Lenstra received his doctorate from the University of Amsterdam in 1977 and became a professor there in 1978. In 1987, he was appointed to the faculty of the University of California, Berkeley; starting in 1998, he divided his time between Berkeley and the University of Leiden, until 2003, when he retired from Berkeley to take a full-time position at Leiden.^[1]

Three of his brothers, Arjen Lenstra, Andries Lenstra, and Jan Karel Lenstra, are also mathematicians. Jan Karel Lenstra is the former director of the Netherlands Centrum Wiskunde & Informatica (CWI). Hendrik Lenstra was the Chairman of the Program Committee of the International Congress of Mathematicians in 2010.^[2]

Lenstra has worked principally in computational number theory. He is well known for:

• Co-discovering of the Lenstra–Lenstra–Lovász lattice basis reduction algorithm (in 1982);
• Developing an polynomial-time algorithm for solving a feasibility integer programming problem when the number of variables is fixed (in 1983);^[3]
• Discovering the elliptic curve factorization method (in 1987);^[4]
• Computing all solutions to the inverse Fermat equation (in 1992);^[5]
• The Cohen-Lenstra heuristics - a set of precise conjectures about the structure of class groups of quadratic fields.^[6]

In 1984, Lenstra became a member of the Royal Netherlands Academy of Arts and Sciences.^[7] He won the Fulkerson Prize in 1985 for his research using the geometry of numbers to solve integer programs with few variables in time polynomial in the number of constraints.^[8] He was awarded the Spinoza Prize in 1998,^[9] and on 24 April 2009 he was made a Knight of the Order of the Netherlands Lion. In 2009, he was awarded a Gauss Lecture by the German Mathematical Society. In 2012, he became a fellow of the American Mathematical Society.^[10]

• 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, ISBN 0-444-88071-2, ISBN 0-262-22038-5.
• 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

• Print Gallery (M. C. Escher)

• "Home Page: Emeritus professor, Department of Mathematics, University of California, Berkeley".
• "Hendrik W. Lenstra"., Homepage at the Leiden Mathematisch Instituut
• Hendrik Lenstra at the Mathematics Genealogy Project