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.

But mathematics is the only science in which a "theory" can be
_logically proven_.

Is math, thusly, a pseudo science?

Math is a different type of science. For instance, it's the only
situation (science or otherwise) where you can actually use the verb
"to be" in its literal sense.

For instance, the chant "Fur is murder" REALLY means "In my belief,
animals should not be killed to make certain types of garments."
(However, this chant is not as emotional as "Fur is murder", just like,
"Eat the cheeseburger, astronaut boy!"*) The physics law "Force is mass
times acceleration" really means "In all the tests so far, the force
and mass times acceleration have agreed in value."

--- Christopher Heckman

* From the TV show "Upright Citizens Brigade", an example of Discordian
comedy. They satirize discrimination by having "astronaut" being the
least desirable occupation possible, even below "politician".