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(Lobachevski was the first to publish non-Euclidean geomet...)
Lobachevski was the first to publish non-Euclidean geometry. Originally titled: Geometrical Researches on The Theory of Parallels. This is an unabridged printing, to include all figures, from the translation by Halsted.
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Science and Method
Henri Poincaré
Translated by Georg...)
Science and Method
Henri Poincaré
Translated by George Bruce Halsted
Jules Henri Poincaré: 29 April 1854 – 17 July 1912, was a French mathematician, theoretical physicist, engineer, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist by Eric Temple Bell, since he excelled in all fields of the discipline as it existed during his lifetime.
I bring together here different studies relating more or less directly to questions of scientific methodology. The scientific method consists in observing and experimenting; if the scientist had at his disposal infinite time, it would only be necessary to say to him: ‘Look and notice well’; but, as there is not time to see everything, and as it is better not to see than to see wrongly, it is necessary for him to make choice. The first question, therefore, is how he should make this choice. This question presents itself as well to the physicist as to the historian; it presents itself equally to the mathematician, and the principles which should guide each are not without analogy. The scientist conforms to them instinctively, and one can, reflecting on these principles, foretell the future of mathematics.
We shall understand them better yet if we observe the scientist at work, and first of all it is necessary to know the psychologic mechanism of invention and, in particular, that of mathematical creation. Observation of the processes of the work of the mathematician is particularly instructive for the psychologist.
Introduction
Book I. Science and the Scientist
• The Choice of Facts
• The Future of Mathematics
• Mathematical Creation
• Chance
Book II. Mathematical Reasoning
• The Relativity of Space
• Mathematical Definitions and Teaching
• Mathematics and Logic
• The New Logics
• The Latest Efforts of the Logisticians
Book III. The New Mechanics
• Mechanics and Radium
• Mechanics and Optics
• The New Mechanics and Astronomy
Book IV. Astronomic Science
• The Milky Way and the Theory of Gases
• French Geodesy
• General Conclusions
The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method
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George Bruce Halsted was an American mathematician. He was professor of mathematics at the University of Texas from 1884 to 1903.
Background
George Bruce Halsted was born on November 25, 1853, in Newark, New Jersey, United States; he descended in the sixth generation from Timothy Halsted who came from England about 1660 to settle at Hempstead, Long Island. His father was Oliver Spencer Halsted and his mother Adela (Meeker) Halsted, a member of a one-time wealthy family of Charleston, South Carolina. He could point with pardonable pride to the fact that the rolls of the College of New Jersey, at Princeton, bore not only the names of his brother and himself, but also those of his father, an uncle, his grandfather, a great-uncle, and his great-grandfather.
Education
Halsted entered Princeton in 1872, and received his bachelor’s degree in 1875 and his master’s degree in 1878, having led his class throughout his entire course. He then proceeded to the Johns Hopkins University, becoming the first pupil of J. J. Sylvester, who was beginning to lay the foundations for advanced mathematical research in America.
Career
Receiving the degree of doctor of philosophy in 1879, Halsted returned to Princeton, for a time, as an instructor in graduate mathematics. From 1884 to 1903 he was professor of mathematics at the University of Texas, and it was there that his most important work was done. For a short period he taught at St. John’s College, Annapolis, Maryland, and for three years, 1903-1906, was a member of the faculty at Kenyon College, Ohio. He closed his teaching career at the Colorado State Teachers College, 1906-1912, formerly known as the State Normal School. After his retirement Halsted devoted himself for a time to electrical engineering, but in 1918 his health began to fail, and three years later he had to give up all work. He died at Roosevelt Hospital, New York.
Halsted’s chief interest lay in the field of geometry, and he did much to make the nonEuclidean theories known in the United States. His translations of certain treatises on the subject included: Janos Bolyai’s The Science Absolute of Space Independent of the Truth or Falsity of Euclid’s Axiom XI (1891), Girolamo Saccheri’s Euclides Vindicatus (1920), Lobachevskii’s Geometrical Researches on the Theory of Parallels (1891) and New Principles of Geometry with Complete Theory of Parallels , A. V. Vasiliev’s Nicolai Ivdnovich Lobachevsky (1894); and The Introduction to Lobachevski’s New Elements of Geometry (pamphlet, 1897). He also wrote Metrical Geometry: An Elementary Treatise on Mensuration (1881), Elements of Geometry (1885), Elementary Synthetic Geometry (1892), Projective Geometry (1896), Rational Geometry (1904), and On the Foundation and Technic of Arithmetic (1912). He translated Henri Poincare, The Foundations of Science and Hypothesis, the Value of Science, Science and Method (1913), with a special preface by Poincare and an introduction by J. Royce; and contributed some ninety articles on geometry and on the lives of eminent mathematicians to the American Mathematical Monthly.
Achievements
George Halsted is a well-known 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 to the works by Bolyai, Lobachevski, Saccheri, and Poincaré. He also wrote an elementary geometry text, Rational Geometry, based on Hilbert's axioms, which was translated into French, German, and Japanese.
(Lobachevski was the first to publish non-Euclidean geomet...)
Membership
Halsted was a member of the American Mathematical Society.
Personality
George Bruce Halsted was a man of ability in his chosen field, but certain eccentricities prevented him from attaining the success, either as a teacher or as a writer, which his powers seemed in his youthful years to promise.
Connections
George Bruce Halsted was married to Margaret Swearingen, with whom he had three sons.
