The Theory of Games and Economic Behavior, written
with Oskar Morgenstern (1902–76), which essentially
founded the field of
GAME THEORY
. He also made
major contributions to the development of the modern
computer, both as a practical design problem and as a
theoretical investigation into the nature and capabilities
of
AUTOMATA
. He was the first to devise a way of stor-
ing programs inside a computer.
Von Neumann demonstrated an incredible aptitude
for mathematics at a very early age. He received private
tutoring in mathematics from faculty members at the
University of Budapest while he was a high-school stu-
dent, and by age 18 he had written and published a
coauthored mathematics paper. Although von Neumann
was admitted into the mathematics program at the Uni-
versity in 1921, he followed his father’s wishes and pur-
sued chemistry at the University of Berlin and at the
Technische Hochschule in Zürich. Remarkably, without
ever attending a class at the University of Budapest, von
Neumann continued his work in mathematics privately,
passed the University mathematics examination, wrote
an influential thesis on the topic of set theory, and was
awarded a degree there in 1926, all the while pursuing a
degree in chemical engineering in Zürich. In 1930 von
Neumann accepted a professorship in mathematics at
Princeton University in the United States.
In 1932 he published his groundbreaking work
Mathematische Grundlagen der Quantenmechanik
(Mathematical foundations of quantum mechanics) on
theoretical quantum mechanics, which led him to the
study of operator algebras and functional analysis for
the years that followed. In 1938 he was awarded the
Bôcher Prize from the American Mathematical Society
for his work in this field. In the early 1940s von Neu-
mann’s interests turned to applied mathematics, and
in 1944 he published his famous piece on the topic of
game theory. His subsequent work in the logical
design of computers and the theory of automata
seemed, to von Neumann, a natural extension of all
his previous studies.
During and after World War II von Neumann
served as a consultant to the Defense Department and
to the Los Alamos Scientific Laboratory. In 1955 Presi-
dent Eisenhower appointed him to the Atomic Energy
Commission, and in 1956 he was awarded the Enrico
Fermi Award for all his contributions in this regard.
The same year he was honored in academia with the
Albert Einstein Commemorative Award.
Von Neumann was elected to a large number of
academic societies throughout his life, including the
National Academy of Sciences (the United States), The
American Academy of Arts and Sciences, Instituto
Lomdardo do Scienze e Lettere (Italy), and the Royal
Netherlands Academy of Sciences and Letters. He died
in Washington, D.C., on February 8, 1957.
Newton, Sir Isaac (1642–1727) British Calculus,
Mechanics, Dynamics, Optics, Astronomy, Natural
philosophy Born on January 4, 1642, in Woolsthorpe,
England, Sir Isaac Newton is remembered as one of the
greatest scientific scholars of all time. He dominated
and revolutionized the mathematics and the physics of
the 17th century. Newton is responsible for the devel-
opment of differential and integral
CALCULUS
and the
discovery of the
FUNDAMENTAL THEOREM OF CALCULUS
that unites the two fields. He also generalized the
BINO
-
MIAL THEOREM
to incorporate noninteger exponents;
developed numerical methods for solving
DIFFERENTIAL
EQUATION
s, approximating
LIMIT
s, and computing inte-
grals; and discovered many important results in the
theory of equations. In physics, he is remembered for
his formulation of a system of mechanics capable of
precise and accurate descriptions of the motions of all
objects and for his universal law of gravitation through
an
INVERSE SQUARE LAW
. He outlined this work in his
1687 work Philosophiae naturalis principia mathemat-
ica (The mathematical principles of natural philoso-
phy), often referred to simply as Principia. This is
today regarded as one of the most important scientific
works of all time.
Newton entered the Trinity College, Cambridge, in
1661 to study law and philosophy, but he soon discov-
ered an interest in mathematics, optics, and mechanics.
A personal notebook from the time reveals that he
read, and worked through in detail, the works of
E
UCLID
(ca. 300–260
B
.
C
.
E
.) and R
ENÉ
D
ESCARTES
(1596–1650) on the topic of geometry, of G
ALILEO
G
ALILEI
(1564–1642) on the mechanics of the universe,
and of F
RANÇOIS
V
IÈTE
(1540–1603) and J
OHN
W
AL
-
LIS
(1616–1703) on algebra. Newton extended some of
Wallis’s techniques for finding the area of curved fig-
ures and worked on new approaches to infinite
SERIES
.
He graduated from Cambridge with a bachelor’s degree
in 1665, but he did not attract the attention of his pro-
fessors as a particularly gifted scholar at the time.
Newton, Sir Isaac 351