In mathematics, Edwin Bidwell Wilson (1879-1964) was an American mathematician notable for being the sole protégé of American engineer Willard Gibbs and for later having mentored economic thermodynamicist Paul Samuelson.

Education
Wilson received his AB from Harvard College in 1899 and his PhD in 1901, dissertation "The Decomposition of the General Collineation in Space into Three Skew Reflections", at Yale with Gibbs as his advisor. In 1900 he became instructor in mathematics at Yale, but took leave during the year 1902-1903 to study mathematics at Paris, chiefly at the Ecole Normale Superieure; thereafter returning to teach at Yale. He became assistant professor of mathematics at Yale in 1906. In 1907, he became when to MIT where he became an associate professor of mathematics; full professor in 1911, then professor of mathematical physics, and head of the department of physics in 1917. [1]

Vector analysis
Wilson’s first major accomplishment was the preparation, in 1901, of Willard Gibbs lecture notes on vector analysis, as presented in the 1902 textbook Vector Analysis. [2] Prior to this time, various competing techniques for handling vector quantities were at hand: William Hamilton’s 1843 quaternions, lavishly popularized by Peter Tait and the Quaternion Society, Hermann Grassman’s 1844 Ausdehnungslehre (theory of extensive magnitudes), and the physical ideas of James Maxwell and Oliver Heaviside. In his lectures, Gibbs modified the techniques of Grassman to fit the ideas of Maxwell and Heaviside as well as his own work. His resulting “vector calculus” was presented in lecturers at Yale and in an unpublished brief set of lecture notes (“Elements of Vector Anslysis”, 1881 and 1884). This work established the dominant use of the vector notation, over that of quaternion notation, whereby those, such as American physicists, use boldface notation for vectors, with a dot • for scalar products and X for vector products, exactly as initiated by Gibbs and presented in the Gibbs-Wilson textbook. [1]

References
1. Hunsaker, Jerome and Mac Lane, Saunders. (1973). “Edwin Bidwell Wilson (1879-1964)”, 38-pages. National Academy of Sciences.
2. (a) Gibbs, Josiah W. and Wilson, Edwin B. (1902). Vector Analysis: a Text-book for the use of Students of Mathematics and Physics, Founded upon the Lectures of J. Willard Gibbs. Charles Scribner’s and Sons.
(b) Vector Analysis (book) – Wikipedia.

Further reading
● Wilson, Edwin B. (1912). Advanced Calculus: a Text upon Select parts of Differential Calculus, differential equations, integral calculus, theory of functions; with numerous exercises (keyword: thermodynamics, pgs. 94, 106-107, 124, 294; section 91: Integrating factors, pgs. 207-08). Ginn and Co.

External links
● Edwin Bidwell Wilson – Wikipedia.
● Edwin Bidwell Wilson – Mathematics Genealogy Project.