The History of Mathematics: A Brief Course

5. NORTH AMERICA 67

programs in mathematics in places such as Harvard and the University of Michigan,

but now such programs began to multiply. Bryn Mawr College opened in the mid-

1880s with a graduate program in mathematics. The founding of Clark University

in Worcester, Massachusetts and the University of Chicago in the late 1880s and

early 1890s promised that the United States would soon begin to make respectable

contributions to mathematical research. An account of this development giving the

details of the mathematical areas studied in American universities can be found

in the article by David Rowe (1997). A review of a number of professional "self-

studies" made by American mathematicians can be found in the article by Karen

Hunger Parshall (2000); both of these articles contain extensive bibliographies on

the development of mathematics in the United States. We now continue our list of

prominent mathematicians.

George William Hill. The mathematical side of astronomy, known as celestial me-

chanics, was pursued in the United States by the Canadian Simon Newcomb, who

is discussed below, and by George William Hill (1838-1914). Hill worked for a time

at the Nautical Almanac Office in Cambridge, Massachusetts, but was perfectly

content to work in isolation at his home in Nyack, New York, most of his life. His

work on the motion of the Moon was so profound that it received extravagant praise

from Henri Poincare (1854-1912), one of the greatest mathematicians of the late

nineteenth and early twentieth centuries. In a paper on the motion of the lunar

perigee published in the Swedish journal Acta mathematica in 1886, Hill derived a

differential equation that bears his name and even today continues to generate new

work.

Although the rise of the United States to a position of world leadership in

mathematics after World War II was partly the result of the turbulence of the

1930s and 1940s, which drove many of the best European intellectuals to seek

refuge far from the dangers that threatened them in their homelands, one should

not think that the country was intellectually backward before that time. Americans

had made significant contributions to algebra and logic in the nineteenth century,

and in the early twentieth century a number of Americans achieved worldwide fame

for their mathematical contributions. We mention only two here.

George David Birkhoff. Harvard professor George David Birkhoff (1884-1944) made

contributions to differential equations, difference equations, ergodic theory, and

mathematical physics (the kinetic theory of gases, in which the ergodic theorem

plays a role, quantum mechanics, and relativity). He was held in such high esteem

that a crater on the Moon now bears his name.

Norbert Wiener. An early prodigy who graduated from high school at age 11 and

received the doctoral degree at age 18, despite having changed universities and ma-

jors more than once, Norbert Wiener (1894-1964) contributed to harmonic analy-

sis, probability, quantum mechanics, and cybernetics, of which he was one of the

founders. (The name comes from the Greek word kybernetes, meaning a ship's

captain or pilot.)

Like American schools of the same period, English-language Canadian insti-

tutions of higher learning tended to rely on British textbooks such as those of

Charles Hutton (1737-1823, a professor at the Miltary School in Woolwich). In

French Canada there was a long tradition of educational institutions, and a French