Andrew Victor Sutherland 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, mathematical structure, structure, space, Mathematica ...

and Principal Research Scientist at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private Land-grant university, land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern t ...

. His research focuses on computational aspects of

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...

and

arithmetic geometry In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties. ...

. He is known for his contributions to several projects involving large scale computations, including the Polymath project on bounded gaps between primes, the L-functions and Modular Forms Database, the sums of three cubes project, and the computation and classification of Sato-Tate distributions.

Education and career

Sutherland earned a bachelor's degree in mathematics from MIT in 1990. Following an entrepreneurial career in the software industry he returned to MIT and completed his doctoral degree in mathematics in 2007 under the supervision of

Michael Sipser Michael Fredric Sipser (born September 17, 1954) is an American theoretical computer scientist who has made early contributions to computational complexity theory. He is a professor of applied mathematics and was the Dean of Science at the Massa ...

and Ronald Rivest, winning the George M. Sprowls prize for this thesis. He joined the MIT mathematics department as a Research Scientist in 2009, and was promoted to Principal Research Scientist in 2011. He is one of the principal investigators in the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation, a large multi-university collaboration involving

Boston University Boston University (BU) is a private research university in Boston, Massachusetts. The university is nonsectarian, but has a historical affiliation with the United Methodist Church. It was founded in 1839 by Methodists with its original c ...

Brown Brown is a color. It can be considered a composite color, but it is mainly a darker shade of orange. In the CMYK color model used in printing or painting, brown is usually made by combining the colors orange and black. In the RGB color model use ...

, Harvard, MIT, and

Dartmouth College Dartmouth College (; ) is a private research university in Hanover, New Hampshire. Established in 1769 by Eleazar Wheelock, it is one of the nine colonial colleges chartered before the American Revolution. Although founded to educate Native ...

, and he currently serves as an Associate Editor of

Mathematics of Computation ''Mathematics of Computation'' is a bimonthly mathematics journal focused on computational mathematics. It was established in 1943 as ''Mathematical Tables and other Aids to Computation'', obtaining its current name in 1960. Articles older than f ...

, Editor in Chief of Research in Number Theory, Managing Editor of the L-functions and Modular Forms Database, and President of the Number Theory Foundation.

Contributions

Sutherland has developed or improved several methods for

counting points on elliptic curves An important aspect in the study of elliptic curves is devising effective ways of counting points on the curve. There have been several approaches to do so, and the algorithms devised have proved to be useful tools in the study of various fields s ...

and

hyperelliptic curve In algebraic geometry, a hyperelliptic curve is an algebraic curve of genus ''g'' > 1, given by an equation of the form y^2 + h(x)y = f(x) where ''f''(''x'') is a polynomial of degree ''n'' = 2''g'' + 1 > 4 or ''n'' = 2''g'' + 2 > 4 with ''n'' dis ...

s, that have applications to

elliptic curve cryptography Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide e ...

hyperelliptic curve cryptography Hyperelliptic curve cryptography is similar to elliptic curve cryptography (ECC) insofar as the Jacobian of a hyperelliptic curve is an abelian group in which to do arithmetic, just as we use the group of points on an elliptic curve in ECC. Defin ...

elliptic curve primality proving In mathematics, elliptic curve primality testing techniques, or elliptic curve primality proving (ECPP), are among the quickest and most widely used methods in primality proving. It is an idea put forward by Shafi Goldwasser and Joe Kilian in 1986 ...

, and the computation of

L-functions In mathematics, an ''L''-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An ''L''-series is a Dirichlet series, usually convergent on a half-plane, that may give ...

. These include improvements to the Schoof–Elkies–Atkin algorithm that led to new point-counting records, and average polynomial-time algorithms for computing zeta functions of hyperelliptic curves over

finite fields In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subt ...

, developed jointly with David Harvey. Much of Sutherland's research involves the application of fast point-counting algorithms to numerically investigate generalizations of the Sato-Tate conjecture regarding the distribution of point counts for a curve (or

abelian variety In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functi ...

) defined over the rational numbers (or a

number field In mathematics, an algebraic number field (or simply number field) is an extension field K of the field of rational numbers such that the field extension K / \mathbb has finite degree (and hence is an algebraic field extension). Thus K is a ...

) when reduced modulo prime numbers of increasing size.. It is conjectured that these distributions can be described by

random matrix In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathemat ...

models using a "Sato-Tate group" associated to the curve by a construction of Serre. In 2012 Francesc Fite, Kiran Kedlaya, Victor Rotger and Sutherland classified the Sato-Tate groups that arise for genus 2 curves and abelian varieties of dimension 2, and in 2019 Fite, Kedlaya, and Sutherland announced a similar classification to abelian varieties of dimension 3. In the process of studying these classifications, Sutherland compiled several large data sets of curves and then worked with Andrew Booker and others to compute their

and incorporate them into the L-functions and Modular Forms Database. More recently, Booker and Sutherland resolved Mordell's question regarding the representation of 3 as a sum of three cubes.

Recognition

Sutherland was named to the 2021 class of fellows of the American Mathematical Society "for contributions to number theory, both on the theoretical and computational aspects of the subject". He was selected to deliver the Arf Lecture in 2022.

Selected publications

* * * * *

References

External links

Andrew Sutherland's profile
at MIT
Andrew Sutherland's profile
on

MathSciNet MathSciNet is a searchable online bibliographic database created by the American Mathematical Society in 1996. It contains all of the contents of the journal '' Mathematical Reviews'' (MR) since 1940 along with an extensive author database, links ...

Andrew Sutherland's profile
on

zbMath zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructur ...

Andrew Sutherland's profile
on

Google Scholar Google Scholar is a freely accessible web search engine that indexes the full text or metadata of scholarly literature across an array of publishing formats and disciplines. Released in beta in November 2004, the Google Scholar index includes p ...

Andrew Sutherland's preprints
on

arXiv arXiv (pronounced " archive"—the X represents the Greek letter chi ⟨χ⟩) is an open-access repository of electronic preprints and postprints (known as e-prints) approved for posting after moderation, but not peer review. It consists o ...

{{DEFAULTSORT:Sutherland, Andrew Year of birth missing (living people) Living people 21st-century American mathematicians Number theorists Massachusetts Institute of Technology School of Science alumni Massachusetts Institute of Technology School of Science faculty Fellows of the American Mathematical Society