Hendrik Willem Lenstra Jr. (born 16 April 1949,
Zaandam
Zaandam () is a city in the province of North Holland, Netherlands. It is the main city of the municipality of Zaanstad, and received city rights in 1811. It is located on the river Zaan, just north of Amsterdam.
The statistical district Zaand ...
) 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, structure, space, models, and change.
History
On ...
.
Biography
Lenstra received his
doctorate
A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism ''li ...
from the
University of Amsterdam
The University of Amsterdam (abbreviated as UvA, nl, Universiteit van Amsterdam) is a public research university located in Amsterdam, Netherlands. The UvA is one of two large, publicly funded research universities in the city, the other being ...
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 land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...
; starting in 1998, he divided his time between Berkeley and the
University of Leiden
Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William, Prince of Orange, as a reward to the city of Le ...
, 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 currently a professor at the École Polytechnique Fédérale de Lausanne (EPFL) where he heads of the Laborator ...
, Andries Lenstra, and
Jan Karel Lenstra, are also mathematicians. Jan Karel Lenstra is the former director of the
Netherlands
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Centrum Wiskunde & Informatica
The (abbr. CWI; English: "National Research Institute for Mathematics and Computer Science") is a research centre in the field of mathematics and theoretical computer science. It is part of the institutes organization of the Dutch Research Co ...
(CWI). Hendrik Lenstra was the Chairman of the Program Committee of the
International Congress of Mathematicians 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
The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and László Lovász in 1982. Given a basis \mathbf = \ with ''n''-dimensional int ...
(in 1982);
* Developing an polynomial-time 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 number theory, the ideal class group (or class group) of an algebraic number field is the quotient group where is the group of fractional ideals of the ring of integers of , and is its subgroup of principal ideals. The class group is a mea ...
s of
quadratic field
In algebraic number theory, a quadratic field is an algebraic number field of degree two over \mathbf, the rational numbers.
Every such quadratic field is some \mathbf(\sqrt) where d is a (uniquely defined) square-free integer different from 0 a ...
s.
Awards and honors
In 1984 Lenstra became member of the
Royal Netherlands Academy of Arts and Sciences. 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 in \mathbb R^n, and the study of these lattices provides fundamental informatio ...
to solve
integer programs with few variables in time polynomial in the number of constraints. He was awarded the
Spinoza Prize
The Spinoza Prize ( nl, Spinozapremie) is an annual award of 2.5 million euro, to be spent on new research given by the Dutch Research Council (NWO). The award is the highest scientific award in the Netherlands. It is named after the philosopher ...
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 ( nl, De Orde van de Nederlandse Leeuw, french: L'Ordre du Lion Néerlandais) is a Dutch order of chivalry founded by King William I of the Netherlands on ...
. In 2009, he was awarded a
Gauss Lecture by the
German Mathematical Society
The German Mathematical Society (german: Deutsche Mathematiker-Vereinigung, DMV) is the main professional society of German mathematicians and represents German mathematics within the European Mathematical Society (EMS) and the International Math ...
. 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, , .
Bulletin of the AMS, vol. 26, 1992, pp. 211–244.
''Primality testing algorithms.''
Séminaire Bourbaki 1981.
* with Stevenhagen
''Artin reciprocity and Mersenne Primes.''
Nieuw Archief for Wiskunde 2000.
* with Stevenhagen: '' Chebotarev and his density theorem.'' Mathematical Intelligencer 1992 (Online at Lenstra's Homepage).
''Profinite Fibonacci Numbers'', December 2005, PDF
See also
* Print Gallery (M. C. Escher)
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
University of Amsterdam faculty
Leiden University faculty
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