Hendrik Willem Lenstra Jr. (born 16 April 1949,

Zaandam Zaandam () is a city in the Provinces of the Netherlands, province of North Holland, Netherlands. It is the main city of the municipality of Zaanstad and received City rights in the Netherlands, city rights in 1811. It is located on the river Zaan ...

) is a Dutch

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 ...

Biography

Lenstra received his

doctorate A doctorate (from Latin ''doctor'', meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' licentia docendi'' ("licence to teach ...

from the

University of Amsterdam The University of Amsterdam (abbreviated as UvA, ) is a public university, public research university located in Amsterdam, Netherlands. Established in 1632 by municipal authorities, it is the fourth-oldest academic institution in the Netherlan ...

in 1977 and became a professor there in 1978. In 1987, he was appointed to the faculty of the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

; starting in 1998, he divided his time between Berkeley and the

University of Leiden Leiden University (abbreviated as ''LEI''; ) is a public research university in Leiden, Netherlands. Established in 1575 by William, Prince of Orange as a Protestant institution, it holds the distinction of being the oldest university in the Neth ...

, until 2003, when he retired from Berkeley to take a full-time position at Leiden. Three of his brothers,

Arjen Lenstra Arjen Klaas Lenstra (born 2 March 1956, in Groningen) is a Dutch mathematician, cryptographer and computational number theorist. He is a professor emeritus from the École Polytechnique Fédérale de Lausanne (EPFL) where he headed of the Labora ...

, Andries Lenstra, and Jan Karel Lenstra, are also mathematicians. Jan Karel Lenstra is the former director of the

Netherlands , Terminology of the Low Countries, informally Holland, is a country in Northwestern Europe, with Caribbean Netherlands, overseas territories in the Caribbean. It is the largest of the four constituent countries of the Kingdom of the Nether ...

Centrum Wiskunde & Informatica (CWI). Hendrik Lenstra was the Chairman of the Program Committee of the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

in 2010.

Scientific contributions

Lenstra has worked principally in

computational number theory In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithm ...

. He is well known for: * Co-discovering of the Lenstra–Lenstra–Lovász lattice basis reduction algorithm (in 1982); * Developing an

polynomial-time In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations p ...

algorithm for solving a feasibility

integer programming An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective ...

problem when the number of variables is fixed (in 1983); * Discovering the elliptic curve factorization method (in 1987); * Computing all solutions to the inverse Fermat equation (in 1992); * The Cohen-Lenstra heuristics - a set of precise conjectures about the structure of

class group In mathematics, the ideal class group (or class group) of an algebraic number field K is the quotient group J_K/P_K where J_K is the group of fractional ideals of the ring of integers of K, and P_K is its subgroup of principal ideals. The class ...

s of

quadratic field In algebraic number theory, a quadratic field is an algebraic number field of Degree of a field extension, degree two over \mathbf, the rational numbers. Every such quadratic field is some \mathbf(\sqrt) where d is a (uniquely defined) square-free ...

Awards and honors

In 1984, Lenstra became a member of the

Royal Netherlands Academy of Arts and Sciences The Royal Netherlands Academy of Arts and Sciences (, KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed in the Trippenhuis in Amsterdam. In addition to various advisory a ...

. He won the

Fulkerson Prize The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at e ...

in 1985 for his research using the

geometry of numbers Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice (group), lattice in \mathbb R^n, and the study of these lattices provides fundam ...

to solve integer programs with few variables in time polynomial in the number of constraints. He was awarded the Spinoza Prize in 1998, and on 24 April 2009 he was made a Knight of the

Order of the Netherlands Lion The Order of the Netherlands Lion, also known as the Order of the Lion of the Netherlands (, ) is a Dutch honours system, Dutch order of chivalry founded by William I of the Netherlands on 29 September 1815. The Order of the Netherlands Lion wa ...

. In 2009, he was awarded a Gauss Lecture by the

German Mathematical Society The German Mathematical Society (, DMV) is the main professional society of German mathematicians and represents German mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU). It was founded in ...

. In 2012, he became a fellow 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, ...

.List of Fellows of the American Mathematical Society
retrieved 2013-01-27.

Publications

* ''Euclidean Number Fields.'' Parts 1-3, Mathematical Intelligencer 1980 * with A. K. Lenstra: ''Algorithms in Number Theory.'' pp. 673–716, In Jan van Leeuwen (ed.): ''Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity.'' Elsevier and MIT Press 1990, , .
''Algorithms in Algebraic Number Theory.''
Bulletin of the AMS, vol. 26, 1992, pp. 211–244.
''Primality testing algorithms.''
Séminaire Bourbaki 1981. * with Peter Stevenhagen
''Artin reciprocity and Mersenne Primes.''
Nieuw Archief for Wiskunde 2000. * with Peter Stevenhagen: '' Chebotarev and his density theorem.'' Mathematical Intelligencer 1992 (Online at Lenstra's Homepage).
''Profinite Fibonacci Numbers'', December 2005, PDF

References

External links

* * , Homepage at the Leiden Mathematisch Instituut * {{DEFAULTSORT:Lenstra, Hendrik 1949 births Living people 20th-century Dutch mathematicians 21st-century Dutch mathematicians Members of the Royal Netherlands Academy of Arts and Sciences Number theorists Spinoza Prize winners University of Amsterdam alumni Academic staff of the University of Amsterdam Academic staff of Leiden University University of California, Berkeley College of Letters and Science faculty Fellows of the American Mathematical Society Dutch expatriates in the United States People from Zaanstad