In article . com, "Proginoskes" writes:

Mathematics Lover wrote:
Physics and biology are sciences because they put theories up to
falsifiable tests.

The equivalent for mathematics would be "conjectures", like Goldbach's
Conjecture. This is a statement which has been proven to be true for a
large number of "tests", but no absolute proof found. (Every even
number found so far _can_ be written as the sum of two primes.)
However, tomorrow, it may be proven false. At best, it can be suspected
that the conjecture is true or false.

A conjecture that has been disproven (especially in individual
research) is tossed aside, like a physics concept which has been tested
and found not to exist.

But most of the esoteric math theorems in abstract set, algebra,
geometry, and field
theory have not been tested. Moreover, they cannot be tested. Thus,
they cannot be
scientifically verified or falsified.

Yes, mathematics is unique in this sense. Mathematics works
independently of the universe; for instance, hyperbolic geometry (I
think that's the one) has nothing to do with the real world, but you
can still calculate within it.

Well, the significant difference of math and science (put in "physical
sciences" if you prefer) is as follows: In any given branch of math
the axioms are known and the question may be whether a specific result
follows from the axioms. In physics, the results may be known (to
some accuracy) the question is "what are the axioms?"

Mati Meron | "When you argue with a fool,
| chances are he is doing just the same"