1874
G
EORG
C
ANTOR
(1845–1918) develops
SET THEORY
and his theory of
CARDINALITY
.
1882
F
ERDINAND VON
L
INDEMANN
(1852–1939) proves that
πis transcendental and hence that the challenge of
SQUARING THE CIRCLE
is impossible.
1883
Françoise-Edouard-Anatole Lucas (1842–91) invents
the
TOWER OF
H
ANOI
puzzle.
1896
J
ACQUES
H
ADAMARD
(1865–1963) and C
HARLES DE
LA
V
ALLÉE
-P
OUSSIN
(1866–1962) independently prove
the
PRIME NUMBER THEOREM
first conjectured by
GAUSS
in 1792.
1899
German mathematician D
AVID
H
ILBERT
(1862–1943)
provides a complete axiomatic treatment of E
UCLIDEAN
GEOMETRY
.
1900
At the International Congress of Mathematicians in
Paris,
HILBERT
presents his famous list of 23 problems
to challenge scholars of the 20th century.
1901
H
ENRI
L
ÉON
L
EBESGUE
(1875–1941) introduces a revo-
lutionary new approach to
INTEGRAL CALCULUS
.
1903
Swedish mathematician Nils Fabian Helge von Koch
(1870–1924) introduces the K
OCH CURVE
, the first
example of an object later to be classified as a
FRACTAL
.
1904
J
ULES
-H
ENRI
P
OINCARÉ
(1854–1912) conjectures that
any three-dimensional object sharing the same topologi-
cal characteristics as a
SPHERE
must indeed be a sphere.
1905
A
LBERT
E
INSTEIN
(1879–1955) writes five ground-
breaking papers in the field of mathematical physics.
The final two papers develop his famous special theory
of relativity. Einstein publishes his general theory of rel-
ativity in 1916.
1910
B
ERTRAND
A
RTHUR
W
ILLIAM
R
USSELL
(1872–1970)
and Alfred North Whitehead (1861–1947) begin pub-
lication of their three-volume Principia Mathematica,
an ambitious attempt to derive all mathematics by
logical principles from a small set of beginning
AXIOM
s.
1913
Indian mathematician S
RINIVASA
A
IYANGAR
R
AMANU
-
JAN
(1887–1920) begins a five-year collaboration with
British mathematician G
ODFREY
H
AROLD
H
ARDY
(1877–1947).
1921
German mathematician A
MALIE
N
OETHER
(1882–1935)
publishes her theory of
RING
s, directing research in alge-
bra away from the study of calculation toward the
study of abstract structures.
1925
S
IR
R
ONALD
A
YLMER
F
ISHER
(1890–1962) publishes
Statistical Methods for Research Workers, an influen-
tial work that provides the basis for modern experi-
mental design.
1928
James Alexander (1888–1971) develops the Alexander
polynomial, the first invariant in
KNOT THEORY
. Subse-
quently, John Conway defined the Conway polynomial
in 1968, and Vaughn Jones the Jones polynomial in
1985.
1931
K
URT
G
ÖDEL
(1906–78) stuns the mathematical com-
munity by establishing a pair of “incompleteness the-
orems.” Gödel proves that within any logically
rigorous system there will necessarily be statements
that can neither be proved nor disproved. The goal
pursued by
RUSSELL
and Whitehead is proved
unattainable.
1938
C
LAUDE
E
LWOOD
S
HANNON
(1916–2001) establishes
that B
OOLEAN ALGEBRA
can be successfully applied to
computer design. He founds the field of
INFORMATION
THEORY
in 1949.
1944
Hungarian-American mathematician J
OHN VON
N
EU
-
MANN
(1903–57) and American economist Oskar Mor-
genstern (1902–77) found
GAME THEORY
.
1963
Edward Lorenz develops
CHAOS
theory.
544 Appendix I