By a well-ordered set we understand any well-defined set whose elements are related by a well-determined given succession according to which there is a first element in the set and for any element (if it is not the last one) there is a certain next following element. Furthermore, for any finite or infinite set of elements there is a certain element which is the next following one for all these elements (except for the case that such an element which is the next following one to these elements does not exist).This translation was taken from Cantor's Philosophical Views by Walter Purkert.
WHITE NOISE. Originally the term referred to a form of sound or of electrical interference but it now also refers to a type of random process. "Inside the plane ... we hear all frequencies added together at once, producing a noise which is to sound what white light is to light." (L. D. Carson, W. R. Miles & S. S. Stevens, "Vision, Hearing and Aeronautical Design," Scientific Monthly, 56, (1943), 446-451). S. Goldman's book on radio engineering, Frequency Analysis, Modulation and Noise (1948), has a mathematical treatment of white noise.
By 1953 white noise had entered the stochastic process literature, as in "On the Fourier Expansion of Stationary Random Processes" by R. C. Davis (Proceedings of the American Mathematical Society, 4, 564-569) [John Aldrich].
WHOLE NUMBER. See integer.
WIENER PROCESS appears in M. Kac's "On Deviations Between Theoretical and Empirical Distributions," Proc. Nat. Acad. Sciences, 35, (1949), 252-257. The name recalls N. Wiener's analysis of "the Brownian movement" in "Differential-space" J. Math. and Phys. 2 (1923) 131-174. (See Brownian motion.) [John Aldrich]
WILSON'S THEOREM was given its name by Edward Waring (1734-1798) for his friend, John Wilson (1741-1793). The first published statement of the theorem was by Waring in his Meditationes algebraicae (1770), although manuscripts in the Hanover Library show that the result had been found by Leibniz.
WINDOW in Statistics, particularly time series analysis. The term was introduced in B. Blackman & J. W. Tukey’s "The Measurement of Power Spectra," Bell System Technical Journal, 37, (1958). It appears in several forms, including data window, lag window and spectral window [John Aldrich].
WINSORIZED is found in 1960 in W. J. Dixon, "Simplified Estimation from Censored Normal Samples," The Annals of Mathematical Statistics, 31, 385-391 (David, 1998).
WITCH OF AGNESI. Luigi Guido Grandi (1671-1742) studied this curve in 1703 and is believed to have been the first to call it versiera or versoria in Latin, meaning "turning in every direction." According to Boyer in History of Analytic Geometry, Grandi coined the Italian word la versiera in 1718. The term appears in Father Guido Grandi's commentary on the Trattato del Galileo del moto naturalmente accelerato (Opere di G. Galilei, III, Firenze, 1718, p. 393): "...sarebbe quella curve, che io descrivo nel mio libro delle quadrature alla prop. 4, nata da seni versi, che da me suole chiamarsi la versiera in latino però versoria..."
In 1748, Maria Gaetana Agnesi (1718-1799), in Istituzioni Analitiche, the first calculus book written by a woman, also called the curve la versiera, using the name twice.
The British mathematician John Colson (1680-1760), translating Agnesi's work into English, translated the Italian word versiera as "the Witch." He wrote, "...and therefore [equation] or [equation] will be the equation of the curve to be described, which is vulgarly called the Witch." He also wrote, "Let the curve to be described be that of Prob. III. n. 238, called the Witch, the equation of which is [equation]." Colson gave the name a third time, in a marginal note, "Another example of the curve called the Witch."
According to the translator's preface to the 1801 English edition of Analytical Institutions, Colson learned Italian for the sole purpose of translating this work.
Witch of Agnesi is found in English in 1875 in An elementary treatise on the integral calculus by Benjamin Williamson (1827-1916): "Find the area between the witch of Agnesi xy2 = 4a2 (2a - x) and its asymptote" (OED2).
WORKING HYPOTHESIS occurs in 1871 in R. H. Hutton, Ess. I. v. 112: "If it be only a working hypothesis, to keep us, while confined in the human, from blindly and unconsciously dashing ourselves against the laws of the divine" (OED2).
WORKING MATHEMATICIAN. In an article "The Ignorance of Bourbaki" (The Mathematical Intelligencer vol. 14, no 3, 1992), A. R. D. Mathias suggests that this phrase is due to Bourbaki. However, Carlos César de Araújo has found it in a paper by Eliakim Hastings Moore, "On the foundations of mathematics" (Bull. A. M. S., 1903, p. 406).
The term WRONSKIAN (for Höené Wronski) was coined by Thomas Muir (1844-1934) in 1881 (Cajori 1919, page 310).