1629
French mathematician P
IERRE DE
F
ERMAT
(1601–65)
uses algebra to solve geometric problems but does not
publish his results. French mathematician and philoso-
pher R
ENÉ
D
ESCARTES
(1596–1650) later developed
similar techniques and is today credited as the founder
of this approach.
1635
Italian mathematician B
ONAVENTURA
C
AVALIERI
(1598–1647) introduces a method of indivisibles for
comparing volumes (a precursor to the methods of
INTEGRAL CALCULUS
) and C
AVALIERI
’
S PRINCIPLE
.
ca. 1637
FERMAT
introduces modern
NUMBER THEORY
. He
writes a problem in the margin of a text that confounds
mathematicians for centuries. F
ERMAT
’
S LAST THEOREM
was finally solved by A
NDREW
W
ILES
in 1994.
1639
French mathematician G
IRARD
D
ESARGUES
(1591–1661)
publishes a treatise on his newly discovered
PROJEC
-
TIVE GEOMETRY
. The work is essentially ignored for
200 years.
1654
Mathematician B
LAISE
P
ASCAL
(1623–62) begins a cor-
respondence with
FERMAT
about questions of games of
chance. Through five consecutive letters, they together
create the theory of
PROBABILITY
.
1662
The R
OYAL
S
OCIETY
of London is established. British
mathematician L
ORD
W
ILLIAM
B
ROUNCKER
(1620–84)
is elected as its first president.
1666
S
IR
I
SAAC
N
EWTON
(1642–1727) develops
DIFFEREN
-
TIAL
and
INTEGRAL CALCULUS
but does not publish his
results until 1711.
1673
German mathematician G
OTTFRIED
W
ILHELM
L
EIBNIZ
(1646–1716) develops
DIFFERENTIAL
and
INTEGRAL
CALCULUS
independently of
NEWTON
. Leibniz begins
publishing his results in 1684, and Newton accuses him
of plagiarism. A bitter dispute between the two men
ensues, lasting four decades.
1687
Under the urging of astronomer Edmund Halley, New-
ton publishes Principia, today considered one of the
greatest scientific works of all time. Newton outlines
his laws of motion and the
INVERSE SQUARE LAW
for
gravitation.
1693
Halley compiles the first set of
LIFE TABLES
and makes
use of
STATISTICS
to analyze birth and death rates.
1696
French scholar M
ARQUIS DE
G
UILLAUME
F
RANÇOIS
A
NTOINE L
’H
ÔPITAL
(1661–1704) publishes the first
textbook on
CALCULUS
.
1703
NEWTON
is elected president of the
ROYAL SOCIETY
of
London. Eight years later, after an official investiga-
tion, the society concludes that Newton, not
LEIBNIZ
, is
the true inventor of
CALCULUS
. It is later revealed that
Newton, as president, wrote the final proclamation.
The verdict is not considered valid today.
1718
French mathematician A
BRAHAM
D
E
M
OIVRE
(1667–1754) publishes Doctrine of Chances, the most
advanced text on the theory of
PROBABILITY
of its time.
De Moivre later develops the result today known as
S
TIRLING
’
S FORMULA
.
1736
Swiss mathematician L
EONHARD
E
ULER
(1707–83)
solves the
SEVEN BRIDGES OF
K
ÖNIGSBERG PROBLEM
,
thereby establishing the fields of
TOPOLOGY
and
GRAPH
THEORY
. Throughout his life Euler also discovers,
among many accomplishments, the number e, his
famous formula relating the trigonometric functions to
this number, specific values of the
ZETA FUNCTION
, and,
in geometry, the E
ULER LINE
. Euler also introduces the
notion of a
FUNCTION
and popularizes the use of the
symbol πfor the ratio of the circumference of a circle
to its diameter.
1742
C
HRISTIAN
G
OLDBACH
(1690–1764) writes to E
ULER
posing the problem that has since become known as
G
OLDBACH
’
S CONJECTURE
.
1748
M
ARIA
G
AËTANA
A
GNESI
(1718–99) publishes her two-
volume survey of elementary and advanced mathematics.
1750
Swiss mathematician G
ABRIEL
C
RAMER
(1704–52) pub-
lishes C
RAMER
’
S RULE
.
542 Appendix I