Mathematics is the body of knowledge centered on concepts such as quantity, structure, space, and change, and the academic discipline which studies them. It evolved, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.

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• 1 Sourced
• 2 Unsourced
• 3 Misattributed
• 4 See also
• 5 External links

Sourced

• Any author who uses mathematics should always express in ordinary language the meaning of the assumptions he admits, as well as the significance of the results obtained. The more abstract his theory, the more imperative this obligation. In fact, mathematics are and can only be a tool to explore reality. In this exploration, mathematics do not constitute an end in itself, they are and can only be a means.
  • Maurice Allais, La formation scientifique, Une communication du Prix Nobel d’économie, Maurice Allais, address to the Académie des Sciences Morales et Politiques (1997).

• Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.
  • W.S. Anglin, in Mathematics and History, elucidating the symmetry between the creative and logical aspects of mathematics.

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Mon Oct 26 05:40:11 2009