Maclaurin, Colin (1698–1746) British Calculus Born
in February 1698 (his exact birth date is not known),
in Kilmodan, Scotland, scholar Colin Maclaurin is con-
sidered the foremost British mathematician of the gen-
eration that followed S
IR
I
SAAC
N
EWTON
. In his two
famous texts Geometrica organica (Organic geometry)
of 1720, and Treatise of Fluxions of 1742, Maclaurin
developed and extended the subject of
CALCULUS
and
offered many original results. The famous series that
bears his name, however, is a special case of the work
of B
ROOK
T
AYLOR
(1685–1731), as Maclaurin appro-
priately acknowledged. He also wrote an influential
elementary textbook, A Treatise on Algebra, on the
application of algebra to geometry.
Orphaned at age 10, Maclaurin entered the Univer-
sity of Glasgow in 1709, which, at the time, was
deemed an acceptable alternative to a secondary school
education. There he studied the works of E
UCLID
,
which sparked in him a passion for mathematics. At
age 14 he completed the basic degree of master and
gave a public lecture on Newton’s theory of gravita-
tion, exhibiting a level of scientific knowledge compa-
rable with that of scholars of the day.
In 1717 Maclaurin was appointed professor of
mathematics at Marischal College in the University of
Aberdeen. This position provided him the opportunity
to travel to London in 1719, where he met S
IR
I
SAAC
N
EWTON
(1642–1727) and continued his studies in
mathematics and physics. Maclaurin’s work was well
received, and he was elected a fellow of the R
OYAL
S
OCIETY
that same year. Two years later he was also
awarded the grand prize from the French Académie des
Sciences for his work on the impact of bodies. At the
same time, he had written and published his famous
treatise Geometrica organica, which garnered him con-
siderable regard as a fine scholar in geometry.
In an attempt to settle the criticisms of Newton’s
newly developed calculus, Maclaurin published his own
account of the theory. His lengthy Treatise of Fluxions
appealed to geometry to bring rigor to Newton’s use of
FLUXION
s and fluents. He also developed the theory of
infinite
SERIES
, produced new tests of convergence, and
discussed
POWER SERIES
expansions of functions (T
AYLOR
SERIES
). This work was very influential, and in honor of
his achievement, his name remains attached to the series
he considered—the Maclaurin
SERIES
. Maclaurin also
provided many new applications of calculus in this work.
Maclaurin received a second prize from the
Académie des Sciences in 1740, this time for his study
of tides. That the prize was also awarded to L
EONHARD
E
ULER
(1707–83) and Daniel Bernoulli (1707–82) of
the B
ERNOULLI FAMILY
that same year shows that
Maclaurin was regarded as an equal with the top two
mathematicians of his day. He died in Edinburgh, Scot-
land, on January 14, 1746.
Maclaurin series See T
AYLOR SERIES
.
Madhava of Sangamagramma (ca. 1350–1425) Indian
Trigonometry, Astronomy Born near Cochin in south-
western India, Madhava is remembered for his brilliant
discoveries in
ANALYSIS
. He computed, for example, the
equivalent of the T
AYLOR SERIES
of the sine, cosine, and
324
M