Kenneth Alan Ribet (; born June 28, 1948) is an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

working in

algebraic number theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...

and

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

. He is known for the

Herbrand–Ribet theorem In mathematics, the Herbrand–Ribet theorem is a result on the class group of certain number fields. It is a strengthening of Ernst Kummer's theorem to the effect that the prime ''p'' divides the ideal class group, class number of the cyclotomic f ...

and

Ribet's theorem Ribet's theorem (earlier called the epsilon conjecture or ε-conjecture) is part of number theory. It concerns properties of Galois representations associated with modular forms. It was proposed by Jean-Pierre Serre and proven by Ken Ribet. The ...

, which were key ingredients in the proof of

Fermat's Last Theorem In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been k ...

, as well as for his service as President of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

from 2017 to 2019. He is currently a professor of mathematics at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

Early life and education

Kenneth Ribet was born in

Brooklyn Brooklyn () is a borough of New York City, coextensive with Kings County, in the U.S. state of New York. Kings County is the most populous county in the State of New York, and the second-most densely populated county in the United States, be ...

New York New York most commonly refers to: * New York City, the most populous city in the United States, located in the state of New York * New York (state), a state in the northeastern United States New York may also refer to: Film and television * '' ...

to parents David Ribet and Pearl Ribet, both Jewish, on June 28, 1948. As a student at

Far Rockaway High School Far Rockaway High School was a public high school in New York City, at 821 Bay 25th Street in Far Rockaway in the borough of Queens. It operated from 1897 to 2011. Its alumni include three Nobel Prize laureates and convicted fraudster Bernard M ...

, Ribet was on a competitive mathematics team, but his first field of study was

chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...

. Ribet earned his

bachelor's degree A bachelor's degree (from Middle Latin ''baccalaureus'') or baccalaureate (from Modern Latin ''baccalaureatus'') is an undergraduate academic degree awarded by colleges and universities upon completion of a course of study lasting three to six ...

and

master's degree A master's degree (from Latin ) is an academic degree awarded by universities or colleges upon completion of a course of study demonstrating mastery or a high-order overview of a specific field of study or area of professional practice.

from

Brown University Brown University is a private research university in Providence, Rhode Island. Brown is the seventh-oldest institution of higher education in the United States, founded in 1764 as the College in the English Colony of Rhode Island and Providenc ...

in 1969. In 1973, Ribet received his Ph.D. from

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

under the supervision of

John Tate John Tate may refer to: * John Tate (mathematician) (1925–2019), American mathematician * John Torrence Tate Sr. (1889–1950), American physicist * John Tate (Australian politician) (1895–1977) * John Tate (actor) (1915–1979), Australian act ...

Career

After receiving his doctoral degree, Ribet taught at

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

for three years before spending two years doing research in Paris. In 1978, Ribet joined the Department of Mathematics at the

, where he served three separate terms as supervisor of the department's graduate program, supervisor of the department's undergraduate program, and supervisor of the department's development. Ribet has served as an editor for several mathematics journals, a book series editor for the

Cambridge University Press Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing hou ...

, and a book series editor for

Springer Springer or springers may refer to: Publishers * Springer Science+Business Media, aka Springer International Publishing, a worldwide publishing group founded in 1842 in Germany formerly known as Springer-Verlag. ** Springer Nature, a multinationa ...

. He also served on the United States National Committee for Mathematics, representing the United States at the

International Mathematical Union The International Mathematical Union (IMU) is an international non-governmental organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Science Council (ISC) and supports ...

, and was the Chair of the Mathematics section of the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

. From February 1, 2017 to January 31, 2019, Ribet was President of the American Mathematical Society.

Research

Ribet's contributions in number theory and algebraic geometry were described by Benedict Gross and Barry Mazur as being "key to our understanding of the connections between the theory of modular forms and the ℓ-adic representations of the

absolute Galois group In mathematics, the absolute Galois group ''GK'' of a field ''K'' is the Galois group of ''K''sep over ''K'', where ''K''sep is a separable closure of ''K''. Alternatively it is the group of all automorphisms of the algebraic closure of ''K'' tha ...

of the field of rational numbers." Ribet is credited with paving the way towards

Andrew Wiles Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specializing in number theory. He is best known for proving Fermat's Last Theorem, for which he was awar ...

's proof of

. In 1986, Ribet proved that the ''

epsilon conjecture Epsilon (, ; uppercase , lowercase or lunate ; el, έψιλον) is the fifth letter of the Greek alphabet, corresponding phonetically to a mid front unrounded vowel or . In the system of Greek numerals it also has the value five. It was der ...

'' formulated by

Jean-Pierre Serre Jean-Pierre Serre (; born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the ina ...

was 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 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. For an abelian variety A defined over a field F with ring of intege ...

s, sufficed. An earlier theorem of Ribet's, the

, is the converse to Herbrand's theorem on the divisibility properties of

Bernoulli number In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in analysis. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, ...

s and is also related to Fermat's Last Theorem.

Awards and honors

Ribet received the

Fermat Prize The Fermat prize of mathematical research biennially 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 * Numb ...

in 1989 jointly with Abbas Bahri. He was elected to the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...

in 1997 and the National Academy of Sciences in 2000. In 2012, he became a Fellow of the

. In 2017, Ribet received the

Brouwer Medal The Brouwer Medal is a triennial award presented by the Royal Dutch Mathematical Society and the Royal Netherlands Academy of Sciences. The Brouwer Metal gets its name from Dutch mathematician L. E. J. Brouwer and is the Netherlands’ most prestigi ...

. In 1988, Ribet was inducted as a vigneron d'honneur by the Jurade de

Saint-Émilion Saint-Émilion (; Gascon: ''Sent Milion'') is a commune in the Gironde department in Nouvelle-Aquitaine in southwestern France. In 2016, it had a population of 1,938. In the heart of the country of ''Libournais'' (the area around Libourne), i ...

. In 1998, Ribet received an honorary doctorate from Brown University.

Personal life

Ribet is married to statistician Lisa Goldberg.

References

External links

*
Ken Ribet's webpageKen Ribet's faculty page at UC Berkeley
*
Ken Ribet's Author Profile on MathSciNet
{{DEFAULTSORT:Ribet, Kenneth Alan Living people Arithmetic geometers Members of the United States National Academy of Sciences Fellows of the American Mathematical Society 20th-century American mathematicians 21st-century American mathematicians Brown University alumni Harvard University alumni University of California, Berkeley faculty Far Rockaway High School alumni 1948 births Fermat's Last Theorem Presidents of the American Mathematical Society Mathematicians from New York (state)