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Thread: Is Mathematics Science?

  1. #1 Is Mathematics Science? 
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    This has been debated before. I think most philosophers of science would say that it is.

    What are some of the arguments that have been used to say that math is not science?

    I am asking this because I am really kind of ignorant on this. I am hoping someone will give me some clarity on this.


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    TO my mind Science is an attempt to understand the world around us, mathematics is merely one of the many tools used to explain it.


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  4. #3 Re: Is Mathematics Science? 
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    Quote Originally Posted by papazulu
    This has been debated before. I think most philosophers of science would say that it is.

    What are some of the arguments that have been used to say that math is not science?

    I am asking this because I am really kind of ignorant on this. I am hoping someone will give me some clarity on this.
    Science (from the Latin scientia, 'knowledge'), is the effort to understand, or to understand better, how nature works, with observable physical evidence as the basis of that understanding. It is done through observation of phenomena, and/or through experimentation that tries to simulate events under controlled conditions. It incorporates the philosophies of naturalism and employs reasoning.
    Mathematics is knowledge. So, yes, it's science.
    We hold these truths to be self evident, that all men are created equal, that they are endowed by their Creator with certain unalienable rights, that among these are life, liberty and the pursuit of happiness.
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  5. #4  
    Forum Ph.D. streamSystems's Avatar
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    Quote Originally Posted by Megabrain
    TO my mind Science is an attempt to understand the world around us, mathematics is merely one of the many tools used to explain it.

    What other ways are there??

    If mathematics is one of many tools that science employs, what other tools does science employ???
    Does a theory of everything therefore need to be purely theoretical and only account for the known laws and forces in handling the improbability of fortune telling?

    the www feature below can explain it better.
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  6. #5  
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    I just read most of the wikipedia article on the scientific method, and it seems to me that by the definition of science, mathematics doesn't make the cut. It is a separate but interactive discipline. This is the view of many important scholars on the subject and I am going to be researching this further so I can give brief outline of reasons for above assertion.

    For now I will just provide wiki quote on the debate:

    "Many philosophers believe that mathematics is not experimentally falsifiable,[citation needed] and thus not a science according to the definition of Karl Popper. However, in the 1930s important work in mathematical logic showed that mathematics cannot be reduced to logic, and Karl Popper concluded that "most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently."[16] Other thinkers, notably Imre Lakatos, have applied a version of falsificationism to mathematics itself."
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    I think the crux of the matter lies in the role of experimentation in mathematics. Although the ultimate goal in pure mathematics is proof, not experimental evidence, experimentation does play a vital role. Numerical data and explicit examples can motivate, corroborate, or provide counterexamples to conjectures.

    The question then becomes, to me at least, is mathematical experimentation a form of scientific experimentation? Many of the discussions of the scientific given above and on Wikipedia state that experimentation must have observable physical results. This seems to be the one criterion that mathematical experimentation may not meet: do the results of mathematical experiments lie in the observable and physical?

    Suppose I have two sequences of numbers given by two different methods which I can explicitly calculate with a computer. I suspect for some reason that the sequences are equal, but I don't have a proof of such. However, no matter how many terms of each sequence I compute, the two match up term by term. This is certainly a mathematical experiment in the sense that I have a hypothesis, I observe the phenomena in question, and I make a judgment as to the truth of my hypothesis (a positive one in this case). But is this observable and physical? I see the results on the computer screen, and these results were calculated by some physical processes which were determined by the constraints of the mathematical problem at hand. So my test subjects manifested themselves physically, at least in some indirect sense. But is this stretching what is meant by observable and physical? I'm not really concerned with the physical phenomena that occur.

    What if I were able to do this computation on paper and pencil? Now the mathematical phenomena are putting constraints on my thought processes, physical observations, and movements. But now we're getting someplace a bit fuzzier--cognitive science, psychology, linguistics... My understanding of the physical processes at hand is much more limited than above. Can I really consider my mathematical experimentation to be a physical observation, or am I opening up a whole can of worms by viewing my experiment as something physical as opposed to something purely logical? But I view this process to be just as mathematically rigorous as the computer simulation, so how can this be a scientific experiment if the mathematical value of these two processes are equal whereas the physical understanding of what's going on in the former case is much greater than that of the latter?
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