(These claims can be proved by making use of the
DIS
-
TANCE FORMULA
to establish that the distance between
the centers of two touching circles equals the sum of
the radii of the two circles.)
Fermat, Pierre de (1601–1665) French Number the-
ory, Calculus, Probability theory Born on August 17,
1601, in Beaumont-de-Lomagne, France, Pierre de Fer-
mat is remembered as a leading mathematician in the
first half of the 17th century, recognized for his founding
work in the theory of numbers. Fermat is also responsi-
ble for some pioneering work in
CALCULUS
and the the-
ory of tangents to curves,
PROBABILITY
theory, and
analytic
GEOMETRY
. His 1679 piece Isagoge ad locos
planos et solidos (On the plane and solid locus), pub-
lished posthumously, foreshadowed the work of R
ENÉ
D
ESCARTES
(1596–1650) on the application of algebra to
geometry, allowing him to define algebraically important
curves such as the
HYPERBOLA
and the
PARABOLA
. In
optics, he is acknowledged as the first scholar to formu-
late the “fundamental property of least time,” stating
that light always follows the shortest paths. Perhaps
most notably, Fermat is remembered for the enigmatic
comment he scribed in the margin of one of his reading
books claiming to have solved a novel problem in num-
ber theory. Search for a solution to this problem (if not
the one Fermat had in mind) spurred three centuries of
important and spirited research in mathematics. F
ER
-
MAT
’
S LAST THEOREM
was finally resolved in 1994.
Fermat received a bachelor’s degree in civil law
from the University of Orléans in 1631 and began
work as a lawyer for the local parliament of Toulouse
that same year. He followed this career path through-
out his entire life—accepting a position as a criminal
court judge in 1638 and, finally, the high position of
king’s counselor in 1648. Fermat’s work in mathemat-
ics was an outside interest.
Fermat first developed a passion for reading and
“restoring” classic Greek texts. This meant completing
the mathematics of any passages that were missing
from the records that survived from ancient times. His
work on the text Plane loci by A
POLLONIUS OF
P
ERGA
(ca. 262–190
B
.
C
.
E
.) garnered the attention of the
mathematics community at the time, not only for the
restoration work itself, but also for the new geometric
methods Fermat had devised for computing tangents to
curves and solving maxima/minima problems. Fermat
developed a correspondence with French monk M
ARIN
M
ERSENNE
(1588–1648), who served the role of dis-
persing mathematical information to the notable schol-
ars of the time. Despite the attention Fermat received,
he did not seek fame by publishing any of his work.
(He published one small piece in his life, which he did
anonymously.) Fermat shared his discoveries and
results with Mersenne and other scholars, but not his
methods for obtaining them. This both inspired and
frustrated mathematicians at the time.
In 1654 notable scholar B
LAISE
P
ASCAL
(1623–62)
wrote to Fermat with some mathematical questions
about gambling and games of chance. The correspon-
dence that ensued led to the joint development of a
new mathematical theory of probability. Fermat is
today considered one of the founders of the field. How-
ever, Fermat had developed a great interest in the the-
ory of numbers, in particular, the properties of whole
numbers. This topic was of little interest to mathemati-
cians at the time—perhaps because of its lack of appar-
ent immediate application—but Fermat attempted to
spark interest in the subject by posing challenging ques-
tions to his contemporaries. He asked scholars to
prove, for instance, that the equation x2+ 2 = y3has
only one positive integer solution. His colleagues, how-
ever, regarded questions such as these as too specific to
be of serious concern and often dismissed then. Fermat,
on the other hand, realized that understanding the
solutions to such specific questions provides a gateway
to great insight on the very general and mysterious
properties of whole numbers. It was not until Fermat’s
son Samuel published Fermat’s annotated copy of the
Arithmetica by the classic scholar D
IOPHANTUS OF
A
LEXANDRIA
(ca. 200–284
C
.
E
.)—the text containing
the famous marginal note—that interest in number the-
ory was revived and Fermat’s brilliant work on the
topic was fully recognized.
Fermat died in Castres, France on January 12,
1665. The claim posed in the note scrawled in the mar-
gin of Arithmetica is called Fermat’s last theorem. It
inspired over three centuries of intense mathematical
research in the field of
NUMBER THEORY
.
See also
MAXIMUM
/
MINIMUM
.
Fermat’s last theorem Since ancient times, scholars
have been aware of many, in fact infinitely many, dif-
ferent integer solutions to the equation x2+ y2= z2.
Fermat’s last theorem 189