G. B. Halsted
Encyclopedia
George Bruce Halsted was a 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.
He was a member of the University of Texas at Austin
Department of Pure and Applied Mathematics (1884-1903), where he held the chair of pure and applied mathematics. He taught mathematicians R. L. Moore and L. E. Dickson among other students. He explored the foundations of geometry and explored many alternatives to Euclid's development, culminating with his Rational Geometry. Halsted frequently contributed to the early American Mathematical Monthly
.
In 1903, Halsted was fired from UT Austin after having published several articles that criticized the university for having hired for an instructor post a well-connected but not as good local candidate instead of R. L. Moore, a young promising mathematician at the time, whom Halsted hoped to have as an assistant.
He completed his teaching career at St. John's College, Annapolis; Kenyon College, Gambier, Ohio (1903-1906); and the Colorado State College of Education, Greeley (1906-1914).
Halsted was a member of the American Mathematical Society
and served as vice president of the American Association for the Advancement of Science
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who explored foundations of geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
and introduced Non-Euclidean geometry
Non-Euclidean geometry
Non-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...
into the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
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
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
. He wrote an elementary geometry text, Rational Geometry, based on Hilbert's axioms, which was translated into French
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...
, German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
, and Japanese
Japanese language
is a language spoken by over 130 million people in Japan and in Japanese emigrant communities. It is a member of the Japonic language family, which has a number of proposed relationships with other languages, none of which has gained wide acceptance among historical linguists .Japanese is an...
.
Halsted was a tutor and instructor at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
. 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
Johns Hopkins University
The Johns Hopkins University, commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States...
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.
He was a member of the University of Texas at Austin
University of Texas at Austin
The University of Texas at Austin is a state research university located in Austin, Texas, USA, and is the flagship institution of the The University of Texas System. Founded in 1883, its campus is located approximately from the Texas State Capitol in Austin...
Department of Pure and Applied Mathematics (1884-1903), where he held the chair of pure and applied mathematics. He taught mathematicians R. L. Moore and L. E. Dickson among other students. He explored the foundations of geometry and explored many alternatives to Euclid's development, culminating with his Rational Geometry. Halsted frequently contributed to the early American Mathematical Monthly
American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894. It is currently published 10 times each year by the Mathematical Association of America....
.
In 1903, Halsted was fired from UT Austin after having published several articles that criticized the university for having hired for an instructor post a well-connected but not as good local candidate instead of R. L. Moore, a young promising mathematician at the time, whom Halsted hoped to have as an assistant.
He completed his teaching career at St. John's College, Annapolis; Kenyon College, Gambier, Ohio (1903-1906); and the Colorado State College of Education, Greeley (1906-1914).
Halsted was a member of the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
and served as vice president of the American Association for the Advancement of Science
American Association for the Advancement of Science
The American Association for the Advancement of Science is an international non-profit organization with the stated goals of promoting cooperation among scientists, defending scientific freedom, encouraging scientific responsibility, and supporting scientific education and science outreach for the...
.
Writings
- Metrical geometry; An elementary treatise on mensuration (Boston, Ginn, 1890)
- The elements of geometry (New York, Wiley, 1889)
- Synthetic projective geometry (New York, Wiley, 1906)
- On the foundation and technic of arithmetic (Chicago, Open Court, 1912)