# What is Pure mathematics: Definition and 49 Discussions

Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, but pure mathematicians are not primarily motivated by such applications. Instead, the appeal is attributed to the intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles.
While pure mathematics has existed as an activity since at least Ancient Greece, the concept was elaborated upon around the year 1900, after the introduction of theories with counter-intuitive properties (such as non-Euclidean geometries and Cantor's theory of infinite sets), and the discovery of apparent paradoxes (such as continuous functions that are nowhere differentiable, and Russell's paradox). This introduced the need to renew the concept of mathematical rigor and rewrite all mathematics accordingly, with a systematic use of axiomatic methods. This led many mathematicians to focus on mathematics for its own sake, that is, pure mathematics.
Nevertheless, almost all mathematical theories remained motivated by problems coming from the real world or from less abstract mathematical theories. Also, many mathematical theories, which had seemed to be totally pure mathematics, were eventually used in applied areas, mainly physics and computer science. A famous early example is Isaac Newton's demonstration that his law of universal gravitation implied that planets move in orbits that are conic sections, geometrical curves that had been studied in antiquity by Apollonius. Another example is the problem of factoring large integers, which is the basis of the RSA cryptosystem, widely used to secure internet communications.It follows that, presently, the distinction between pure and applied mathematics is more a philosophical point of view or a mathematician's preference than a rigid subdivision of mathematics. In particular, it is not uncommon that some members of a department of applied mathematics describe themselves as pure mathematicians.

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1. ### What and how to study for a pure maths education at university?

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2. ### Introduction to pure mathematics

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15. ### Advice for a potential career in Pure mathematics

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16. ### Pure Mathematics study - question

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17. ### DePauls M.S in Pure Mathematics

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18. ### Programs How many hours, on average, of pure learning for bachelor degree?

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19. ### Spectrum of careers for Pure Mathematics?

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23. ### Schools Applied mathematics vs. pure mathematics in high school?

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25. ### A Math Student's Dilemma: To Pursue Physics or Pure Mathematics?

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26. ### Math Pure mathematics or statistics

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28. ### Math Careers using pure mathematics

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29. ### Looking for a book similar to Synopsis of Pure Mathematics by G. S. Carr

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30. ### Pure mathematics vs Mechanical engineering

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31. ### Can You Combine Pure and Applied Mathematics in Your Studies?

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32. ### Programs Masters in Pure Mathematics (Geometry, Topology) before Theoretical Physics Phd?

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33. ### Is pure mathematics the basis for all thought?

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34. ### G H Hardy A course in pure mathematics

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35. ### Math Is there any job for a person who loves pure mathematics?

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36. ### General Relativity is pure Mathematics

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37. ### Applied and Pure mathematics with focus on modelling

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38. ### Books for beginning to learn Pure Mathematics

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39. ### Pure Mathematics vs. Applied Math vs. Discrete Math

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40. ### Can 10^n + 1 Be Expressed as a*a*c?

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Thanks
42. ### Square Root Of 2 (from Hardy Course Of Pure Mathematics )

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43. ### He Unreasonable Effectiveness of Pure Mathematics

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44. ### Nonselfish Reasons to Pursue Pure Mathematics

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45. ### Courses Is A Course on Pure Mathematics by G.H. Hardy Worth Reading?

have anyone read "A Course on Pure Mathematics" by G. H. Hardy? is it a good book?
46. ### What Jobs Can I Get with a Degree in Pure Mathematics?

i am now studying pure maths in uni. is it possible for someone to tell me wht kind of jobs would pure maths lead to? i believe it would be some jobs tht requires analytical and theorectical skill. bt is tht any exact examples pleasE?
47. ### Schools Pure Mathematics Phd from Ivy League University, Need Advice

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48. ### Exploring Pure Mathematics: What Does it Describe & What are its Laws?

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49. ### Why pure mathematics is beyond me

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