work in the field of mathematical physics, and over the
next six years they together produced three papers on
the topics of electricity and hydrodynamics. At the
advice of Bromhead, Green entered Cambridge Univer-
sity in 1833, at age 40, to start an undergraduate
degree in mathematics. Green published six more
papers after completing the program. He died on May
31, 1841, in Nottingham.
Gregory, David (1659–1708) British Calculus, Geom-
etry Born on June 3, 1659, in Aberdeen, Scotland,
David Gregory is remembered for his expository writ-
ings. In 1684 he published Exercitatio geometrica
(Exercises in geometry), outlining many of the results of
J
AMES
G
REGORY
, his uncle, on infinite
SERIES
. He also
published some of S
IR
I
SAAC
N
EWTON
’s results on
mathematics and astronomy, and he was the first to
teach the “modern” Newtonian theories at Cambridge.
In 1703 he issued the first-ever complete collection of
all of E
UCLID
’s works.
Gregory studied at Marischal College, part of the
University of Aberdeen, and accepted a professorship
of mathematics at the University of Edinburgh in 1683.
He lectured on the topics of mathematics, mechanics,
and hydrostatics. In 1691 he was elected Savilian Pro-
fessor at Oxford, the same year he was awarded mem-
bership to the R
OYAL
S
OCIETY
of London.
In 1702 Gregory published Astronomiae physicae
et geometricae elementa (Astronomical physics and ele-
ments of geometry), which was a popular account of
Newton’s work, and a year later, his edition of the col-
lected works of Euclid. Gregory strongly supported
Newton in the debate over whether it was he, or Ger-
man mathematician G
OTTFRIED
W
ILHELM
L
EIBNIZ
,
who had first discovered
CALCULUS
.
Gregory also completed his own work on the study
of series, and published work on the topic of optics. He
died on October 10, 1708, in Berkshire, England.
Not noted as an outstanding mathematician, Gre-
gory is remembered primarily for the role he played in
preserving the papers and recording the verbal commu-
nications passed to him by his uncle James Gregory
and by Sir Isaac Newton.
Gregory, James (1638–1675) British Calculus Born
in November 1638 (the exact date is not known), Scot-
tish mathematician James Gregory independently discov-
ered and explained important concepts in
CALCULUS
before the subject was later fully developed by founders
S
IR
I
SAAC
N
EWTON
and G
OTTFREID
W
ILHELM
L
EIBNIZ
.
Gregory was aware of the
FUNDAMENTAL THEOREM OF
CALCULUS
, was the first to distinguish between conver-
gent and divergent
SERIES
, and knew of T
AYLOR SERIES
40 years before B
ROOK
T
AYLOR
published his results. In
mathematics he is remembered, in particular, for the
series that bears his name. Outside of mathematics, Gre-
gory is best remembered for his theoretical description of
a revolutionary type of reflecting telescope.
Gregory was home-schooled in mathematics before
undertaking studies at Marischal College in Aberdeen.
He studied the mathematics of optics and in 1661 pub-
lished a text on the subject, Optica promota (The
advancement of optics), written in a purely mathemati-
cal style. Beginning with five postulates and 37 defini-
tions, Gregory developed the theory of reflection and
refraction of light in a systematic and rigorous manner,
culminating with the description of a new principle for
the construction of a telescope.
In 1664 Gregory traveled to Italy to stay at the
University of Padua to pursue interests in mathematics.
During this time Gregory developed the foundations of
“infinitesimal geometry,” the details of which he pub-
lished as Geometriae pars universalis (The universal
part of geometry). Today we would describe this book
as a systematic treatment of topics in calculus.
Gregory was the first to discuss the convergence
and divergence of series, work which led him in 1671
to the discovery of series expansions of functions. He
refrained from publishing his discoveries, however,
having heard a rumor that Newton may have already
developed similar results. (Actually Newton was not
aware of the key theorem needed to put this theory on
a sound footing and so was unable to develop the the-
ory.) Brook Taylor later discovered the same key
result and published his description of the topic in
1715.
Throughout his short life, Gregory maintained an
interest in astronomy. He died at the age of 36 in late
October 1675, shortly after suffering a stroke he
incurred while observing the moons of Jupiter with
some students. Gregory did not achieve fame as a
mathematician during his life. It is only in retrospect
that historians today realize the important influence he
had in helping Newton develop his ideas.
See also G
REGORY SERIES
.
240 Gregory, David