George Bruce Halsted

George Bruce Halsted
G. B. Halsted, geometer
Born	(1853-11-25)November 25, 1853 Newark, New Jersey
Died	March 16, 1922(1922-03-16) (aged 68) New York City
Nationality	United States
Alma mater	Princeton University Johns Hopkins University
Known for	Foundations of geometry
Spouse(s)	Margaret Swearingen
Scientific career
Fields	Geometry
Institutions	University of Texas, Austin Kenyon College Colorado State Teachers College
Thesis	Basis for a Dual Logic (1879)
Doctoral advisor	J. J. Sylvester
Notable students	R. L. Moore L. E. Dickson
Influenced	Alexander Macfarlane

George Bruce Halsted (November 25, 1853 – March 16, 1922), usually cited as G. B. Halsted, was an American mathematician who explored foundations of geometry and introduced non-Euclidean geometry into the United States through his own work and his many important translations. Especially noteworthy were his translations and commentaries relating to non-Euclidean geometry, including works by Bolyai, Lobachevski, Saccheri, and Poincaré. He wrote an elementary geometry text, Rational Geometry, based on Hilbert's axioms, which was translated into French, German, and Japanese.

Halsted was a tutor and instructor at Princeton University. He held a mathematical fellowship while a student at Princeton. Halsted was a fourth generation Princeton graduate, earning his Bachelor's degree in 1875 and his Master's in 1878. He went on to Johns Hopkins University where he was J. J. Sylvester's first student, receiving his Ph.D. in 1879. After graduation, Halsted served as an instructor in mathematics at Princeton until beginning his post at the University of Texas at Austin in 1884.

From 1884 to 1903, Halsted was a member of the University of Texas at Austin Department of Pure and Applied Mathematics, eventually becoming its chair. He taught mathematicians R. L. Moore and L. E. Dickson, among other students, who frequently joked that his primary criterion for the rationality of a geometric system was the simplicity of the terms in which it could express the closed space figure formed by the contours of his mustache. He explored the foundations of geometry and explored many alternatives to Euclid's development, culminating with his Rational Geometry. In the interest of hyperbolic geometry in 1891 he translated the work of Nicolai Lobachevsky on theory of parallels. In 1893 in Chicago, Halsted read a paper Some salient points in the history of non-Euclidean and hyper-spaces at the International Mathematical Congress held in connection with the World's Columbian Exposition. Halsted frequently contributed to the early American Mathematical Monthly. In one article he championed the role of J. Bolyai in the development of non-Euclidean geometry and criticized C. F. Gauss. See also on 3 September 1912.