1874
GEORG CANTOR (1845–1918) develops SET THEORY
and his theory of CARDINALITY.
1882
FERDINAND VON LINDEMANN (1852–1939) proves that
π is transcendental and hence that the challenge of
SQUARING THE CIRCLE is impossible.
1883
Françoise-Edouard-Anatole Lucas (1842–91) invents
the TOWER OF HANOI puzzle.
1896
JACQUES HADAMARD (1865–1963) and CHARLES DE
LA VALLÉE-POUSSIN (1866–1962) independently prove
the PRIME NUMBER THEOREM first conjectured by
GAUSS in 1792.
1899
German mathematician DAVID HILBERT (1862–1943)
provides a complete axiomatic treatment of EUCLIDEAN
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
HENRI LÉON LEBESGUE (1875–1941) introduces a revolutionary new approach to INTEGRAL CALCULUS.
1903
Swedish mathematician Nils Fabian Helge von Koch
(1870–1924) introduces the KOCH CURVE, the first
example of an object later to be classified as a FRACTAL.
1904
JULES-HENRI POINCARÉ (1854–1912) conjectures that
any three-dimensional object sharing the same topological characteristics as a SPHERE must indeed be a sphere.
1905
ALBERT EINSTEIN (1879–1955) writes five groundbreaking papers in the field of mathematical physics.
The final two papers develop his famous special theory
of relativity. Einstein publishes his general theory of relativity in 1916.
1910
BERTRAND ARTHUR WILLIAM RUSSELL (1872–1970)
and Alfred North Whitehead (1861–1947) begin publication of their three-volume Principia Mathematica,
an ambitious attempt to derive all mathematics by
logical principles from a small set of beginning
AXIOMs.
1913
Indian mathematician SRINIVASA AIYANGAR RAMANUJAN (1887–1920) begins a five-year collaboration with
British mathematician GODFREY HAROLD HARDY
(1877–1947).
1921
German mathematician AMALIE NOETHER (1882–1935)
publishes her theory of RINGs, directing research in algebra away from the study of calculation toward the
study of abstract structures.
1925
SIR RONALD AYLMER FISHER (1890–1962) publishes
Statistical Methods for Research Workers, an influential work that provides the basis for modern experimental design.
1928
James Alexander (1888–1971) develops the Alexander
polynomial, the first invariant in KNOT THEORY. Subsequently, John Conway defined the Conway polynomial
in 1968, and Vaughn Jones the Jones polynomial in
1985.
1931
KURT GÖDEL (1906–78) stuns the mathematical community by establishing a pair of “incompleteness theorems.” 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
CLAUDE ELWOOD SHANNON (1916–2001) establishes
that BOOLEAN ALGEBRA can be successfully applied to
computer design. He founds the field of INFORMATION
THEORY in 1949.
1944
Hungarian-American mathematician JOHN VON NEUMANN (1903–57) and American economist Oskar Morgenstern (1902–77) found GAME THEORY.
1963
Edward Lorenz develops CHAOS theory.
544 Appendix I
GEORG CANTOR (1845–1918) develops SET THEORY
and his theory of CARDINALITY.
1882
FERDINAND VON LINDEMANN (1852–1939) proves that
π is transcendental and hence that the challenge of
SQUARING THE CIRCLE is impossible.
1883
Françoise-Edouard-Anatole Lucas (1842–91) invents
the TOWER OF HANOI puzzle.
1896
JACQUES HADAMARD (1865–1963) and CHARLES DE
LA VALLÉE-POUSSIN (1866–1962) independently prove
the PRIME NUMBER THEOREM first conjectured by
GAUSS in 1792.
1899
German mathematician DAVID HILBERT (1862–1943)
provides a complete axiomatic treatment of EUCLIDEAN
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
HENRI LÉON LEBESGUE (1875–1941) introduces a revolutionary new approach to INTEGRAL CALCULUS.
1903
Swedish mathematician Nils Fabian Helge von Koch
(1870–1924) introduces the KOCH CURVE, the first
example of an object later to be classified as a FRACTAL.
1904
JULES-HENRI POINCARÉ (1854–1912) conjectures that
any three-dimensional object sharing the same topological characteristics as a SPHERE must indeed be a sphere.
1905
ALBERT EINSTEIN (1879–1955) writes five groundbreaking papers in the field of mathematical physics.
The final two papers develop his famous special theory
of relativity. Einstein publishes his general theory of relativity in 1916.
1910
BERTRAND ARTHUR WILLIAM RUSSELL (1872–1970)
and Alfred North Whitehead (1861–1947) begin publication of their three-volume Principia Mathematica,
an ambitious attempt to derive all mathematics by
logical principles from a small set of beginning
AXIOMs.
1913
Indian mathematician SRINIVASA AIYANGAR RAMANUJAN (1887–1920) begins a five-year collaboration with
British mathematician GODFREY HAROLD HARDY
(1877–1947).
1921
German mathematician AMALIE NOETHER (1882–1935)
publishes her theory of RINGs, directing research in algebra away from the study of calculation toward the
study of abstract structures.
1925
SIR RONALD AYLMER FISHER (1890–1962) publishes
Statistical Methods for Research Workers, an influential work that provides the basis for modern experimental design.
1928
James Alexander (1888–1971) develops the Alexander
polynomial, the first invariant in KNOT THEORY. Subsequently, John Conway defined the Conway polynomial
in 1968, and Vaughn Jones the Jones polynomial in
1985.
1931
KURT GÖDEL (1906–78) stuns the mathematical community by establishing a pair of “incompleteness theorems.” 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
CLAUDE ELWOOD SHANNON (1916–2001) establishes
that BOOLEAN ALGEBRA can be successfully applied to
computer design. He founds the field of INFORMATION
THEORY in 1949.
1944
Hungarian-American mathematician JOHN VON NEUMANN (1903–57) and American economist Oskar Morgenstern (1902–77) found GAME THEORY.
1963
Edward Lorenz develops CHAOS theory.
544 Appendix I