Mathematics is not a science

Your original question wasn't well thought out. One of your intial statements ran along the lines maths is all proofs whereas science is conjectures leading to hypothesis that may be tested for validity.

Well maths has an inifite span of conjectures that may be true but can't be tested to be true. There is alot of experimental maths - see the millennium problems for a start.

For example Fermi last theorum took over 150 years to prove. The mathematical techniques to resolve the theorum as true hadn't evolved until the turn of this century. We still can't prove that NP <> P.

Maths has just as much high end spectulation and discovery as any other field of science - you seemed to miss this understanding.

Ah, the analytic-synthetic dichotomy for the lose.

It is possible for axioms to be grounded in reality. If the system you're using is based on axioms grounded in reality, mathematics can be scientific.

That wasn't so hard, was it? What was that about being a trivial point for anyone who ever took a philosophy class? Sorry, I adhere to a rational philosophy, not the garbage taught in colleges.

There's something much more wrong here than just your belief that mathematics is necessarily true, yet arbitrary. And that is your belief in the analytic-synthetic dichotomy itself.

The dichotomy arises out of a theory of concepts where the meaning of a concept is its definition. If the meaning of a concept is its definition, then any property of the referent not included in the definition is contingent.

In contrast to this theory, is a much better theory of concepts where the meaning of a concept is its referents. This makes every property that the referents have in common necessary.

Here's an example. We're stating two truths about the nature of ice.
A: Ice is solid water.
B: Ice floats.

If the meaning of a concept is its definition, then A is an analytic truth, and B is a synthetic truth. Ice being solid water is taken to be necessary (since that's part of its definition), but detached from reality. B is taken to be true, but only because we just so happen to be observing it to be so. (Ice floating isn't part of its definition, after all.)

If the meaning of a concept is its referents, then suddenly, both A and B are necessary because they are properties of ice. The nature of ice is such that not only can you be sure it is solid water, but you can be sure it floats (in water). Because that's what ice does. Every referent of the concept "ice", that is, every piece of ice, floats (in water).

You're probably going to rage at me for this, if you aren't already. But this is basically the Objectivist criticism of the analytic-synthetic dichotomy. I am an Objectivist. If you're interested, you can read Introduction to Objectivist Epistemology, by Ayn Rand, to learn her theory of concepts. At the end of the book is an essay, The Analytic-Synthetic Dichotomy, by Dr. Leonard Peikoff, that goes into more detail to explain what I just did, and how Ayn Rand's theory of concepts undercuts the dichotomy.

What about Goldbach's conjecture? Is that necessarily true?

Science is more about making inductive inferences from empirical observations made, and mathematics is about deducing conclusions from conceptual axioms.

Well summarized.

I'm not a Scientist, I'm an Engineer (Chemical and Nuclear by education). I've always viewed science as a knowledge data base and mathematics as a tool.

Rap

Be sure to tell this to the editors of Webster's dictionary. It offers several definitions of the word science, yet none of them requires that a discipline restrict itself to contingent truths as opposed to necessary truths. Every definition in the dictionary that covers physics also seems to cover mathematics. Granted, your definition of the word "science" may be different. But that only proves you are using the English language in a nonstandard way. It doesn't prove that general usage errs in identifying maths as a science.

Would anyone agree that Science consists of a "method" employing the INTERACTION between inductive empirical observation and deductive mathematical reasoning?

Science without math is to remove the head from the body.

Yes, for Science narrowly defined, but there are areas of Social Science that have little to do with math, even statistics.

The so-called social sciences are difficult to tie down into simple theorums, because there are too many variables at play. They can use statistics, but that's past history, and not reliable for future use.

Can you identify any of the social sciences that are reliable indicators of the future?

I object to the use of the word science, they should be referred to as the Social Studies.

In science hypotheses requires repeated validation and refinement until a theory capable of making predictions prevails. In studies conflicting hypotheses are frequently both held as valid without the rigor of validation and refinement.

Rap

Theories not theorems-Science Theories, Math Theorems.

Rap

Thank you, raprap. I'll try to remember that.

I share your objection Raprap. Social science lacks the rigor of the physical, and, to a lesser degree, the natural or biological sciences. It's self-definition is too broad in that sense, but it claims a scientific orientation on the grounds that it seeks to be as rigorous, reflexive and non-ideological as possible. Science is its ideal rather than its method, one might say.
Thanks for your reminder of the difference between theories and theorems.

Your explanation for Social Studies is spot on! Many may call it science, but that's a total misnomer.

Mathematics is a formal science.

The most rigorous of the social "sciences" is economics, and we know that if you know the economist's political persuasion you have a good chance of predicting his/her "scientific" predictions.
Social studies provide interpretations, not theories in any formal sense. There are some "universals", like The Principle of Reciprocity, but that is not very formal; I see it as a grand empirical impression.

All you needed was:
http://en.wikipedia.org/wiki/Science

Also, if you meditate upon the basis of knowledge, what is identity, that is, an entity and it's unique id, or what makes it forever apart from another entity, you will probably discover a fundamental reality to all possible physical realities. You'll also discover pure abstraction, but not by abstracting and observing results, but the other way around. For example you should observe that if the things that makes an entity distinct are not internal, they are external. Even if it is theorised that entities can coexist at some time in the same space, the context of existance and view is limited in number of dimensions, while they are still apart from a larger perspective or point of view. Then you'll also know what math is. Science is a definition. Math is not just a science. Math is

"Ur philosophy are fail"

Mathematics is not a science because it is an accurate,measurable and valued subject and science is imaginary and happening. Mathematics is proved and theortical but science is practical.