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what is the definition of Mathematics ?

I would like to know if mathematics is considered a science? I've searched the internet and asked many people for insight to no avail. I thought science was based on observation, experimentation and falsification. I don't understand how mathematics can satisfy all the above. Especially, when there are some branches of mathematics that need not actually correspond to the physical world. Maybe I have a naive definition or unsophisticated understanding of both mathematics and science.

Thank you in advance.

Sincerely, Maxwell

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Have a look at this question. –  Harald Hanche-Olsen Jan 28 '13 at 14:09
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Many philosophers believe that mathematics is not experimentally falsifiable, 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." from here –  Ilya Jan 28 '13 at 14:10
    
Dear Maxwell: There are a couple answers at the link @Harald provided that addresses your question (one of two questions asked in that post). So I have voted to close as a duplicate. But that is not to say that your question is "bad"...it's a very understandable and perfectly good question, just one that's already been addressed. In particular, the accepted answer has a link to an essay that discusses your very question: Is Mathematics a Science? by Arturo Magidin. –  amWhy Jan 28 '13 at 14:20
    
See also Is Mathematics a Science? by Stefan Bilaniuk. You can google "Is mathematics a science?" - to find many such commentaries. –  amWhy Jan 28 '13 at 14:28
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marked as duplicate by Arthur Fischer, amWhy, Ilya, Davide Giraudo, Javier Álvarez Jan 28 '13 at 14:44

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You wrote: "I thought science was based on observation, experimentation and falsification". Isn´t that philosophy ? And what is good literature without observation; trying new forms of writing, that is experimenting; and adding some non existing facts and invented stories, that is falsifying ? Yet i do not understand why you define maths as in part (one third) a falsification. History, a story told by those who won, is very often false; but why do you think maths is?

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The problem also is we should have to define exactly first, without ambiguity what is science before we try to decide. –  user55514 Jan 28 '13 at 14:40
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