The Norwegian Academy of Science and Letters has awarded the 2026 Abel Prize to Gerd Faltings of the Max Planck Institute for Mathematics in Bonn, Germany, "for introducing powerful tools in arithmetic geometry and resolving long-standing diophantine conjectures of Mordell and Lang."
At age 71, Faltings becomes the latest recipient of an annual lifetime achievement award modelled on the Nobel Prize and bestowed each spring in Oslo. He is the first German mathematician to receive the Abel Prize — and the first German to hold both an Abel Prize and a Fields Medal, the latter awarded to him in 1986 for the same body of work that now earns this recognition. The prize carries a monetary award of 7.5 million Norwegian kroner, roughly US$873,000.
The Mathematics
The conjecture Faltings is most celebrated for proving had stood open for sixty years. Stated in 1922 by American mathematician Louis Mordell, it asserted that a broad class of Diophantine equations — polynomial equations in which solutions must be rational numbers — can have at most a finite number of solutions, except in special cases.
To appreciate the depth of this claim, consider a concrete analogy. The Pythagorean equation admits infinitely many integer solutions: , , and so on without end. Mordell conjectured that once you raise the complexity of the curve — measured by a quantity called the — solutions become scarce. Specifically, for a smooth algebraic curve of genus defined over the rationals, there are only finitely many rational points.
x2+y2=z2
(3,4,5)
(5,12,13)
genus
g≥2
In 1983, Faltings, aged 28, proved it. He used a combination of methods drawn from Arakelov theory and the arithmetic of abelian varieties, techniques that had not previously been brought to bear on the problem in that configuration. The proof surprised the community not only because it worked, but because of how much extra machinery it produced along the way.
The theorem is now known eponymously as Faltings's theorem. Its proof does not produce an algorithm to find the finitely many solutions — it asserts their finiteness by structural argument alone. The curve, in Faltings's framework, is studied not just as a geometric object but as an arithmetic one, sitting inside a rich ambient structure of abelian varieties and their endomorphism rings.
Faltings continued to extend his reach. In 1991, he proved a vast generalisation of his earlier work, and also contributed decisively to the Mordell–Lang conjecture and to p-adic Hodge theory — a framework that provides powerful methods for studying p-adic representations of Galois groups and their cohomological properties, and which has since become foundational to modern work in the Langlands programme.
About the Recipient
Faltings was born in 1954 in West Germany. In secondary school he won a national prize for mathematics, and after his PhD spent a year as a research fellow at Harvard. At 28 he became a full professor at the University of Wuppertal; the following year he proved Mordell's conjecture. He later held a full professorship at Princeton University before joining the Max Planck Institute for Mathematics in Bonn in 1994, where he has remained since.
His reaction to the prize was characteristically understated. "Near the beginning of my career, I got the Fields Medal. And near the end, I'm getting the Abel Prize," Faltings said. "It's a nice duality."
The Abel Prize ceremony will take place in Oslo on 26 May 2026, with the prize presented by Crown Prince Haakon.
