**Virgil Snyder**'s parents were Ephraim Snyder and Eliza Jane Randall. The Snyder family were originally from Germany having, at that time, the name Schneider. It was Johannes Schneider who emigrated from Germany to the USA in 1777, settling in Pennsylvania. His descendant Ephraim Snyder was a farmer in Iowa while his wife Eliza Jane, from New England but of English-French descent, had been a school teacher. Virgil attended Iowa State College from 1886 to 1889 being awarded his Sc.B. in 1889. He remained at Cornell as a graduate student during 1890-92 and in these years he became a founder member of the Cornell Mathematical Club which held its first meeting on 24 January 1891. The aim of the Club was to involve both students and staff in a German style mathematical seminar. The Club encouraged many students to go to Germany to study for their doctorates and Snyder went to Germany in 1892 having been awarded an Erastus W Brooks fellowship. James Oliver, who had been Felix Klein's student before returning to Cornell, wrote to Klein (see for example [1]):-

Remembering your kindness to myself, and the inspiration and enlarged outlook that I got from your lectures, I could think of no one else whose advice and instruction was likely to help[Mr Snyder]so much. You will find[him]an earnest student and a thoroughly honourable and loyal man. He has made a good record in his works here, and I value him highly, both as a student and as a friend.

Snyder studied for his doctorate at Göttingen, attending lectures by Klein and participating in his seminar. He was awarded a doctorate in December 1894 for his dissertation *Über die linearen Komplexe der Lie'schen Kugelgeometrie* written under Klein's supervision. Arthur B Coble writes [2]:-

Professor Snyder began his work at a time when geometers were exploring the superstructures of their subject, particularly in space and hyperspace. By adding the radius of a sphere to its coefficients, Lie had defined a sphere by six homogeneous coordinates subject to a non-singular quadratic relation. This situation also occurs with the Plücker line-coordinates so that the parallel between line geometry in three-space and Lie's "Kugelgeometrie" was apparent. Snyder's doctoral dissertation(Göttingen,1895)was concerned with linear complexes of spheres. Of twenty-one papers he published in the next ten years, twelve were concerned with the metric side of this parallel and dealt with annular, tubular, and developable surfaces, their asymptotic lines, and lines of curvature, or with the development of collateral algebra.

Snyder married Margarete Glesinger on 28 December 1894; they had two sons Herbert and Norman. He returned to Cornell University as an Instructor in Mathematics in 1895. He was to spend the rest of his career at Cornell, promoted to assistant professor in 1903 and then to full professor in 1910. He retired in 1938 after a career which is summed up by Raymond Archibald in [5] as follows:-

During more than forty years at Cornell University, Professor Snyder has devoted himself whole-heartedly, and with high idealism, to improving the teaching of mathematics, to promoting the welfare of his students and guiding them into research, and to carrying on his own original work in the fields of geometry of the line and sphere, configurations of ruled surfaces, and birational transformations.

After retiring from Cornell, Snyder was a Visiting Professor at Brown University in 1942-43 and then a Visiting Professor at Rollins College, Winter Park, Florida in 1943-44.

As to his interest in the teaching of mathematics, mentioned in the above quote, let us give an example by quoting from Snyder's paper* Relating to the Teaching of Axonometry* published in 1915 in the *American Mathematical Monthly*:-

About ten years ago one of our trustees ... suggested that the department of mathematics introduce a regular course in descriptive geometry as an alternative for those Arts students who ought to have some mathematics, but who found the calculus too difficult or too unattractive to be studied with profit. ... the department gave me the task of working out the course and it has been given every second year since then. This work is not to overlap with the instruction given in descriptive geometry by the technical colleges of the university, but is planned to furnish an insight into the processes and methods of graphical representation of various kinds. As now given the course comprises four chapters: orthogonal projection, plane projection, perspective, and axonometry. The last chapter was given in fifteen lessons and six drawing periods. We took up orthogonal and oblique representation and did considerable reading on military and cavalier projections. Pedagogically the experiment has been interesting. A considerable number of students took the course who were not taking other work in mathematics and a goodly number of them are now taking further courses. My smallest class had six members, and the largest, twenty-eight.

Karen Parshall and David Rowe write in [1] about Snyder's importance:-

Up until the1920s, Snyder's prolific output and his talents as a teacher made him, together with Frank Morley of Johns Hopkins, one of the most influential algebraic geometers in the nation. Together with Henry White, in fact, Snyder emerged as a principal heir to Klein's geometric legacy.

Another significant contribution by Snyder was his textbooks. He published (with James McMahon) *Treatise on Differential Calculus* (1898), (with John I Hutchinson) *Differential and Integral Calculus* (1902), (with John H Tanner) *Plane and Solid Geometry* (1911), (with John I Hutchinson) *Elementary Textbook on the Calculus* (1912), and (with Charles H Sisam) *Analytic Geometry of Space* (1914). In a review of this last mentioned textbook, Gordon Bill writes [2]:-

It is probable that in no branch of elementary mathematics has there been such need of a good, teachable book as in the analytic geometry of space. ... Taken as a whole the book[by Snyder and Sisam]is noteworthy for its literary style. It is a delight to read it. Simple, forceful language is employed throughout, the theorems are models of clear expression and, when a paragraph is completed, its connection with the rest of the subject is apparent. We are glad to note that, when the proof of some theorem has been standardised on account of its elegance, the authors have not felt obliged to bring forth an outrageous, new demonstration. The reviewer will never agree that desire for change is sufficient excuse to mangle a natural, tried and beautiful development. The book is arranged so that its contents fall very naturally into materials for two courses, the first eight chapters constituting a course of some thirty-five lessons and the last six one of about fifty lessons. The outstanding feature of the first eight chapters, and to the reviewer the finest thing in the book, is the natural and immediate introduction of certain geometric concepts which most authors seem to feel are better left out of a first course, such concepts as plane coordinates, homogeneous coordinates of points and planes, elements at infinity, imaginary elements, the absolute, circular points and isotropic planes. ... Let me say in conclusion that, with its splendid style, its fine choice and arrangement of material and its pedagogical excellences, I believe this book one of the best contributions to American textbooks made in recent years.

Snyder was honoured by being elected to the American Academy of Arts and Sciences in 1919. He was also a member of the German Mathematical Society and the Mantematical Circle of Palermo. He served as an editor of the Bulletin of the American Mathematical Society from 1903 to 1921, was a member of the American Mathematical Society Committee on Publications 1907-1921 and was Review Editor from 1938 until his death. He was vice-president of the American Mathematical Society in 1916 and president of the Society from 1927 to 1928. He was awarded an honorary degree by the University of Padua in 1922, at the celebrations for the 700^{th} anniversary of its foundation. From 1926 to 1929 he was a member of the National Research Council. He was the National Research Council and International Mathematical Union delegate at the International Congress of Mathematicians in Toronto in 1924, in Bologna in 1928 and in Zürich in 1932. He was also the United States Government delegate to the International Congress of Mathematicians in Bologna in 1928 and in Oslo in 1936. From 1924 to 1934 he was chairman of the National Research Council Committee on Rational Transformations and during this time five of his papers appeared under the title *Selected Topics in Algebraic Geometry* in the Bulletin No. 63 (1928) and four papers under the title *Selected Topics in Algebraic Geometry II. Supplemental Report* in Bulletin No. 96 (1934).

In [5] Archibald describes his interests outside mathematics as follows:-

... a lover of travel ... intensely interested in politics ... His favourite recreation is mountain climbing and going on long hikes with Mrs Snyder as companion.

He was also a member of the Tennis Club.

**Article by:** *J J O'Connor* and *E F Robertson*