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Re: physics before math????



My statement (somewhat out of context) was:

> ..... Physics is validated by experiment. Math is validated
> by rigor. ....

To which on Sat, 22 Jan 2000, Ludwik Kowalski objected:

That is what philosophers say. They want laymen think that in
mathematics proofs come before discoveries and in physics
discoveries are made in laboratories, according to "experimental
method". In reality, as pointed out by others on this list, neither
physicists nor mathematicians feel obliged to follow the paths
prescribed by philosophers. The proof is in the pudding, not in
the way in which it was prepared. Each of us can give examples
of accidental discoveries in science, or discoveries based on the
basis of who knows what.

* For real-world puddings, the proof is in the eating.
* For mathematical theorems, the proof is in the proof!!!!

I agree that in neither case does it matter how the (pudding/theorem) was
brought into existence.

Yes, a logical
derivation is an agreed upon method of validation of mathematical
theorems

OK, we agree on that.

but "applied math" people are not waiting for formal
proofs. They verify postulated relations numerically and use them
in applications. A proof is more often than not the last step which
has nothing to do with the way in which a relation was actually
discovered.

These remarks appear to contradict my out-of-context statement, but in fact
support the point I was making about the distinction between pure math and
applied math. I insist there is a place for mathematical purity, rigor,
and abstraction. We agree that math-instruction that is tightly coupled to
physics-instruction has obvious advantages; my point remains that it has
corresponding disadvantages, notably that it tends to over-emphasize
applied math while short-changing pure math.

I note with thanks that at 01:22 PM 1/22/00 -0800, John Mallinckrodt made a
similar point.