Gerd Faltings Awarded 2026 Abel Prize for Resolving the Mordell and Lang Conjectures in Arithmetic Geometry

Oslo, 19 March 2026 — The Norwegian Academy of Science and Letters today announced that the 2026 Abel Prize has been awarded to Gerd Faltings, professor emeritus at the University of Bonn and director emeritus at the Max Planck Institute for Mathematics, for "introducing powerful tools in arithmetic geometry and resolving long-standing diophantine conjectures of Mordell and Lang."

The Abel Prize, often described as the "Nobel Prize of Mathematics," carries a monetary award of 7.5 million Norwegian kroner (approximately $700,000 USD) and is presented annually by the Norwegian Academy of Science and Letters. The 2026 award ceremony took place on 26 May 2026 at the University Aula in Oslo, with the prize presented by Crown Prince Haakon of Norway.

A Towering Figure in Arithmetic Geometry

Faltings is widely regarded as one of the most influential mathematicians of the late twentieth and early twenty-first centuries. His work unites geometric and arithmetic perspectives, applying tools from algebraic geometry to solve problems in number theory that had resisted attack for generations.

The Mordell Conjecture: A 60-Year-Old Riddle

At the heart of Faltings' most celebrated achievement is the Mordell conjecture, posed by the British mathematician Louis Mordell in 1922. The conjecture concerns diophantine equations — equations for which one seeks solutions in integers or rational numbers. These problems represent one of the oldest and most central areas of mathematics, dating back to the ancient Greek mathematician Diophantus of Alexandria.

The Mordell conjecture states that a wide class of algebraic curves of genus greater than one can have only finitely many rational solutions. In simpler terms, for most complex curves defined by polynomial equations, there are only a finite number of points whose coordinates are rational numbers (fractions of integers).

Faltings did not initially set out to solve the conjecture. "My first goal was to get tenure, so I could make a living out of mathematics," he recalled in a 2024 interview. But while working on related problems in arithmetic geometry, he developed the tools needed to crack the riddle. In 1983, at the age of 28, he published his proof, becoming famous overnight in the mathematical world.

The proof amazed experts not only for its conclusion but for its methodology. Faltings employed sophisticated tools from algebraic geometry, including the theory of heights (a way of measuring the arithmetic complexity of algebraic points) and Arakelov theory (which combines geometric and analytic techniques), to establish the finiteness result.

The Mordell-Lang Conjecture and the Product Theorem

In the following decades, Faltings continued to produce landmark results. In 1989, the mathematician Paul Vojta found an alternative proof of the Mordell conjecture. Inspired by Vojta's approach, Faltings developed a new tool known as the Faltings product theorem and used it to prove the Mordell-Lang conjecture — a significant generalisation of the Mordell conjecture that extends the finiteness result to more general algebraic varieties and group settings.

The Mordell-Lang conjecture, which subsumes several earlier conjectures in diophantine geometry, represents one of the deepest results in the field. Faltings' proof demonstrated the power of his new techniques and cemented his reputation as a mathematician capable of resolving problems that had resisted all previous approaches.

From Wuppertal to Princeton to Bonn

Gerd Faltings was born in 1954 in West Germany. In secondary school, he won a national prize for mathematics. After completing his Ph.D., he spent a year as a research fellow at Harvard University. At the age of 28, in 1982, he became a full professor at the University of Wuppertal in Germany. The following year, he proved the Mordell conjecture.

In 1985, Faltings took up a full professorship at Princeton University, where he and his wife Angelika Tschimmel — a fellow mathematician whom he married in 1984 — had two daughters. He was also a visiting scholar at the Institute for Advanced Study on several occasions.

The family returned to Germany in 1994, when Faltings accepted a position as director at the Max Planck Institute for Mathematics in Bonn. The directorship gave him exceptional freedom to pursue his research, and under his leadership the institute became a worldwide centre for arithmetic algebraic geometry, attracting leading talent from across the globe.

Faltings became an emeritus director in 2023 but continues his research. "I'm still doing maths, but I don't have to go to administrative meetings," he said in a recent interview.

A Distinguished Record of Honours

The Abel Prize adds to an extraordinary list of awards and honours accumulated over Faltings' career:

He is a member of numerous academies, including the Royal Society (UK), the National Academy of Sciences (US), Academia Europaea, and the Norwegian Academy of Science and Letters.

The Abel Prize Legacy

The Abel Prize was established by the Norwegian government in 2002 to mark the 200th anniversary of the birth of the Norwegian mathematician Niels Henrik Abel (1802–1829). Abel himself made groundbreaking contributions to mathematics before his death at age 26. The prize has been awarded annually since 2003 and is administered by the Norwegian Academy of Science and Letters on behalf of the Norwegian Ministry of Education and Research.

Previous laureates include Karen Uhlenbeck (2019), the first woman to receive the prize; Dennis Sullivan (2024); and Michel Talagland (2024, shared with Sullivan). Faltings becomes the first German mathematician to receive the Abel Prize.

Sources

• The Norwegian Academy of Science and Letters, "Gerd Faltings awarded the 2026 Abel Prize," 19 March 2026, abelprize.no
• The Abel Prize, "Abel Laureate 2026: Gerd Faltings," abelprize.no
• Max Planck Institute for Mathematics, University of Bonn, uni-bonn.de
• Academia Europaea, "2026 Abel Prize," ae-info.org
• European Mathematical Society, euromathsoc.org