Content deleted Content added
mNo edit summary |
|||
Line 4:
[[File:Euclid.jpg|thumb |[[Euclid]], Greek mathematician, 3rd century BC, as imagined by [[Raphael]] in this detail from ''[[The School of Athens]]''.<ref>No likeness or description of Euclid's physical appearance made during his lifetime survived antiquity. Therefore, Euclid's depiction in works of art depends on the artist's imagination (''see [[Euclid]]'').</ref>]]
'''Mathematics''' (from [[Greek language|Greek]] μάθημα ''máthēma'', “knowledge, study, learning”) is the art and science of
Through the use of [[abstraction (mathematics)|abstraction]] and [[logic]]al [[reasoning]], mathematics developed from [[counting]], [[calculation]], [[measurement]], and the systematic study of the [[shape]]s and [[motion (physics)|motions]] of physical objects. Practical mathematics has been a human activity for as far back as [[History of Mathematics|written records]] exist. [[Logic|Rigorous arguments]] first appeared in [[Greek mathematics]], most notably in [[Euclid|Euclid's]] ''[[Euclid's Elements|Elements]]''. Mathematics developed at a relatively slow pace until the [[Renaissance]], when mathematical innovations interacting with new [[timeline of scientific discoveries|scientific discoveries]] led to a rapid increase in the rate of mathematical discovery that continues to the present day.<ref>Eves</ref>
[[Galileo Galilei]] (1564-1642) said, 'The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth'.<ref>[[Marcus du Sautoy]], ''[http://www.bbc.co.uk/programmes/b00sr3fm A Brief History of Mathematics: 1. Newton and Leibniz]'', [[BBC Radio 4]], 27/09/2010.</ref> [[Carl Friedrich Gauss]] (1777–1855) referred to mathematics as "the Queen of the Sciences".<ref>Waltershausen</ref> [[Benjamin Peirce]] (1809-1880) called mathematics "the science that draws necessary conclusions".<ref>Peirce, p. 97.</ref> David Hilbert said of mathematics: "We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise."<ref>Hilbert, D. (1919-20), Natur und Mathematisches Erkennen: Vorlesungen, gehalten 1919-1920 in Göttingen. Nach der Ausarbeitung von Paul Bernays (Edited and with an English introduction by David E. Rowe), Basel, Birkhäuser (1992).</ref> [[Albert Einstein]] (1879-1955) stated that "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".<ref name=certain/>
| |||