Mathematics and Statistics

Mathematics and Statistics. Mathematics has been part of American higher education since the founding of Harvard College in 1636. In the seventeenth century, however, the level of instruction was low—arithmetic and the rudiments of Euclidean geometry—reflecting the primitive state of elementary education and the underlying aim of preparing young men for the ministry.

By 1800, new colleges had been founded that focused more on liberal education. The mathematics curriculum grew accordingly to include algebra, trigonometry, and sometimes even Newton's fluxional calculus. Colonial professors of mathematics drew, however, from Great Britain, a country that had fallen behind the Continent—especially France—in pedagogical innovations and original research.

This situation began to change by the 1820s. Beginning in 1817, the U.S. Military Academy at West Point followed the example of France's state‐of‐the‐art école Polytechnique and incorporated into its curriculum not only Leibnizian calculus but also the descriptive geometry that had been developed by Gaspard Monge. At midcentury at Harvard, Benjamin Peirce (1809–1880) crafted a curriculum in the mathematical sciences for the new Lawrence Scientific School (1847) that included some of the latest foreign research. Nevertheless, prior to 1876, America's colleges were almost exclusively undergraduate institutions. Research was not part of the faculty's mission, although some, like Peirce with his abstract theory of algebras (1870), pursued research anyway.

Colleges were not the sole locus of mathematical activity in nineteenth‐century America. In a few instances, mathematicians worked individually: Robert Adrain discovered the law of least squares in 1809 independently of Carl Friedrich Gauss, while Nathaniel Bowditch translated and wrote penetrating mathematical commentary on Pierre Simon de Laplace's challenging Mécanique céleste (1828–1839). The federal government supported mathematical activity in its U.S. Coast Survey and Nautical Almanac Office, where George William Hill did ground‐breaking work on the three‐body problem (1877).

After 1870, new research‐oriented universities were founded and many colleges began to emphasize research. The first mathematics program to offer research‐level training opened in 1876 at Johns Hopkins University under a British algebraist, James Joseph Sylvester. Following Sylvester's departure in 1883, mathematically inclined Americans turned to Germany, particularly the University of Göttingen and Felix Klein. There they absorbed the latest mathematics and the notion that academic mathematics encompassed both teaching and research. Returning to American institutions newly receptive to this ideal, they set up graduate programs and pursued their research agendas. By 1900, a professional community of mathematical researchers supported programs, notably at the University of Chicago under Eliakim Hastings Moore and at Harvard under William Fogg Osgood and Maxime Bôcher, and sustained at least four research journals as well as the American Mathematical Society (1888).

While American mathematicians embraced all of pure mathematics, certain areas of strength emerged. At Chicago, Leonard Eugene Dickson and his student A. Adrian Albert established a center for algebra. Princeton, with Oswald Veblen, Luther Pfahler Eisenhart, James Alexander, and Solomon Lefschetz, excelled in geometry and topology. Robert L. Moore created a school of point set topology at the University of Texas at Austin. Harvard built on its strength in analysis with George David Birkhoff, Joseph Walsh, and Marshall Stone.

Newer mathematical areas strengthened in the 1920s and 1930s owing both to the influx of European refugees and to the establishment of new research venues. Statistics as a tool for social analysis had grown during the Progressive Era with its practitioners conveying their findings through the American Statistical Association (1839). Activists such as Harry Carver at the University of Michigan, however, worked to establish statistics as a more mathematical field. Their efforts, including the formation of the Institute for Mathematical Statistics in 1935, received a considerable boost after the rise of Nazism brought refugees such as Jerzy Neyman to Berkeley and Mark Kac to Cornell. Others also fled to American shores, among them Hermann Weyl to Princeton's Institute for Advanced Study; Richard von Mises to Harvard; and Emil Artin, Richard Brauer, and Emmy Noether. Applied mathematics likewise profited from the European influx, as well as from the formation of industrial‐research facilities like Bell Telephone Laboratories (1925). During World War II, the Applied Mathematics Panel within the federal Office of Research and Development coordinated mathematical work on war‐related questions.

Thanks partly to wartime successes, the postwar period witnessed a dramatic increase in federal support of mathematics, as the National Science Foundation led an institutionalization of academic grants that contributed to an explosive growth of American mathematical research. Late twentieth‐century American mathematicians solved such noted problems as the Bieberbach conjecture, the classification of finite simple groups, the four‐color problem, and Fermat's Last Theorem. The immigration of mathematicians from China, the former Soviet bloc, and elsewhere also contributed to the country's mathematical strength as the century ended.
See also Coast and Geodetic Survey, U.S.; Education: Collegiate Education; Education: The Rise of the University; Research Laboratories, Industrial; Service Academies, Military.

Bibliography

Florian Cajori , The Teaching and History of Mathematics in the United States, 1890.
Peter L. Duren, Richard A. Askey, Harold M. Edwards, and Uta C. Merzbach, eds., A Century of Mathematics in America: Parts I–III, 1988–1989.
Larry Owens , Mathematics at War: Warren Weaver and the Applied Mathematics Panel, 1942–1945, in The History of Modern Mathematics, eds. David E. Rowe and John McCleary, 2 vols., 1989, II: 287–305.
Karen Hunger Parshall and and David E. Rowe , The Emergence of the American Mathematical Research Community, 1876–1900: J.J. Sylvester, Felix Klein, and E.H. Moore, 1994.
Patti Wilger Hunter , Drawing the Boundaries: Mathematical Statistics in 20th‐Century America, Historia Mathematica 23 (February 1996): 7–30.

Karen Hunger Parshall