Get your torches ready! Here is my opinion about whether mathematics is a science or not:

Mathematics is most definitely not a science. In science, it is assume that

there are a set of fundamental rules, the laws of nature,

and the task is to figure out what the rules are by observing the

results that occur when the rules are followed. Basically, it's an

attempt to reverse-engineer the machinery of the universe.

In math, it's the other way around. You get to choose the rules, and

the task is to discover the results of choosing any particular set of

rules. There is a superficial similarity, which leads some people to confuse

the two pursuits. In science, the way you test a theory is to codify

it as a set of rules, and then explore the consequences of those rules

- in effect, to predict what would happen if those rules were true.

You do the same thing in math, and in fact, the way it's done in math

serves as a model for the way it's done in science. But here is the big difference:

In science, as soon as your predictions conflict with experimental data, you're done.

You know that your rules are wrong, and you need to start putting together a

new set.

In math, this kind of conflict can't arise, because there is no

necessary connection between any mathematical theory and the world.

The way you test a set of rules in math is see whether the results

they produce are interesting enough to induce mathematicians to keep

playing with them.

We might summarize the situation this way: Science is the pursuit of

the correct description of our particular world; whereas math is

the pursuit of interesting descriptions of possible worlds. Whereas

scientific theories are right or wrong, mathematical theories are

merely interesting or uninteresting. 8-[ Solitary