revolution was initiated in the last midcentury, with the introduction of digital computers. In many subfields, there has been a fundamental change in the attitude of practicing theoreticians toward their theory, primarily a change of practical goals. There is no longer a well-defined barrier between theory for the sake of understanding and theory for the sake of predicting quantitative data. Given modern resources of computational power and the coevolving development of efficient algorithms and widely accessible computer program tools, a formal theoretical insight can often be exploited very rapidly, and verified by quantitative implications for experiment. A growing archive records experimental controversies that have been resolved by quantitative computational theory.