Perhaps the hardest scientific problems to solve are those most scientists believe have already been solved, but which have not. Any model we make of an astronomical process is doomed to be incomplete at some level; the “broad-brush” picture of stellar structure and evolution is often accepted as a solved problem, but in fact many discrepancies exist between our models and the observations.

For example, the “standard solar model” fails to predict the observed neutrino flux from the Sun, and its insistence that the Sun’s luminosity increased by 30% over geological time is not in accord with the evidence. White dwarf stars were thought to be stable against pulsation because the models did not pulsate, and it took a long time to improve them to the point where they did, and could then begin to match our observations of pulsating white dwarfs. For several years their outer hydrogen layers were thought to be extremely thin because models with thicker layers did not pulsate; once the zoning problem was found and solved in the models they could begin to match observations better. These past difficulties illustrate a common danger: it is very easy to confuse our models with the observed reality they try to mimic, and to assume they match better than they do. In what follows I will try to keep the observations and our models of them separate.