Vallée-Poussin, Charles-Jean de la (1866–1962) Belgian Analysis, Number theory Born on August 14,
1866, in Louvain, Belgium, Charles-Jean de la ValléePoussin is remembered as one of the two mathematicians who independently proved the famous PRIME
NUMBER THEOREM first conjectured by CARL FRIEDRICH
GAUSS (1777–1855). The second mathematician to
prove the result was French mathematician JACQUES
HADAMARD (1865–1963). Even though both scholars
applied complex function theory to the ZETA FUNCTION
to establish the result, the two proofs utilized very different logical arguments.
Vallée-Poussin studied mathematics at the University 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 EQUATIONs 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 conjecture. (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 published 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 discussions 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 Institute 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 International Mathematical Union. He died in Louvain on
March 2, 1962.
See also GEORG FRIEDRICH BERNHARD RIEMANN.
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 x
2 + 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 x must 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 = n
2 for n = 1,2,3,…,10.”
In this expression, the value of the variable n is not
518
V
1866, in Louvain, Belgium, Charles-Jean de la ValléePoussin is remembered as one of the two mathematicians who independently proved the famous PRIME
NUMBER THEOREM first conjectured by CARL FRIEDRICH
GAUSS (1777–1855). The second mathematician to
prove the result was French mathematician JACQUES
HADAMARD (1865–1963). Even though both scholars
applied complex function theory to the ZETA FUNCTION
to establish the result, the two proofs utilized very different logical arguments.
Vallée-Poussin studied mathematics at the University 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 EQUATIONs 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 conjecture. (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 published 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 discussions 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 Institute 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 International Mathematical Union. He died in Louvain on
March 2, 1962.
See also GEORG FRIEDRICH BERNHARD RIEMANN.
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 x
2 + 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 x must 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 = n
2 for n = 1,2,3,…,10.”
In this expression, the value of the variable n is not
518
V