25 - Superconductivity and Other Insoluble Problems

Summary

Before they are solved, scientific problems often seem very difficult, perhaps impossible. But once they have been solved, the solutions sometimes seem obvious, even inevitable. But are there some scientific problems that are genuinely insoluble? If so, what are they? And how would we know?

On this fiftieth anniversary of BCS (Superconductivity, not the Bowl Championship Series) it's hard to recapture the very great difficulty (even conjectured insolubility) this problem appeared to present just half a century ago. Many of the greatest names in physics had tried or were trying their hand – Einstein, Bohr, Heisenberg, and Feynman, among many others. The contrast between then (impossible) and now (safely ensconced in textbooks) leads me to reflect a bit about problems, past and present, thought to be insoluble.

Problems are thought to be insoluble for different reasons: it may be too soon, as Newton's attempts to understand the properties of matter, or Einstein's 1922 attempt to construct a theory of superconductivity before a quantum theory of metals was in place. It maybe that existing science does not contain the solution – a new postulate or law of nature is required, as Max Planck's 1901 quantum hypothesis. Or might it sometimes be that no solution is possible? Put another way: Are there limits to what we can understand? Are there limits to science as we do it? Are some questions inaccessible to human intellect?