After graduating with an A.B. in 1882, White was appointed as an assistant to John Monroe Van Vleck in the astronomical observatory at the Wesleyan University, then he moved to Centenary Collegiate Institute, Hackettstown, New Jersey where he taught mathematics and chemistry for a year before returning to the Wesleyan University to become a tutor. In 1887, following advice from John Monroe Van Vleck, he decided to study for his doctorate in Germany and travelled to Leipzig to begin working with Study and Lie. However, he spent only one semester in Leipzig and during this time he was mostly taken up with improving his knowledge of German. White's friend, William J James, had studied under Klein at Göttingen and also under Kronecker and Fuchs in Berlin. James gave White what he described in  as:-
... very valuable advice.James :-
... held up Klein as not only the leading research mathematician but also as a magazine of driving power, whoses students received personal attention and stimulus, and in most cases became themselves productive investigators.Taking James' advice, White went to study at the University of Göttingen for his doctorate between 1887 and 1890 under Klein's supervision. When he arrived he discovered that he was one of six American students undertaking mathematics research at Göttingen. Since he had missed the first semester of Klein's advanced course on hyperelliptic functions, he decided not to attend the second half of the course but instead to wait for the start of an advanced course in the next academic year. White did attend one of Klein's courses from the time he arrived, however, taking the slightly less advanced course on potential theory. White's other task was to use this semester to learn background on abelian functions so that he could start Klein's three semester course on that topic in the next academic year. He later wrote :-
Klein received me kindly and admitted me to his seminar course ... in abelian functions [in the summer of 1888], ... Klein expected hard work, and soon had in succession Haskell, Tyler, Osgood, and myself working up the official Heft or record of his lectures, always kept for reference in the mathematical Lesezimmer. This gave the fortunate student extra tuition, since what the Göttingen geometer gave in one day's lecture (two hours) must be edited and elaborated and submitted for Klein's own correction and revision within 48 hours.White's doctorate was awarded for the thesis Abelsche Integrale auf singularitätenfreien, einfach überdeckten, vollständigen Schnittkurven eines beliebig ausgedehnten Raumes in 1891.
In fact White returned to the United States in March 1890, before completing his doctorate, to take up a temporary position in a school attached to Northwestern University in Evanston, Illinois. Later that year he married Mary Willard Gleason; they had three children. He was appointed to Clark University, which opened in Worcester, Massachusetts, in 1887, and began teaching there at the start of session 1890-91. Clark University was established by Jonas Gilman Clark, a Worcester native and successful merchant, and G Stanley Hall, a psychologist and first president of the university. The university started as a graduate institution, the first undergraduates entering only in 1902. The University hired some excellent mathematicians, and there White became a colleague of Story and Bolza. White began teaching advanced courses in his area of research interest, in particular on algebraic geometry, projective geometry, and invariant theory. However a serious political situation arose at Clark University and a vote of no confidence was passed in the president G Stanley Hall. Nine of the eleven members of faculty left Clark including both White and Bolza.
Eliakim Moore tried to arrange an appointment for White at the University of Chicago, but this did not work out. Instead he became an associate professor of pure mathematics at Northwestern University in 1892 being promoted to full professor there two years later. Parshall writes :-
The thirteen years White spent in Evanston, Illinois, proved fruitful for him both mathematically and relative to the wider arena of the developing American mathematical research community. In 1893 he, together with Eliakim Moore, Oskar Bolza, and Heinrich Maschke of the University of Chicago, organised the Mathematical Congress of the World's Columbian Exposition in Chicago, the first major mathematical meeting held on American shores.Klein attended the Columbian Exposition and then went to Evanston to spend two weeks there at White's invitation to give a series of lectures on contemporary mathematical research. The result was the Evanston Colloquium lectures which were published by Macmillan and Co. in 1894. White's success here led him to approach the American Mathematical Society suggesting that such Colloquium lectures should become a feature. White wrote to Fiske in 1896:-
Our summer meeting last year was profitable in various ways; but not specially, perhaps, as a stimulus to mathematical thought. One would likely derive more direct advantage from an hour in any one of several lecture rooms in this country. Yet each one found two or three papers out of the program of high interest. Now, why would it not be possible to combine with this miscellaneous program (which ought by all means to be kept up) something more akin to university models? Would not a series of three or six lectures on nearly related topics, if well chosen, prove attractive and useful to larger numbers?White's proposal was indeed taken up by the American Mathematical Society and the result was the American Mathematical Society Colloquium lectures which are published as the American Mathematical Society Colloquium Publication series.
In 1905 White was appointed as professor at Vassar College in Poughkeepsie, New York. This may seem like a rather strange career move, but the reason was a personal one, namely the illness of his mother. Vassar College was then a college for women, founded to provide women with a quality of education previously only available to men. Grace Hopper was one who benefited from the quality education provided there. White retired from Vassar College in 1936.
White was an excellent research mathematician. He worked on invariant theory, the geometry of curves and surfaces, algebraic curves and twisted curves. Examples of the papers he wrote are: Two elementary geometrical applications of determinants (1899), Conics and cubics connected with a plane cubic by certain covariant relations (1900), Plane cubics and irrational covariant cubics (1900), On twisted cubic curves that have a directrix (1903), Triangles and quadrilaterals inscribed to a cubic and circumscribed to a conic (1906), Triple-systems as transformations, and their paths among triads (1913), and The multitude of triad systems on 31 letters (1915). In  Archibald describes in detail a theorem proved by White in 1915:-
If seven points on a twisted cubic be joined, two and two, by twenty-one lines, then any seven planes that contain these 21 lines will osculate a second cubic curve. This theorem is more strictly fundamental than von Staudt's ... [which] can be deduced from White's.Despite White's impressive mathematical contributions, he may be most important for his work for the American Mathematical Society. Having instigated the Colloquium Lectures, as we described above, he was a Colloquium Lecturer himself in 1903 when he lectured on Linear systems of curves on algebraic surfaces. White was vice-president of the American Mathematical Society in 1901 and then president from 1907 to 1908. He was an editor of the Annals of Mathematics (1899-1905) and editor of the Transactions of the American Mathematical Society (1907-1914). The papers we mentioned above all appear in one of these two journals. He was elected to the National Academy of Sciences (United States) in 1915.
In  Archibald notes his love of music and the fact that White's wife was the composer Mary Gleason. White is described as:-
Wise, kind, the soul of courtesy.Coble writes in the preface to :-
White was one of perhaps a dozen men who furnished the inspiration and set the pattern for the development of the present school of American mathematics.
Article by: J J O'Connor and E F Robertson