we all study mathematics , and all of us learn mathematical methods to solve problems , we learn how to prove , how to think mathematically
but the question is, what is mathematics ? how can we define it as a branch of science ?
2026-03-30 05:32:21.1774848741
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what is the definition of Mathematics ?
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The term mathematics is defined by usage: mathematics comprises those things that people call mathematics. Thus, the definition changes over time, and even at any one time the term means different things to different people. In this it is no different from many other terms, e.g., science fiction.
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There is no such definition in wide use, and it is hard to conceive of one that would be fit or useful or interesting or worth making or agreeable.
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To address one part of your question,
how can we define it as a branch of science ?
many would argue that mathematics is not a branch of science at all, although it does have a close relationship to the sciences. As Einstein said, "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." For further discussion, see Wikipedia and the essay "Is Mathematics a Science?" by Arturo Magidin.
You might be interested in this post about classifications of mathematics, its vastness and branches, etc., and also the links available in the answers.
In particular, visit the Mathematical Atlas's website, and explore its links and its Maths Map
I would say the "space" of mathematics has no "limit points"! And math is definitely not a "subset" of science. Their intersection is certainly not empty, indeed, math, in one way or another, has non-empty intersections with just about any domain of study you can think of.