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Gerd Faltings to Receive the 2026 Abel Prize

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The Norwegian Academy of Science and Letters has awarded the 2026 Abel Prize to Gerd Faltings, director emeritus at the Max Planck Institute for Mathematics in Bonn and professor emeritus at the University of Bonn, "for introducing powerful tools in arithmetic geometry and solving long-standing diophantine conjectures by Mordell and Lang."

 

The prize will be presented by His Royal Highness Crown Prince Haakon at a ceremony on May 26, 2026, in Oslo. It consists of 7.5 million Norwegian kroner, equivalent to €670,000, and is funded by the Norwegian government. Gerd Faltings is the first German mathematician to receive this highest honor in mathematics.

In its citation, the prize committee honors Gerd Faltings as “a towering figure in arithmetic geometry. 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. His exceptional achievements unite geometric and arithmetic perspectives and exemplify the power of deep structural insight.”

 

Surprising Solution to a Mathematical Puzzle

 

In 1983, Gerd Faltings became famous overnight in the mathematical community when he surprisingly proved Mordell’s conjecture using entirely novel methods.

 

The idea behind Mordell’s conjecture is thousands of years old. Already Diophantus of Alexandria wanted to find out how many integer solutions an equation such as a² + b² = c² has. Because of the Pythagorean theorem, this corresponds to the practical question of how many right-angled triangles with integer side lengths there are. It is now clear: There are infinitely many of them. In 1637, Pierre de Fermat proposed the now-proven conjecture that this is an exception for squares and that an+ bn= cn for n > 2 has no integer solutions at all. Why?

 

At the beginning of the 20th century, it gradually became clear that the question of whether and how many integer solutions such polynomial equations have depends on a geometric property: If one solves them not for integers but for complex numbers, the set of solutions is often a smooth closed surface, such as the surface of a sphere, a torus, or a pretzel. Such surfaces can be classified by the number of their “holes,” which in mathematics is called the genus of the surface. For example, a spherical surface has genus 0, a doughnut with one hole has genus 1, a pretzel has genus 3, and so on.

 

The number of integer or rational solutions now depends crucially on the genus of these surfaces. Equations with surfaces of genus 0, the simplest case, have either no rational solutions or infinitely many. Equations with genus 1, called elliptic curves, can have infinitely many rational solutions, but these can be constructed from a finite number of solutions. In 1922, Louis Mordell conjectured that equations with fields of genus greater than 1 can have at most a finite number of rational solutions. For over 60 years, this conjecture stubbornly resisted all attempts at proof. It had come to be regarded as unsolvable when Gerd Faltings, at the age of 28, surprised the scientific community with his proof. Since then, Mordell’s conjecture has been known as Faltings’ theorem.

 

The equation  an + bn  = cn  is of genus > 1 for n > 3. It therefore follows from Faltings’ Theorem that there can be at most a finite number of rational and thus also integer solutions. The theorem is one of the decisive steps in the proof of Fermat’s Last Theorem. However, Faltings’ result is much more general and has numerous other applications. With many other results of comparable significance, Gerd Faltings became one of the leading figures in arithmetic geometry.

 

Gerd Faltings was born in Gelsenkirchen in 1954, the son of a physicist and a chemist. During his school years, he was twice a winner in the National Mathematics Competition for students. After graduating from high school, he studied mathematics and physics at the University of Münster. In 1978, he completed his studies with a doctorate under Hans-Joachim Nastold. In 1978–79, he was a visiting scholar at Harvard University in Cambridge, Massachusetts. Upon his return to Münster, he became an assistant to Professor Nastold in 1979 and earned his habilitation in 1981. In 1982, he was appointed to the University of Wuppertal and, at the age of 27, became the youngest full professor of mathematics in Germany. In 1985, he accepted a position at Princeton University in the United States. As his daughters grew older, he returned to Germany in 1994, where he has since been conducting research at the Max Planck Institute for Mathematics in Bonn and teaching at the University of Bonn. Since 2023, he has been director emeritus at the Max Planck Institute for Mathematics in Bonn and remains an associate member of the Hausdorff Center for Mathematics at the University of Bonn. Gerd Faltings has two daughters, is a connoisseur of opera and classical music, loves good wine, enjoys working in his garden, and is a fan of the soccer club FC Schalke 04.

 

Honors

 

 

Gerd Faltings is also a member of the North Rhine-Westphalian Academy of Sciences, the German Academy of Sciences Leopoldina, and the Academia Europaea.

 

The Max Planck Institute for Mathematics in Bonn is one of 82 research institutes of the Max Planck Society. The Institute was founded in 1980, and has soon become one of the world’s most prestigious research institutes for mathematics. It is managed by the directors Dennis Gaitsgory, Peter Scholze, Catharina Stroppel, and Peter Teichner. It's active emeritus directors are Werner Ballmann, Gerd Faltings, and Don Zagier. With only a small number of permanent research and administrative staff, the Institute’s guest program attracts over 400 research mathematicians from around the globe every year. The Institute is home to around 100 long-term guest researchers at all times. Research at the Institute covers most areas of pure mathematics. The Max Planck Institute for Mathematics is also one of the six institutes of the Hausdorff Center for Mathematics of the University of Bonn.

 

Press contact:

Dr. Christian Blohmann

Max Planck Institute for Mathematics, Bonn

Phone: +49-228-402302

blohmann@mpim-bonn.mpg.de

 

Photo credit: Peter Badge / The Abel Prize

 
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