give the youth of Britain the same opportunity to bene-
fit from this remarkable text as the young scholars
from Italy had been able to enjoy.
Alembert, Jean Le Rond d’ (1717–1783) French
Differential equations, Analysis, Philosophy Born on
November 17, 1717, in Paris, France, scholar Jean le
Rond d’Alembert is best remembered for his 1743 trea-
tise Traité de dynamique (Treatise on dynamics), in
which he attempted to develop a firm mathematical
basis for the study of mechanics. D’Alembert pioneered
the study of partial
DIFFERENTIAL EQUATION
s and their
use in physics. He is also noted for his work on vibrat-
ing strings.
After briefly pursuing theology and medicine at the
Jansenist Collège des Quatre Nations, d’Alembert set-
tled on mathematics as his choice of academic study.
He graduated from the Collège in 1735 to then pursue
interests in fluid mechanics. In 1740 he presented a
series of lectures on the topic to members of the Paris
Academy of Science, which earned him recognition as a
capable mathematician and admittance as a member of
the academy. He remained with the institution for his
entire career.
D’Alembert came to believe that the topic of
mechanics should be based on logical principles, not
necessarily physical ones, and that its base is funda-
mentally mathematical. In his 1743 treatise Traité de
dynamique, he attempted to refine the work of S
IR
I
SAAC
N
EWTON
(1642–1727) and clarify the underpin-
nings of the subject. The following year d’Alembert
published a second work, Traité de l’équilibre et du
mouvement des fluides (Treatise on the equilibrium and
movement of fluids), that applied his results to the
study of fluid motion and introduced some beginning
results on the study of partial differential equations. He
developed these results further over the following
years. In 1747 d’Alembert submitted a paper “Réflex-
ions sur la cause générale des vents” (Reflections on the
general cause of air motion) for consideration for the
annual scientific prize offered by the Prussian Academy.
He did indeed win.
At the same time d’Alembert also began work as a
writer and science editor for the famous French Ency-
clopédie ou dictionnaire raisonné des sciences, des arts,
et des métiers (Encyclopedia and dictionary of the
rationales of the sciences, arts, and professions), taking
responsibility for the writing of the majority of mathe-
matical entries. The first volume of the 28-volume
work was published in 1751.
D’Alembert published several new mathematical
results and ideas in this epic work. For instance, in vol-
ume 4, under the entry differential, he suggested, for
the first time, that the principles of
CALCULUS
should be
based on the notion of a
LIMIT
. He went so far as to
consider defining the derivative of a function as the
limit of a
RATIO
of increments. He also described the
new ratio test when discussing
CONVERGENT SERIES
.
D’Alembert’s interests turned toward literature and
philosophy, and administrative work, in the latter part
of his life. He was elected as perpetual secretary of the
Académie Française in 1772. He died 11 years later on
October 29, 1783.
His work in mathematics paved the way for proper
development of the notion of a limit in calculus, as well
8 Alembert, Jean Le Rond d’
Jean Le Rond d’Alembert, an eminent mathematician of the 18th
century, pioneered the study of differential equations and their
application to mechanics. (Photo courtesy of Topham/
The Image Works)