Jacobi was passionate about theoretical research
and once uttered the following defense for pursuing sci-
ence for its own sake: “The sole aim of science is the
honor of the human mind, and from this point of view
a question about numbers is as important as a question
about the system of the world.”
Jacobi died of smallpox on February 18, 1851.
Jiuzhang suanshu (Chiu-chang Suan-shu)See C
HI
-
NESE MATHEMATICS
.
Jordan, Marie Ennemond Camille (1838–1922)
French Topology, Abstract algebra, Engineering Born
on January 5, 1838, in Lyon, France, Camille Jordan is
remembered for his work on
PERMUTATION
groups and
the theory of equations. He revived interest in the
important work of É
VARISTE
G
ALOIS
and extended
many of his ideas and offered substantial new contribu-
tions. Jordan’s later work on
ANALYSIS
includes the
famous theorem that now bears his name.
Jordan trained and worked throughout his life as
an engineer. His interests in
GROUP THEORY
were moti-
vated by the mathematical study of crystal structures.
In many respects he defined this field of study with the
publication of his 1870 text Traité des substitutions et
des equations algebraique (Treatise on permutations
and algebraic equations), the first book ever published
on the topic. This work stimulated significant further
mathematical research on the subject for the entire cen-
tury that followed. Jordan was awarded the Poncelet
Prize from the Académie des Science for the piece.
After the release of his famous work Jordan contin-
ued work in algebra, establishing important results in
the fields of
LINEAR ALGEBRA
,
NUMBER THEORY
,
DIF
-
FERENTIAL EQUATIONS
, mechanics, and F
OURIER SERIES
.
Work in these latter fields led him to the topics of
TOPOLOGY
and analysis, and the study of continuous
groups, which occupied the final part of his career.
Jordan died in Paris, France, on January 22, 1922.
From 1961 to 1964 René Garnier and Jean Dieudonné
collated all of Jordan’s work and released the four-vol-
ume series Oeuvres de Camille Jordan (The work of
Camille Jordan).
One point of confusion should be settled. Although
Jordan did work in the field of matrix algebra, the
method of G
AUSSIAN ELIMINATION
, often called Gauss-
Jordan elimination, is not named after Camille Jordan,
but rather surveyor Wilhelm Jordan (1842–99). W. Jor-
dan used this elimination method to properly analyze
measurement errors. (The “Jordan canonical form” of
a matrix, however, is due to Camille Jordan.)
See also J
ORDAN CURVE THEOREM
.
Jordan curve theorem In 1893 French mathemati-
cian M
ARIE
E
NNEMOND
C
AMILLE
J
ORDAN
stated a fun-
damental result:
Any loop drawn in the plane that does not
intersect itself divides the plane into two dis-
tinct parts: an inside and an outside.
This utterly obvious theorem, now called the Jordan
curve theorem, is surprisingly difficult to prove. Its
validity says something significant about the geometry
and structure of the surface on which the curve is
drawn. For example, circles drawn on a plane or a
sphere certainly divide those surfaces into two parts,
but this need not be the case for a circle drawn on a
TORUS
, for example: a “loop” that circumnavigates the
donut does not separate the surface into two distinct
pieces. One must first develop a clear understanding of
the geometry of space before results such as the Jordan
curve theorem can be proved. This is a subtle and diffi-
cult issue. American mathematician Oswald Veblen
(1880–1960) was the first to prove the theorem valid.
Josephus problem This famous mathematical puzzle
is based on the difficult story of Josephus Flavius, a
Jewish military leader fighting against the Romans in
the town of Jotapata during the first century
C
.
E
. It is
said that the battle, which took place in the spring of
67, was lost. Rather than submit their fates to the
hands of the Romans, Josephus’s men took brief refuge
in a cave, where they voted to commit group suicide.
Although Josephus did not agree with this plan, he
offered no open opposition to it. Instead, he suggested
that they proceed in as orderly a fashion as possible.
He proposed that they sit in a circle and humanely kill
every third man until only one person was left. That
person would then commit suicide. Josephus, it is said,
cleverly positioned himself so that he would be the
final survivor. Rather than commit suicide, he surren-
dered to the Romans.
288 Jiuzhang suanshu