Lagrange, Joseph-Louis (1736–1813) Italian-French
Analysis, Mechanics, Abstract algebra, Number theory
Born on January 25, 1736, in Turin, Italy, Joseph-Louis
Lagrange is remembered for, among other things, his
definitive 1788 text Mécanique analytique (Analytical
mechanics), in which he lays out a purely formal and
completely rigorous exposition of how and why things
move. In effect, the work summarizes the entire state of
the post-Newton mechanics of the 18th century. The
publication is also famous for featuring no figures or
diagrams. (Lagrange apparently felt that the formulae
he developed captured physical reality sufficiently well
that pictures were not necessary.) He also published two
important memoirs in 1769 and 1770, which he com-
bined into a single 1798 treatise, Traité de la résolution
des équations numériques de tous les degrés (Treatise on
the resolution of numeric equations of all degree), on
the theory of equations, in which he developed general
principles for solving
POLYNOMIAL
equations up to
degree four via principles that we today would label
GROUP THEORY
. The famous “Lagrange’s theorem”
from the study of groups appears in this work, as does
the famous
INTERPOLATION
formula that bears his
name. He also made significant contributions in the
field of
NUMBER THEORY
, proving in 1770, for instance,
that every positive integer is the sum of four square
numbers. Also, in 1771, he was the first to prove what
is today called “Wilson’s theorem,” that a number nis
PRIME
if, and only if, (n– 1)! + 1 is divisible by n.
Although Lagrange was born in Turin and spent
the early part of his life there, he eventually settled in
Paris and identified himself as French. He was intro-
duced to the topics of physics and mathematics at the
College of Turin. He first studied the principles of the
TAUTOCHRONE
and, by 1754, had published some
important discoveries about the topic. He shared the
results with L
EONHARD
E
ULER
(1707–83), who was
suitably impressed. At the young age of 19, Lagrange
was appointed professor of mathematics at the Royal
Artillery School in Turin. There he made significant
progress on the general study of mechanics and wrote a
number of influential papers. In 1756 he was elected to
the Berlin Academy under Euler’s recommendation.
During the 20 years that Lagrange stayed at the
Berlin Academy, he worked on a wide variety of topics.
He lay down the foundations of a subject to become
known as “dynamics” and made significant contribu-
tions to the studies of fluid mechanics, to the integra-
tion of differential equations, and to the solution of
systems of differential equations, as well as to the study
of vibrating strings and the propagation of sound. In
1766 he succeeded Euler as director of mathematics at
the Berlin Academy, and in 1772 he shared one of the
biennial prizes from the Paris Académie des Sciences
with Euler for his work on the “three-body problem”
from physics. He won a prize again from the Paris
Académie in 1774 for his work on the motion of the
moon, and again in 1780 for his mathematical study of
planetary motion.
In 1787 Lagrange left Berlin to take a position at
the Académie des Sciences in Paris. He published his
work Mécanique analytique the following year. He also
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