Vallée-Poussin, Charles-Jean de la (1866–1962) Bel-
gian Analysis, Number theory Born on August 14,
1866, in Louvain, Belgium, Charles-Jean de la Vallée-
Poussin is remembered as one of the two mathemati-
cians who independently proved the famous
PRIME
NUMBER THEOREM
first conjectured by C
ARL
F
RIEDRICH
G
AUSS
(1777–1855). The second mathematician to
prove the result was French mathematician J
ACQUES
H
ADAMARD
(1865–1963). Even though both scholars
applied complex function theory to the
ZETA FUNCTION
to establish the result, the two proofs utilized very differ-
ent logical arguments.
Vallée-Poussin studied mathematics at the Univer-
sity of Louvain, at the University of Berlin, and at the
University of Paris before accepting a faculty position
at Louvain, where he stayed for the remainder of his
career. He specialized in the field of
ANALYSIS
and was
awarded a prize of a couronne from the Belgium Royal
Academy for his work in
DIFFERENTIAL EQUATION
s in
1892. At this time, Vallée-Poussin was studying newly
developed techniques in complex analysis and came to
the realization, in 1896, that all the pieces were in
place to develop a proof of Gauss’s prime-number con-
jecture. (Hadamard came to the same realization the
same year.) Vallée-Poussin also took matters further to
make significant contributions to the general study of
the Riemann zeta function and the Riemann hypothesis
as well as other concerns in analysis. In 1903 he pub-
lished a very popular text Cours d’analyse (A course on
analysis) on these topics, written for both the beginner
and the expert in the field. (Vallée-Poussin wrote the
introductory material in large font and interspersed dis-
cussions on advanced technical points in small font.) In
subsequent years he wrote four revised editions of the
text, as well as the book Intégrales de Lebesgue
(Lebesgue integration), which is seen as an extension of
the piece.
Vallée-Poussin received many honors throughout
his career, including election to the Belgian Academy,
the American Academy of Arts and Sciences, the Insti-
tute of France, and the American National Academy of
Sciences. In 1928, after holding the position of chair of
mathematics at the University of Louvain for 35 years,
the king of Belgium conferred upon him the title of
baron. Vallée-Poussin was also a commander of the
Legion of Honor and honorary president of the Inter-
national Mathematical Union. He died in Louvain on
March 2, 1962.
See also G
EORG
F
RIEDRICH
B
ERNHARD
R
IEMANN
.
variable A symbol, such as x, y, z, or n, that is used
in algebraic equations to represent a quantity whose
value is not known or specified is called a variable. For
example, in the expression x2+ x= 6, the symbol x
represents an unknown number whose sum with its
square equals 6. (The methods of
ALGEBRA
can be
applied to show that xmust either be 2 or –3.)
Variables are used to codify numeric operations. For
example, the operation of squaring the first 10 whole
numbers can be written “y= n2for n= 1,2,3,…,10.”
In this expression, the value of the variable nis not
518
V