The people at the bottom do not have the larger, global view, but at the top they do not have the local view of all the details, many of which can of… - Richard Hamming

The idea that theorems follow from the postulates does not correspond to simple observation. If the Pythagorean theorem were found to not follow from the postulates, we would again search for a way to alter the postulates until it was true. Euclid's postulates came from the Pythagorean theorem, not the other way around.

We must not forget, in all the enthusiasm for computer simulations, occasionally we must look at Nature as She is.

The assumptions and definitions of mathematics and science come from our intuition, which is based ultimately on experience. They then get shaped by further experience in using them and are occasionally revised. They are not fixed for all eternity.