I’ve come across a quote by the great Buckminster Fuller:
When I’m working on a problem, I never think about beauty. I think only how to solve the problem. But when I have finished, if the solution is beautiful, I know it is wrong.
-Richard Buckminster Fuller
I felt satisfied – I always thought that requiring beauty in our solutions (in mathematics, physics, design or elsewhere) is very parochial. If your solution is beautiful, it only means the problem was too easy.
This is not to diminish the aesthetic pleasure of a beautiful proof, particularly clever experiment setup or elegant line of reasoning. Even after so many years, I still remember when I first heard the Cantor’s diagonal argument  and I can re-live the sheer excitement of it.
On the other end of the beauty spectrum we can put the proof of the Four-color theorem. It was derived in the 70s using a computer and because of that it was (and still is) considered inelegant and problematic. Similarly, in physics solutions derived based on simulations are often deemed intellectually unsatisfactory.
However, beauty is a just a heuristic criterion telling us that a description of the system was found, which not only has a high-compression factor (sign of a good theory), but that this compression is in fact high enough to make the model of the system conveniently mind-sized, i.e. that it fits into the very limited memory and processing capacity of a human brain.
This also means, that a more capable cogitor (presumably an artificial intelligence) would have an aesthetic sense that extends far beyond the reaches of human minds and most of its creations would be deemed ugly by our standards. For such a system the difference between the Cantor’s diagonal and the reduction to 1936 submaps in the Four Color Problem might be only a tiny step down in the “beauty” department.
In the general problem space, problem that have solution we deem beautiful occupy only a vanishingly small subvolume. What worries me is that for many of our most important problems (scientific, technological, societal, ecological) there might be no solutions that we will considered beautiful. If we’re looking for beauty we might miss the correct (or at least satisficing) solutions.
One final lesson too: to echo the original quote – if you think you found a citation that beautifully demonstrates your idea, you know it is wrong.
Why? It turns out, that originally I misread the quote and it should in fact read:
When I’m working on a problem, I never think about beauty. I think only how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong.
-Richard Buckminster Fuller
So while Fuller doesn’t calls for looking for beautiful solutions, he still does use it as a correctness criterion. Let’s just hope we are not dismissing a satisfactory solutions, by chasing a mirage of a (non-existing) beautiful solution.
 If you haven’t seen it yet, I almost envy you that you have the experience ahead of you. Do yourself a favor and check it out!