Talk:Mathematics/First paragraph

The goal of this page is to focus the discussion about the lead paragraph and hopefully reach a consensus.

Summary of Debate
This should be reasonably short, with links to the discusion archives for more details.

Other Encyclopedias and authorative definitions
Please insert a quotations from other authorative sources, even copyrighted ones, as this is only for our own discussion.


 * "the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation, and its development has involved an increasing degree of idealization and abstraction of its subject matter." Britannica.com
 * "Mathematics, a way of describing relationships between numbers and other measurable quantities. Mathematics can express simple equations as well as interactions among the smallest particles and the farthest objects in the known universe. Mathematics allows scientists to communicate ideas using universally accepted terminology. It is truly the language of science." MSN Encarta
 * Originally, the collective name for geometry, arithmetic, and certain physical sciences (as astronomy and optics) involving geometrical reasoning. In modern use applied, (a) in a strict sense, to the abstract science which investigates deductively the conclusions implicit in the elementary conceptions of spatial and numerical relations, and which includes as its main divisions geometry, arithmetic, and algebra; and (b) in a wider sense, so as to include those branches of physical or other research which consist in the application of this abstract science to concrete data. When the word is used in its wider sense, the abstract science is distinguished as pure mathematics, and its concrete applications (e.g. in astronomy, various branches of physics, the theory of probabilities) as applied or mixed mathematics. Oxford English Dictionary, 2nd Ed.
 * the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations Merriam-Webster Online Dictionary.
 * the branch of science concerned with number, quantity, and space, either as abstract ideas (pure mathematics) or as applied to physics, engineering, and other subjects (applied mathematics). Compact Oxford English Dictionary.
 * a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement WordNet 2.0, Princeton University, 2003.
 * "MATHEMATICS (Gr. paOiµarLK1), sc. TEXvn or E7rio'7-)µ17; from AecO a, "learning" or "science"), the general term for the various applications of mathematical thought, the traditional field of which is number and quantity. It has been usual to define mathematics as "the science of discrete and continuous magnitude." Even Leibnitz,' who initiated a more modern point of view, follows the tradition in thus confining the scope of mathematics properly so called, while apparently conceiving it as a department of a yet wider science of reasoning. A short ' Cf. La Logique de Leibnitz, ch. vii., by L. Couturat (Paris, 190,). consideration of some leading topics of the science will exemplify both the plausibility and inadequacy of the above definition." Encyclopaedia Britannica, 1911.
 * the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. Random House Unabridged Dictionary, 2006.
 * The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols. American Heritage Dictionary, 4th Ed., 2000.
 * "Yet as a science in the modern sense mathematics only emerges later, on Greek soil, in the fifth and fourth centuries B.C.", Richard Courant and Herbert Robbins, What is Mathematics?, 1941, p. xv.

Proposals
Add your proposed lead paragraph, please use the bottom part of this page to discuss the proposals. Keep the refences section at the bottom, add a new proposal by clicking it's edit link and paste your version above it.

Current lead
Mathematics (abbr. maths or math) is the discipline that deals with concepts such as quantity, structure, space and change. 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.

Listing areas of activity
Mathematics, as a branch of knowledge sometimes regarded as a science,
 * abstracts axioms and definitions from such concepts as quantity, structure, space, and change,
 * states conjectures and theorems that relate these abstractions to each other,
 * regards conjectures as unproven theorems, and
 * proves the truth of theorems by deduction.

Is this the right approach
I wonder if discussing different proposals is the right approach, maybe it should be divided into smaller issues, e.g should science be mentioned in the first paragraph, etc... But I think this is a start at least.--Vesal 12:18, 4 October 2006 (UTC)