because many scholars in mathematics also like to refer
to zero as a whole number, and some also like to
regard any negative integer as a whole number. There is
no standard convention in place in this regard. It is cer-
tain, however, that no mathematician would regard a
number that is not an integer a whole number.
See also
NUMBER
;
NUMBER THEORY
.
Wiles, Andrew John (1953– ) British Algebraic
number theory Born on April 11, 1953, in Cam-
bridge, England, mathematician Andrew Wiles gar-
nered international fame in 1994 as the first person to
solve one of the most elusive and difficult mathemati-
cal problems of all time, F
ERMAT
’
S LAST THEOREM
.
This notorious problem, posed by French number the-
orist P
IERRE DE
F
ERMAT
(1601–65), states that the
equation xn+ yn= znhas no positive integer solutions
if nis an integer greater than 2. Finding a proof of
this apparently simple claim has proved to be an
extraordinarily difficult challenge, one that has frus-
trated professional and amateur mathematicians for
well over 300 years.
Ever since first reading of Fermat’s last theorem at
the age of 10, Wiles dreamed of solving it. As a young-
ster he first tried approaches that he thought Fermat
might have followed in thinking about the theorem
himself. This proved to be useless. At college, Wiles
studied the work of the great 18th- and 19th-century
scholars who had worked on the problem, hoping to
glean any insights as to how one might approach the
challenge. Pursuing mathematics further, Wiles entered
Clare College, Cambridge, and in 1980, was awarded a
Ph.D. in mathematics. In 1982 Wiles traveled to the
United States to take a professorship at Princeton Uni-
versity, New Jersey.
Although Wiles’s thesis and early research work
was not directly connected to solving Fermat’s last the-
orem, Wiles later learned of some important develop-
ments that connected the possible solution of the
problem with some new approaches in elliptic curve
theory, the topic of his thesis. Upon this news, Wiles
abandoned all unrelated research interests to focus
exclusively on solving the theorem. Working for 7 years
straight, essentially in seclusion, Wiles modified and
adapted newly developed advances in many disparate
fields to forge a path that would, hopefully, lead to a
solution to the problem. In 1993, amidst a flurry of
great media excitement, Wiles announced to the mathe-
matical community that he had succeeded. Subsequent
careful review of his work, however, revealed a subtle,
but damaging, error, and all was thought to be lost.
After another 18 months of concerted effort, with
the assistance of colleague Richard Taylor of Cam-
bridge University, Wiles managed to find a way to cir-
cumvent the error and produce, at long last, an
unflawed proof of the famous result. The proof of the
theorem appears in a 1995 volume of the Annals of
Mathematics. It represents one of the greatest intellec-
tual achievements of the 20th century.
Wiles won many awards for his achievement,
including the Wolf Prize in 1995, the Wolfskehl Prize in
1997, the American Mathematical Society Cole Prize in
1997, and the King Faisal Prize in 1998. Because he
was over the age limit of 40, Wiles did not receive a
F
IELDS
M
EDAL
for his work, but he was honored with a
silver plaque during the 1998 Fields Medal ceremony.
Wiles currently resides in Princeton, New Jersey.
Wiles, Andrew John 531