**Kenneth Alan "Ken" Ribet** (born June 28, 1948) is an

AmericanThe United States of America is a federal constitutional republic comprising fifty states and a federal district...

mathematicianA 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, BerkeleyThe 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 theoryAlgebraic 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 geometryAlgebraic 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 WilesSir 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 theoremIn 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 SerreJean-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 curveIn 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 theoremIn 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 numberIn 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 SchoolFar 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 degreeA 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 degreeA 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 UniversityBrown 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, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...

from

Harvard UniversityHarvard 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 SciencesThe 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 SciencesThe 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 PrizeThe 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.

## External links