2018 plan to solve

Mathematics is the science of skillful operations with concepts and rules invented just for this purpose. [this purpose being the skillful operation ....]^[15] Eugene Wigner

Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it needs only patience to ransack; it is not a mine, whose treasures may take long to reduce into possession, but which fill only a limited number of veins and lodes; it is not a soil, whose fertility can be exhausted by the yield of successive harvests; it is not a continent or an ocean, whose area can be mapped out and its contour defined: it is limitless as that space which it finds too narrow for its aspirations; its possibilities are as infinite as the worlds which are forever crowding in and multiplying upon the astronomer's gaze; it is as incapable of being restricted within assigned boundaries or being reduced to definitions of permanent validity, as the consciousness of life, which seems to slumber in each monad, in every atom of matter, in each leaf and bud cell, and is forever ready to burst forth into new forms of vegetable and animal existence.^[16] James Joseph Sylvester

What is mathematics? What is it for? What are mathematicians doing nowadays? Wasn't it all finished long ago? How many new numbers can you invent anyway? Is today's mathematics just a matter of huge calculations, with the mathematician as a kind of zookeeper, making sure the precious computers are fed and watered? If it's not, what is it other than the incomprehensible outpourings of superpowered brainboxes with their heads in the clouds and their feet dangling from the lofty balconies of their ivory towers? Mathematics is all of these, and none. Mostly, it's just different. It's not what you expect it to be, you turn your back for a moment and it's changed. It's certainly not just a fixed body of knowledge, its growth is not confined to inventing new numbers, and its hidden tendrils pervade every aspect of modern life.^[16] Ian Stewart

See also[edit]

• Philosophy of mathematics

References[edit]

1. Jump up ^ Mura, Robert (December 1993), "Images of Mathematics Held by University Teachers of Mathematical Sciences", Educational Studies in Mathematics, 25 (4): 375–385 
2. Jump up ^ Tobies, Renate; Neunzert, Helmut (2012), Iris Runge: A Life at the Crossroads of Mathematics, Science, and Industry, Springer, p. 9, ISBN 3-0348-0229-3, It is first necessary to ask what is meant by mathematics in general. Illustrious scholars have debated this matter until they were blue in the face, and yet no consensus has been reached about whether mathematics is a natural science, a branch of the humanities, or an art form. 
3. ^ Jump up to: ^{a b c} Florian Cajori et al., A History of Mathematics, 5th ed., p. 285–6. American Mathematical Society (1991).
4. ^ Jump up to: ^{a b} James Franklin, "Aristotelian Realism" in Philosophy of Mathematics", ed. A.D. Irvine, p. 104. Elsevier (2009).
5. Jump up ^ Arline Reilein Standley, Auguste Comte, p. 61. Twayne Publishers (1981).
6. Jump up ^ Auguste Comte, The Philosophy of Mathematics, tr. W.M. Gillespie, pp. 17–25. Harper & Brothers, New York (1851).
7. ^ Jump up to: ^{a b} Bertrand Russell, The Principles of Mathematics, p. 5. University Press, Cambridge (1903)
8. ^ Jump up to: ^{a b} Foundations and fundamental concepts of mathematics By Howard Eves page 150
9. Jump up ^ Carl Boyer, Uta Merzbach, A History of Mathematics, p. 426. John Wiley & Sons (2011).
10. ^ Jump up to: ^{a b c} Snapper, Ernst (September 1979), "The Three Crises in Mathematics: Logicism, Intuitionism, and Formalism", Mathematics Magazine, 52 (4): 207–16, doi:10.2307/2689412, JSTOR 2689412 
11. Jump up ^ Sawyer, W.W. (1955). Prelude to Mathematics. Penguin Books. p. 12. ISBN 0486244016. 
12. Jump up ^ "Mathematics. Encyclopædia Britannica from Encyclopædia Britannica 2006 Ultimate reference Suite DVD.
13. Jump up ^ Russell, Bertrand (1901), "Recent Work on the Principles of Mathematics", International Monthly, 4 
14. Jump up ^ "Pi in the Sky", John Barrow
15. Jump up ^ Wigner, Eugene P. (1960). "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," Communications in Pure and Applied Sciences, 13(1960):1–14. Reprinted in Mathematics: People, Problems, Results, vol. 3, ed. Douglas M. Campbell and John C. Higgins, p. 116
16. ^ Jump up to: ^{a b} "From Here to Infinity", Ian Stewart

Further reading[edit]

• Courant, Richard; Robbins, Herbert (1996), What is Mathematics? (2nd ed.), Oxford University Press, ISBN 978-0-19-510519-3 
• Gowers, Timothy; Barrow-Green, June; Leader, Imre, eds. (2008), The Princeton Companion to Mathematics, Princeton University Press, ISBN 978-0-691-11880-2 
• Hersh, Reuben (1999), What is Mathematics, Really?, Oxford University Press, ISBN 978-0-19-513087-4 
• Paulos, John Allen (1991), Beyond Numeracy, Viking, ISBN 978-0-670-83654-3 
• Stewart, Ian (1996), From Here to Infinity, Oxford University Press, ISBN 0-19-283202-6 

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