Gerd Faltings Awarded the 2026 Abel Prize for Transformative Work in Arithmetic Geometry

The Norwegian Academy of Science and Letters announced today that the 2026 Abel Prize goes to Gerd Faltings, director emeritus at the Max Planck Institute for Mathematics in Bonn and professor emeritus at the University of Bonn. The citation reads: “for introducing powerful tools in arithmetic geometry and resolving long-standing diophantine conjectures of Mordell and Lang.”

Faltings becomes the first German mathematician to receive the prize, and the first 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

The Abel Prize was established by the Norwegian government in 2002, on the occasion of the 200th anniversary of Niels Henrik Abel’s birth. It has been awarded annually since 2003. The prize carries an award of 7.5 million Norwegian kroner, equivalent to roughly 670,000 euros, and is presented each spring by the Crown Prince of Norway at a ceremony in Oslo. This year’s ceremony is scheduled for 26 May. Further information, including the full scientific citation and a popular account of Faltings’ work, is available at abelprize.no.

Abel himself died in 1829 at the age of 26, from tuberculosis, having spent most of his short life in poverty. He left behind a body of work that reshaped algebra and analysis, including a proof that the general quintic equation cannot be solved by radicals. The prize named after him was conceived to give mathematics a permanent, high-profile recognition on the level of the Nobel prizes. It took a century from the first proposal to the actual establishment of the award. By that point, the idea had been suggested, abandoned after the dissolution of the Swedish-Norwegian union in 1905, revived, debated, and eventually funded through the national budget.

Previous laureates include Andrew Wiles, Karen Uhlenbeck, Robert Langlands, and Mikhail Gromov. Last year, the prize went to Masaki Kashiwara for his contributions to algebraic analysis and representation theory.

Why Faltings

In 1922, the British mathematician Louis Mordell put forward a conjecture about a specific family of equations. He claimed that any algebraic curve of genus greater than one, defined over the rational numbers, could only have finitely many rational points. In plain terms: past a certain level of geometric complexity, a curve stops being the kind of object where solutions accumulate. There are a few, or there are none, but the supply runs out.

“His ideas and results have reshaped the field, settling major long-standing conjectures, while also establishing new frameworks that have guided decades of subsequent work.”
Abel Prize Committee, 2026

The conjecture sat open for sixty years. Many talented mathematicians came at it, found partial results, and stopped short. By the late 1970s, it had acquired the reputation of a problem that resisted whatever tools the field had available. Then in 1983, Gerd 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 result carries a well-known corollary. The Fermat curves xⁿ + yⁿ = zⁿ have genus greater than one when n is at least 4. Hence, Faltings’ theorem immediately implies that for those exponents, there can only be finitely many rational solutions. It does not prove the count is zero, as Andrew Wiles’ proof of Fermat’s Last Theorem in 1995 did, but it ruled out infinity, which had not been done before.

Faltings did not stop at Mordell. In 1989, Paul Vojta found a different proof of the Mordell conjecture using diophantine approximation. Faltings adapted that approach in 1991 to prove the Mordell-Lang conjecture, a substantially harder generalisation about the distribution of rational points in subvarieties of abelian varieties. The same paper also established the finiteness of integral points on affine subvarieties of abelian varieties, as conjectured by Serge Lang.

Beyond diophantine geometry, Faltings made major contributions to p-adic Hodge theory, proving the main conjectures formulated by Tate and Jean-Marc Fontaine and extending the theory into the non-abelian setting. The tools he introduced there have remained central to the field, including through the subsequent work of Peter Scholze. The Abel committee’s citation describes him as “a towering figure in arithmetic geometry” whose “ideas and results have reshaped the field, settling major long-standing conjectures, while also establishing new frameworks that have guided decades of subsequent work.”

A Career at the Intersection of Geometry and Arithmetic

Faltings was born in Gelsenkirchen in 1954. He studied mathematics and physics at the University of Münster, completing his doctorate there in 1978. A visiting scholarship at Harvard followed, then a return to Münster as an assistant, then his habilitation in 1981. At 27, he was appointed to a full professorship at the University of Wuppertal, the youngest in Germany at the time. In 1985, he moved to Princeton, where he remained for nearly a decade.

He returned to Germany in 1994, when his daughters were older, and has been based at the Max Planck Institute for Mathematics in Bonn ever since. He became director emeritus there in 2023.

Faltings’ work sits at the intersection of number theory and algebraic geometry, a territory that goes by the name of arithmetic geometry. The central questions of the field concern rational or integer solutions to polynomial equations, objects that look like algebra but live on geometric structures. His contribution was not just to answer specific questions but to import an entire set of geometric tools into that arithmetic context, tools that others have continued to develop and apply since.

Outside mathematics, Faltings is known as a devoted opera-goer, a fan of FC Schalke 04, and an enthusiastic gardener.

A Prior Visit to the CRM

Faltings’ connection to Barcelona goes back more than three decades. In June 1991, at the height of his reputation following the Mordell proof and the Fields Medal, he was one of six Fields Medallists invited to participate in the Symposium on the Current State and Prospects in Mathematics, organised by the CRM as part of the Barcelona Cultural Olympiad. The other plenary speakers were Allan Connes, Vaughan Jones, Sergei Novikov, Stephen Smale, and René Thom. The proceedings were published by Springer under the title Mathematical Research: Today and Tomorrow.

The prize will be presented at a ceremony in Oslo on 26 May 2026.