1767
German mathematician J
OHANN
H
EINRICH
L
AMBERT
(1728–77) proves that πis irrational.
1795
France adopts the metric system.
John Playfair (1748–1819) publishes an equivalent
form of the famous
PARALLEL POSTULATE
, today known
as P
LAYFAIR
’
S AXIOM
.
1797
C
ARL
F
RIEDRICH
G
AUSS
(1777–1855) proves the
FUN
-
DAMENTAL THEOREM OF ALGEBRA
. Throughout his life,
Gauss, among many accomplishments, derives the
LEAST SQUARES METHOD
, classifies the
CONSTRUCTIBLE
regular polygons, and makes fundamental contribu-
tions to
NUMBER THEORY
,
GEOMETRY
,
STATISTICS
,
mathematical physics, and astronomy.
1799
Norwegian surveyor Casper Wessel (1745–1818)
publishes the equivalent of an A
RGAND DIAGRAM
as a
means for representing
COMPLEX NUMBERS
. French
bookkeeper and mathematician J
EAN
R
OBERT
A
RGAND
(1768–1822) develops the same method in
1806.
1812
British mathematician and inventor C
HARLES
B
ABBAGE
(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 N
IELS
H
ENRIK
A
BEL
(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 mathe-
matician É
VARISTE
G
ALOIS
(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 A
UGUSTIN
-L
OUIS
C
AUCHY
(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
K
ARL
T
HEODOR
W
ILHELM
W
EIERSTRASS
(1815–97).
1822
French mathematician J
EAN
B
APTISTE
J
OSEPH
F
OURIER
(1768–1830) publishes a treatise on the theory of heat
and develops the notion of a F
OURIER SERIES
.
1829
Russian mathematician N
IKOLAI
I
VANOVICH
L
OBACHEVSKY
(1792–1856) and Hungarian mathe-
matician J
ÁNOS
B
OLYAI
(1802–60) independently dis-
cover
NON
-E
UCLIDEAN GEOMETRY
.
1843
S
IR
W
ILLIAM
R
OWAN
H
AMILTON
(1805–65) discovers
QUATERNIONS
. Two years later A
RTHUR
C
AYLEY
(1821–95) discovers octonians.
1844
J
OSEPH
L
IOUVILLE
(1809–82) discovers the first exam-
ple of a
TRANSCENDENTAL NUMBER
.
1854
British scholar G
EORGE
B
OOLE
(1815–64) establishes
the field of symbolic logic with his development of
B
OOLEAN ALGEBRA
.
German mathematician G
EORG
F
RIEDRICH
B
ERNHARD
R
IEMANN
(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
A
UGUST
F
ERDINAND
M
ÖBIUS
(1790–1868) and Johann
Benedict Listing independently discover the M
ÖBIUS
BAND
.
German mathematician J
ULIUS
W
ILHELM
R
ICHARD
D
EDEKIND
(1831–1916) suggests the notion of a
D
EDEKIND CUT
as a means to properly define the
REAL
NUMBERS
.
CAYLEY
introduces the notion of a
MATRIX
to the study
of algebra.
1872
F
ELIX
C
HRISTIAN
K
LEIN
(1849–1925) unifies the fields
of geometry with his “Erlanger program.” He also dis-
covers the K
LEIN BOTTLE
.
1873
W
ILLIAM
S
HANKS
(1812–82) computes, by hand, the
first 607 decimals of π. He is correct up to the 527th
place.
Appendix I 543