[AmishDude]

Surely it depends on what you want to know. You don't have some natural world as a crutch. Theorems proven with or without the AoC are simply done that way. Your system depends on assumptions. Without the AoC, you are constrained and can only gather certain conclusions. With it, you can get a lot more, but at the cost of an assumption.

A lot of scientists do not realize exactly how many things they assume when they use some ancient model. It's essential to understanding when it fails to predict something.

When you strip the particulars from any problem, you get a much better perspective on the one you care about. You can see how it relates to similar problems and how that was attacked. You can then see that biology is chemistry is physics is engineering in a very broad sense. It's the same issues and the same problems over and over again. But this involves dealing in the abstract.

[donh]

...A lot of scientists do not realize exactly how many things they assume when they use some ancient model. It's essential to understanding when it fails to predict something....

All university-trained scientists I have ever met were familiar with ZFC, and the value of the discovery of isomorphisms between the mathematics of disparate disciplines. Try not to break your armature patting yourself on the Laplace Transform.