I think this is a nice and fair description of the philosophy of Jürgen Ehlers. However I would like to make a comment on the distinction between ”mathematical ” and ”physical ” proofs. I think the situation is a little more complicated especially there are situations in which a proof might be more interesting than the theorem which is proven. Let me give you some examples.

1. The first is based on an article of Halmos whose reference I don’t remember right now. It is about the celebrated 4 color problem. The structure of the proof was known for some time, however the details required a huge amount of calculations which finally were done by a computer and so the complete proof seems not to provide any “new” insight.

2. The same holds for a theorem which is even more famous, the n-body problem in Newtonian gravity. The original problem, as formulated in the King Oscar II price, was to find a global solution which could be expanded by a convergent power series. That problem was not solved, but finally Poincare was awarded for his contribution which lead to the discovery of chaos. 20 years later Sundman proved the theorem as demanded by the scientific board. It turned out however that the power series converges so slowly that it does not provide any qualitative nor quantitative insight. So we have here an example of an important theorem but the proof does not provide any insight.

3. The second example concerns Fermats last theorem. I think Gauss himself complained about some conjectures in number theory saying that he would be able to provide hundreds of similar conjectures. However Wiles proof was celebrated for the new techniques and insights it provides but so much for the fact that the theorem was proven or disproven. (As Halmos puts it: I don’t want to know WHETHER a particular conjecture is true, I want to know WHY it is true or not).

4 The last example would concern a theorem with outstanding importance in the sense that many statements would depend on it, such as the Riemann hypothesis or (maybe) P=NP. In that case any proof would be welcome.