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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.

Avi Wigderson studies computational complexity theory, including the role of randomized algorithms in efficient computation. His research connects pseudorandom generators, computational hardness and derandomization. His book Mathematics and Computation by Avi Wigderson explains how sufficiently strong circuit-hardness assumptions can supply generators that fool efficient computational tests.^[ref]

The mechanism turns a lower-bound assumption into an algorithmic resource. If a generator with a short seed preserves a randomized computation's acceptance probability closely enough, enumerating all seeds can replace sampling random bits. The seed must be short enough for that enumeration to meet the claimed time bound; simply fixing one arbitrary seed does not supply the guarantee. This makes the power of randomness a precise question about computation rather than a visual impression that an output “looks random”.

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]