1767
German mathematician JOHANN HEINRICH LAMBERT
(1728–77) proves that π is irrational.
1795
France adopts the metric system.
John Playfair (1748–1819) publishes an equivalent
form of the famous PARALLEL POSTULATE, today known
as PLAYFAIR’S AXIOM.
1797
CARL FRIEDRICH GAUSS (1777–1855) proves the FUNDAMENTAL THEOREM OF ALGEBRA. Throughout his life,
Gauss, among many accomplishments, derives the
LEAST SQUARES METHOD, classifies the CONSTRUCTIBLE
regular polygons, and makes fundamental contributions to NUMBER THEORY, GEOMETRY, STATISTICS,
mathematical physics, and astronomy.
1799
Norwegian surveyor Casper Wessel (1745–1818)
publishes the equivalent of an ARGAND DIAGRAM as a
means for representing COMPLEX NUMBERS. French
bookkeeper and mathematician JEAN ROBERT
ARGAND (1768–1822) develops the same method in
1806.
1812
British mathematician and inventor CHARLES BABBAGE
(1791–1871) constructs the first mechanical calculator.
In 1823 Babbage obtains funds to build the “difference
engine,” the first digital computer, but the project is
never completed.
ca. 1820
Norwegian algebraist NIELS HENRIK ABEL (1802–29)
proves that there can be no general formula akin to the
famous quadratic formula that solves all fifth-degree
polynomial equations. Soon afterward, French mathematician ÉVARISTE GALOIS (1811–32) begins work to
classify which fifth- and higher-degree equations can be
so solved and consequently founds the field of GROUP
THEORY.
1821
French mathematician AUGUSTIN-LOUIS CAUCHY
(1789–1857) develops the notion of a LIMIT as an
attempt to place CALCULUS on sound mathematical
footing. This idea is later refined by German scholar
KARL THEODOR WILHELM WEIERSTRASS (1815–97).
1822
French mathematician JEAN BAPTISTE JOSEPH FOURIER
(1768–1830) publishes a treatise on the theory of heat
and develops the notion of a FOURIER SERIES.
1829
Russian
mathematician
NIKOLAI
IVANOVICH
LOBACHEVSKY (1792–1856) and Hungarian mathematician JÁNOS BOLYAI (1802–60) independently discover NON-EUCLIDEAN GEOMETRY.
1843
SIR WILLIAM ROWAN HAMILTON (1805–65) discovers
QUATERNIONS. Two years later ARTHUR CAYLEY
(1821–95) discovers octonians.
1844
JOSEPH LIOUVILLE (1809–82) discovers the first example of a TRANSCENDENTAL NUMBER.
1854
British scholar GEORGE BOOLE (1815–64) establishes
the field of symbolic logic with his development of
BOOLEAN ALGEBRA.
German mathematician GEORG FRIEDRICH BERNHARD
RIEMANN (1826–66) offers a universal approach to
geometry. He discovers SPHERICAL GEOMETRY. He later
makes significant advances in the theory of numbers
and the study of PRIME numbers.
1858
AUGUST FERDINAND MÖBIUS (1790–1868) and Johann
Benedict Listing independently discover the MÖBIUS
BAND.
German mathematician JULIUS WILHELM RICHARD
DEDEKIND (1831–1916) suggests the notion of a
DEDEKIND CUT as a means to properly define the REAL
NUMBERS.
CAYLEY introduces the notion of a MATRIX to the study
of algebra.
1872
FELIX CHRISTIAN KLEIN (1849–1925) unifies the fields
of geometry with his “Erlanger program.” He also discovers the KLEIN BOTTLE.
1873
WILLIAM SHANKS (1812–82) computes, by hand, the
first 607 decimals of π. He is correct up to the 527th
place.
Appendix I 543
German mathematician JOHANN HEINRICH LAMBERT
(1728–77) proves that π is irrational.
1795
France adopts the metric system.
John Playfair (1748–1819) publishes an equivalent
form of the famous PARALLEL POSTULATE, today known
as PLAYFAIR’S AXIOM.
1797
CARL FRIEDRICH GAUSS (1777–1855) proves the FUNDAMENTAL THEOREM OF ALGEBRA. Throughout his life,
Gauss, among many accomplishments, derives the
LEAST SQUARES METHOD, classifies the CONSTRUCTIBLE
regular polygons, and makes fundamental contributions to NUMBER THEORY, GEOMETRY, STATISTICS,
mathematical physics, and astronomy.
1799
Norwegian surveyor Casper Wessel (1745–1818)
publishes the equivalent of an ARGAND DIAGRAM as a
means for representing COMPLEX NUMBERS. French
bookkeeper and mathematician JEAN ROBERT
ARGAND (1768–1822) develops the same method in
1806.
1812
British mathematician and inventor CHARLES BABBAGE
(1791–1871) constructs the first mechanical calculator.
In 1823 Babbage obtains funds to build the “difference
engine,” the first digital computer, but the project is
never completed.
ca. 1820
Norwegian algebraist NIELS HENRIK ABEL (1802–29)
proves that there can be no general formula akin to the
famous quadratic formula that solves all fifth-degree
polynomial equations. Soon afterward, French mathematician ÉVARISTE GALOIS (1811–32) begins work to
classify which fifth- and higher-degree equations can be
so solved and consequently founds the field of GROUP
THEORY.
1821
French mathematician AUGUSTIN-LOUIS CAUCHY
(1789–1857) develops the notion of a LIMIT as an
attempt to place CALCULUS on sound mathematical
footing. This idea is later refined by German scholar
KARL THEODOR WILHELM WEIERSTRASS (1815–97).
1822
French mathematician JEAN BAPTISTE JOSEPH FOURIER
(1768–1830) publishes a treatise on the theory of heat
and develops the notion of a FOURIER SERIES.
1829
Russian
mathematician
NIKOLAI
IVANOVICH
LOBACHEVSKY (1792–1856) and Hungarian mathematician JÁNOS BOLYAI (1802–60) independently discover NON-EUCLIDEAN GEOMETRY.
1843
SIR WILLIAM ROWAN HAMILTON (1805–65) discovers
QUATERNIONS. Two years later ARTHUR CAYLEY
(1821–95) discovers octonians.
1844
JOSEPH LIOUVILLE (1809–82) discovers the first example of a TRANSCENDENTAL NUMBER.
1854
British scholar GEORGE BOOLE (1815–64) establishes
the field of symbolic logic with his development of
BOOLEAN ALGEBRA.
German mathematician GEORG FRIEDRICH BERNHARD
RIEMANN (1826–66) offers a universal approach to
geometry. He discovers SPHERICAL GEOMETRY. He later
makes significant advances in the theory of numbers
and the study of PRIME numbers.
1858
AUGUST FERDINAND MÖBIUS (1790–1868) and Johann
Benedict Listing independently discover the MÖBIUS
BAND.
German mathematician JULIUS WILHELM RICHARD
DEDEKIND (1831–1916) suggests the notion of a
DEDEKIND CUT as a means to properly define the REAL
NUMBERS.
CAYLEY introduces the notion of a MATRIX to the study
of algebra.
1872
FELIX CHRISTIAN KLEIN (1849–1925) unifies the fields
of geometry with his “Erlanger program.” He also discovers the KLEIN BOTTLE.
1873
WILLIAM SHANKS (1812–82) computes, by hand, the
first 607 decimals of π. He is correct up to the 527th
place.
Appendix I 543