Is Math Science?

Okay, this one is gonna be interesting. In the Faith Science--Logically Indefensible thread, Faith made the comment that science will never abandon a KNOWN fact. To which Jar replied, of course science will. nwr then replies with "2 + 2 = 4".It is my opinion that math is not science, and I'd like to try and prove it here (seeing as how it will most undoubtedly be ruled off-topic in the mother thread).Onto the proofs:1)science is tentative. What is known as fact today will not be tomorrow. math is not, to the best of my knowledge, tentative. 2 and 2 will always equal four given the rules we use (1984 does not count).2)science has a method for finding out new things and testing old things. It is the logic behemoth known as the scientific method. THese five steps are the rule by which new scientific knowledge is added. Math has a method--for finding out answers known as the order of operations. It is not a method by which to find new formulas. IT is merely, to my knowledge, a method for arriving at the same answer as the person across from you. It is by this that 3 * 4 + 2 = 14, and not 18.3)where is the philosophy? Science is rooted in methodological philosophy. It has a philosophical root, a foundation. As far as I know, math does not. Granted, Pythagoras used numbers as the thing that the universe was made of, but . . .4)since when was a root a tree? Perhaps a crude analogy, but math is a foundation of science, especially in the fields of physics and chemistry. This is the weakest proof.5) E = mc² is a theoretical construct, based off of what we know about how certain things work. If those things work differently, then the formula is incorrect.Is it science would be appropriate, I would think.

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Never thought I'd agree with a tree hugger

I agree. Most mathematicians would probably agree with you. But there, I disagree. You cannot prove that mathematics is, or is not, science. It is a matter of convention, not of proof. This is not a proof. It is a plausibility argument, but it fails as a proof. "Science is tentative" is a characterization of science, but it is not part of the definition of science (if there is such a thing as a definition of science). You might try looking at some of the mathematics research journals. You might discover that they are, indeed, discovering new things (including new formulae). Try meta-mathematics.

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Compassionate conservatism - bringing you a kinder, gentler torture chamber

I think the first thing to debate here is if you are describing maths or arithmetic. There is a a philosophy of maths - the existence (or lack) of numbers: Do mathematical concepts exist objectively and are discovered by man, or does man create mathematical concepts?A quick look via google brings up many discussions on the philosophy of mathematics, the wiki article will probably be a good place to springboard from. The nature of 2, the addition function, the equivalence statement and the nature of the number 4 might be tentative though.However, I don't think that maths is a science. Though an argument might be made to that effect. Maths might make certain predictions based on certain assumptions and can test them out later, which would lend it the air of science.Maths works on principles very similar to science (sometimes the same),but I don't think that means they are the same methodology. It just means that we know certain ways of asking questions are better than others. I'd say they are cousins, perhaps brothers - but they are not the same.Still - I'm willing to hear other opinions on the matter.

I didn't mean to imply that math can't find new things. I'm just unaware of a method by which though go about finding new discoveries.Anywho, I'd say my point one is still a "proof". If tentativity is not a crucial part of a science, then what is the basis for falsification? If I only know something tentatively, then it can be falsified. We know evolution happens, but there still may be something down the road that throws it out--tentative knowledge. Can you falsify "2 + 2 = 4"?I'll check out the metaphysics, but my offhand guess is that it's gonna be somewhat similar to what Pythagoras proposed.

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Falsifaction is not part of the definition of science. Rather, it comes from Popper's philosophy of science, and is somewhat controversial. That's true by definition. But then parts of science are true by definition.

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Compassionate conservatism - bringing you a kinder, gentler torture chamber

I'm not 100% sure. But don't mathematical systems or the concepts of math rest on axioms of mathetmics in a given system? Such that in an axiom as wiki: Whereas science doesn't (abe:have) much in the way of axioms?Edited by Discreet Label, : added Have

Yes, but.A more detailed answer would be long and boring. Suffice to say that the axiomisation of mathematics is a relatively modern trend (you know, last three centuries or so), and Godel and Russell demonstrated that it was never going to entirely work.

This Mathematician (by education, not trade) would agree.

hi Kuresu,As a matter of interest the link below gives a proof that 2+2=4. It involves 2109 subtheorems, apparently!http://au.metamath.org/mpegif/mmset.html#triviaI agree that maths is not science. If scientists were to attempt this kind of formal proof of a hypothesis we would say that science had become maths rather than vice versa.MickEdited by mick, : No reason given.

I have a BSc in Mathematics and I agree that mathematics is distinct form what is generally referred to as science. In the wiki article referred to my views would probalby fit between formalism and logicism.There is an empirical element to mathematics but so far as I can see it is mostly in the application of mathematics to real world problems. From deciding what sort of entities to admit to mathematics (e.g. the natural numbers or lines) too confirming that certain mathematical entities are useful to model certain real-world entities (e..g the application of complex numbers to - IIRC - electricity).

Surely science in it's widest sense has to be the study of the physical world?Maths can be used (with great effect) to decribe the physical world but this is just a useful application of it's methods which could be equally applied to entirely and completely abstract axioms that have no basis in physical reality.I would say that science applies logic to physical phenomenon and that maths is the language of logic.Therefore in answer to the OP,no maths is not science as such but the two are intrinsically linked.I am more interested to know if people think we doscover or invent maths?Edited by Straggler, : No reason given.

At first blush, I would tend to have already said that I think I would "discover" science but "invent" math. When I thought about what multiplication is as was mentally used by me (in thought), it was ... to discover things in science , and will be so used insofar I have not, but I never felt I was "discovering" mulitplication even though the thought was as original (for me) as the application would then uncover through a discovered process. I may think differently if I thought harder about it but I doubt it.Edited by Brad McFall, : making the pattern

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I am more interested to know if people think we doscover or invent maths?

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I would say that at the most basic level math is invented - we make up the entities and teh axioms that describe them. But there is also an element of discovery, in finding the implications of the axioms. Computers have even opened up a field of experimental mathematics (e.g. some of the work in fractals was based on computer experimentation).