Mathematical Statistics
Mathematical statistics is the application of mathematics to statistics, as opposed to techniques for collecting statistical data. Mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory.
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change. It has no generally accepted definition.
Pure Mathematics
Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts. This has been a recognizable category of mathematical activity from the 19th century onwards, at variance with the trend towards meeting the needs of navigation, astronomy, physics, economics, engineering, and so on.
Statistics
Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, for example, a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments. See glossary of probability and statistics.
Mathematics
Mathematics is a versatile art; it can be applied to widely different purposes. Math has no morality; it does not care what it counts or what it proves.
Brian Stableford, Ashes and Tombstones, in Peter Crowther (ed.) Moon Shots (1999), reprinted in David G. Hartwell (ed.) Year's Best SF 5 (2000), p. 412
Pure Mathematics
Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true … If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.
Bertrand Russell, Recent Work on the Principles of Mathematics, published in International Monthly, vol. 4 (1901).
Statistics
The true foundation of theology is to ascertain the character of God. It is by the art of statistics that law in the social sphere can be ascertained and codified, and certain aspects of the character of God thereby revealed. The study of statistics is thus a religious service.
Attributed to Florence Nightingale by F.N. David in Games, Gods, and Gambling: A History of Probability and Statistical Ideas, 1962, page 103.
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