[burzum]

I would agree with the statement that mathematics is not science because it doesn't follow the scientific method. You don't observe data, make a hypothesis, test it, and form a theory. In mathematics you just work from theorem to theorem based on axioms. While you can do something similar in the sciences, you are always constrained to the fact that if your theory doesn't match your data, the theory is wrong. In mathematics, the theorem *makes* the data.

[mwyounce]

A physicist, an engineer and a mathematician were all in a hotel
sleeping when a fire broke out in their respective rooms.

The physicist woke up, saw the fire in his room, ran over to his desk, pulled
out his CRC, and began working out all sorts of fluid dynamics
equations. After a couple minutes, he threw down his pencil, got
a graduated cylinder out of his suitcase, and measured out a
precise amount of water. He threw it on the fire, extinguishing
it, with not a drop wasted, and went back to sleep.

The engineer woke up, saw the fire, ran into the bathroom, turned
on the faucets full-blast, flooding out the entire hotel room,
which put out the fire, and went back to sleep.

The mathematician woke up, saw the fire, ran over to his desk,
began working through theorems, lemmas, hypotheses , you -name-it,
and after a few minutes, put down his pencil triumphantly and
exclaimed, "I have proven that I can put the fire out!"
He then went back to sleep.

[muawiyah]

Alas, here we have the axiom having a quantum source ~ and vice versa (to some).

Science (l. scientium) is simply accumulated knowledge ~ and Mathematics (l. matemateca) is a study of numbers and the accumulated knowledge therefrom.

We now know with certainty that the study of numbers is the study of underlying reality ~ which is much more than a simple accounting for the numbers.

Philosophers have always pointed out that mathematics is mother to science, and now, we have <-> Fur Shur, eh!

[Samwise]

Mathematics is the language of science. IMHO