(These claims can be proved by making use of the DISTANCE 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 theory, Calculus, Probability theory Born on August 17,
1601, in Beaumont-de-Lomagne, France, Pierre de Fermat 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 responsible for some pioneering work in CALCULUS and the theory of tangents to curves, PROBABILITY theory, and
analytic GEOMETRY. His 1679 piece Isagoge ad locos
planos et solidos (On the plane and solid locus), published posthumously, foreshadowed the work of RENÉ
DESCARTES (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 formulate 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 number 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. FERMAT’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 throughout 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 mathematics 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 APOLLONIUS OF PERGA
(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 MARIN
MERSENNE (1588–1648), who served the role of dispersing mathematical information to the notable scholars 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 BLAISE PASCAL (1623–62)
wrote to Fermat with some mathematical questions
about gambling and games of chance. The correspondence 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. However, Fermat had developed a great interest in the theory of numbers, in particular, the properties of whole
numbers. This topic was of little interest to mathematicians at the time—perhaps because of its lack of apparent immediate application—but Fermat attempted to
spark interest in the subject by posing challenging questions to his contemporaries. He asked scholars to
prove, for instance, that the equation x
2 + 2 = y
3 has
only one positive integer solution. His colleagues, however, 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 DIOPHANTUS OF
ALEXANDRIA (ca. 200–284 C.E.)—the text containing
the famous marginal note—that interest in number theory 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 margin 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, different integer solutions to the equation x
2 + y
2 = z
2 .
Fermat’s last theorem 189
the centers of two touching circles equals the sum of
the radii of the two circles.)
Fermat, Pierre de (1601–1665) French Number theory, Calculus, Probability theory Born on August 17,
1601, in Beaumont-de-Lomagne, France, Pierre de Fermat 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 responsible for some pioneering work in CALCULUS and the theory of tangents to curves, PROBABILITY theory, and
analytic GEOMETRY. His 1679 piece Isagoge ad locos
planos et solidos (On the plane and solid locus), published posthumously, foreshadowed the work of RENÉ
DESCARTES (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 formulate 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 number 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. FERMAT’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 throughout 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 mathematics 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 APOLLONIUS OF PERGA
(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 MARIN
MERSENNE (1588–1648), who served the role of dispersing mathematical information to the notable scholars 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 BLAISE PASCAL (1623–62)
wrote to Fermat with some mathematical questions
about gambling and games of chance. The correspondence 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. However, Fermat had developed a great interest in the theory of numbers, in particular, the properties of whole
numbers. This topic was of little interest to mathematicians at the time—perhaps because of its lack of apparent immediate application—but Fermat attempted to
spark interest in the subject by posing challenging questions to his contemporaries. He asked scholars to
prove, for instance, that the equation x
2 + 2 = y
3 has
only one positive integer solution. His colleagues, however, 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 DIOPHANTUS OF
ALEXANDRIA (ca. 200–284 C.E.)—the text containing
the famous marginal note—that interest in number theory 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 margin 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, different integer solutions to the equation x
2 + y
2 = z
2 .
Fermat’s last theorem 189