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The Abel Prize is an international award for outstanding work in mathematics, named after Niels Henrik Abel. It was first awarded in 2003 to Jean-Pierre Serre. The Norwegian Academy of Science and Letters administers the selection.^[ref]

The mathematical work behind an award is more informative than the honour alone. The 2009 award recognized Mikhail Gromov's contributions to geometry and topology, including global geometric questions whose behaviour cannot be read from local coordinates alone.^[ref] The 2021 award to László Lovász and Avi Wigderson recognized contributions connecting discrete mathematics and theoretical computer science.^[ref] The prize's scope therefore spans several mathematical traditions.

Arjen K. Lenstra works in computational number theory and cryptography. With Hendrik W. Lenstra and László Lovász, he authored the 1982 paper introducing the LLL algorithm and applying lattice reduction to factoring polynomials with rational number coefficients in polynomial time.^[ref]

A rational factorization can be converted to an integer-coefficient problem, then studied through modular information and short lattice vectors. Reduction helps recover an exact factor from that indirect arithmetic data. The achievement concerns polynomial factorization; it does not provide a polynomial-time algorithm for general integer factorization. His EPFL interview describes his introduction to randomized algorithms and his approach to teaching mathematical computation.^[ref]

By Arjen K. Lenstra, Hendrik W. Lenstra, László Lovász. Mathematische Annalen261,515–534(1982).

Journal paper scan: www.math.ucdavis.edu/~deloera/MISC/LA-BIBLIO/trunk/Lovasz/LovaszLenstraLenstrafactor.pdf

Institutional record of preprint IW195/82: ir.cwi.nl/pub/9304 . The record names A.K.Lenstra(Arjen), H.W.Lenstra(Hendrik), and L.Lovász(László), and dates the report1982.

Cited locator: Section1, lattice-basis reduction. The initial reduction section develops the geometric algorithm used by the later polynomial-factorization construction.

Hendrik W. Lenstra is a mathematician working in computational number theory. He introduced the elliptic-curve factorization method, replacing the multiplicative groups in an earlier factorization approach by groups of points on variable elliptic curves.^[ref]

The method computes modulo a composite integer $N$ without first knowing its prime divisors. If an elliptic-curve operation requires inverting a denominator $d$ with $1<\gcd (d,N)<N$, the failed inversion reveals a proper divisor. Varying the elliptic curve varies the group orders modulo the unknown primes, offering repeated chances for a favourable order. He also coauthored the LLL algorithm with Arjen K. Lenstra and László Lovász.^[ref]

László Lovász is a mathematician whose work connects combinatorics, graph theory and efficient algorithms. With Arjen K. Lenstra and Hendrik W. Lenstra, he developed the LLL algorithm, which replaces a basis of a Euclidean lattice by a more geometrically controlled basis of the same lattice. Their 1982 paper uses lattice reduction to factor polynomials over the rational numbers in polynomial time.^[ref]

The point of reduction is not to change the lattice: integer basis changes preserve it. Instead, shorter, better organized vectors expose relations hidden by a poor basis. This is a striking bridge from geometric reasoning to exact algebraic computation. Lovász shared the 2021 Abel Prize with Avi Wigderson for contributions linking discrete mathematics and theoretical computer science.^[ref]