[Dn_Ab]

I don't understand how the field of math can change course. I mean Hilbert, Frege, Church had an idea that turned out to be infeasible. But the field in general continued and has not been affected much by that goal nor the consequences of Godel's theorems. In mathematics there is no where in particular we want to go to. This notion of course changing is thus something I am having trouble placing.

As for physics. The idea of not changing course is exactly what sets apart good theories from bad. If you have a new theory and it does not include the old at a limit then it is a good sign that you are doing something wrong. Newton was not wrong, just inaccurate. Einstein did not invalidate Newton, only corrected the extreme cases.