Kenneth Alan Ribet
Encyclopedia
Kenneth Alan "Ken" Ribet (born June 28, 1948) is an American
mathematician
, currently a professor of mathematics at the University of California, Berkeley
. His mathematical interests include algebraic number theory
and algebraic geometry
.
He is credited with paving the way towards Andrew Wiles
's proof of Fermat's last theorem
. Ribet proved that the epsilon conjecture formulated by Jean-Pierre Serre
was indeed true, and thereby proved that Fermat's Last Theorem would follow from the Taniyama-Shimura conjecture. Crucially it also followed that the full conjecture was not needed, but a special case, that of semistable elliptic curve
s, sufficed. An earlier theorem of Ribet's, the Herbrand–Ribet theorem
, the converse to Herbrand's theorem on the divisibility properties of Bernoulli number
s, is also related to Fermat's Last Theorem.
As a student at Far Rockaway High School
, he was on a competitive mathematics team, but his first field of study was chemistry.
He earned his bachelor's degree
and master's degree
from Brown University
in 1969, and his Ph.D.
from Harvard University
in 1973. In 1998, he received an honorary doctorate from Brown University. He was elected to the American Academy of Arts and Sciences
in 1997 and the National Academy of Sciences
in 2000.
He received the Fermat Prize
in 1989.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, currently a professor of mathematics at the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
. His mathematical interests include algebraic number theory
Algebraic number theory
Algebraic number theory is a major branch of number theory which studies algebraic structures related to algebraic integers. This is generally accomplished by considering a ring of algebraic integers O in an algebraic number field K/Q, and studying their algebraic properties such as factorization,...
and algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
.
He is credited with paving the way towards Andrew Wiles
Andrew Wiles
Sir Andrew John Wiles KBE FRS is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory...
's proof of Fermat's last theorem
Fermat's Last Theorem
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....
. Ribet proved that the epsilon conjecture formulated by Jean-Pierre Serre
Jean-Pierre Serre
Jean-Pierre Serre is a French mathematician. He has made contributions in the fields of algebraic geometry, number theory, and topology.-Early years:...
was indeed true, and thereby proved that Fermat's Last Theorem would follow from the Taniyama-Shimura conjecture. Crucially it also followed that the full conjecture was not needed, but a special case, that of semistable elliptic curve
Semistable elliptic curve
In algebraic geometry, a semistable abelian variety is an abelian variety defined over a global or local field, which is characterized by how it reduces at the primes of the field....
s, sufficed. An earlier theorem of Ribet's, the Herbrand–Ribet theorem
Herbrand–Ribet theorem
In mathematics, the Herbrand–Ribet theorem is a result on the class number of certain number fields. It is a strengthening of Ernst Kummer's theorem to the effect that the prime p divides the class number of the cyclotomic field of p-th roots of unity if and only if p divides the numerator of the...
, the converse to Herbrand's theorem on the divisibility properties of Bernoulli number
Bernoulli number
In mathematics, the Bernoulli numbers Bn are a sequence of rational numbers with deep connections to number theory. They are closely related to the values of the Riemann zeta function at negative integers....
s, is also related to Fermat's Last Theorem.
As a student at Far Rockaway High School
Far Rockaway High School
Far Rockaway High School, a public high school in the public school system of New York City, was located on Bay 25 Street in Far Rockaway in the borough of Queens, as part of the New York City Department of Education. The school was founded in 1897, with Sanford J. Ellsworth as principal for over...
, he was on a competitive mathematics team, but his first field of study was chemistry.
He earned his bachelor's degree
Bachelor's degree
A bachelor's degree is usually an academic degree awarded for an undergraduate course or major that generally lasts for three or four years, but can range anywhere from two to six years depending on the region of the world...
and master's degree
Master's degree
A master's is an academic degree granted to individuals who have undergone study demonstrating a mastery or high-order overview of a specific field of study or area of professional practice...
from Brown University
Brown University
Brown University is a private, Ivy League university located in Providence, Rhode Island, United States. Founded in 1764 prior to American independence from the British Empire as the College in the English Colony of Rhode Island and Providence Plantations early in the reign of King George III ,...
in 1969, and his Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
from Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
in 1973. In 1998, he received an honorary doctorate from Brown University. He was elected to the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
in 1997 and the National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
in 2000.
He received the Fermat Prize
Fermat Prize
The Fermat prize of mathematical research rewards research works in fields where the contributions of Pierre de Fermat have been decisive:* Statements of variational principles* Foundations of probability and analytic geometry* Number theory....
in 1989.