The international award recognizes academic work of extraordinary depth and influence on the mathematical sciences and is thus also regarded as a kind of “Nobel Prize for Mathematics.” Gerd Faltings has been active in Bonn since the 1990s, working at the MPIM and the University, and remains an associate member of the latter’s Hausdorff Center for Mathematics (HCM) Cluster of Excellence.
The Abel Prize was set up by the Norwegian government to mark the 200th anniversary of the birth of Norwegian mathematician Niels Henrik Abel (1802–1829). Unlike with the Fields Medal—but like the Nobel Prize—there are no age restrictions on the winner of the Abel Prize. The award is worth 7.5 million Norwegian kroner (around €670,000).
Gerd Faltings was also the first German to win the Fields Medal, doing so back in 1986. Peter Scholze, another mathematics professor from the University of Bonn, followed in his footsteps in 2018. Celebrating the announcement of his illustrious accolade together with the MPIM team, Faltings said: “I feel honored by this prize.”
Rector Professor Michael Hoch was among the first to congratulate him, commenting: “On behalf of the University of Bonn—a University of Excellence—I’d like to extend my warmest congratulations to Gerd Faltings for this truly unique achievement. He has revolutionized many fields of mathematics, especially number theory, the theory of surfaces and Diophantine equations, and shaped their development with his groundbreaking findings. In the Mordell conjecture, he solved a problem that had stumped mathematicians for decades. I’m especially delighted that the first German Abel Prize is coming to Bonn; it underlines yet again that mathematics at the University of Bonn is among the very best in the world and reflects the outstanding achievements produced here, not least in the HCM Cluster of Excellence.”
Early interest in mathematics
Gerd Faltings was born in the Buer district of Gelsenkirchen in 1954. His father held a degree in physics and his mother one in chemistry. While at school, he twice entered the nationwide mathematics competition and was accepted into the German Academic Scholarship Foundation as the German champion. After obtaining his Abitur, he studied mathematics and physics in Münster and was a guest at Harvard University in Cambridge, Massachusetts, in 1978/79. 1979 also saw him take up an assistant position in Münster, where he gained his Habilitation in 1981. This was followed by professorships in Wuppertal and at Princeton University, New Jersey. Faltings returned to Germany in 1994, holding the posts of Director of the MPIM in Bonn and professor in the Faculty of Mathematics and Natural Sciences at the University of Bonn until his acceptance of an emeritus position in 2023.
Widespread recognition
The first few awards to come his way included the 1984 Dannie Heineman Prize from the Göttingen Academy of Sciences and Humanities as well as the 1986 Fields Medal, an accolade that the International Mathematical Union only awards every four years to mathematicians under the age of 40. In Germany, he received the Leibniz Prize in 1996, the von Staudt Prize in 2008, the Heinz Gumin Prize in 2010 and the Georg Cantor Medal in 2017. He has also won international recognition, being awarded the King Faisal International Prize in 2014 and the Shaw Prize one year later.
Faltings is a member of the academies in Düsseldorf, Göttingen, Berlin and Halle as well as the European Academy, the Royal Society in London, the National Academy of Science in Washington and the Order Pour le Mérite.
A Surprising Solution to a Mathematical Problem
Gerd Faltings was awarded the Abel Prize "for introducing powerful tools in arithmetic geometry and for solving the longstanding Mordell and Lang Diophantine conjectures." The prize committee honors him as "an outstanding figure in arithmetic geometry." His ideas and results have shaped the field and led to the resolution of longstanding conjectures. At the same time, he introduced new methods that have influenced subsequent work for decades. His extraordinary achievements have united geometric and arithmetic perspectives, demonstrating the power of profound structural insights.
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 number of integer solutions to a polynomial equation depends on a geometric property. When solved for complex numbers rather than integers, the set of solutions often forms a smooth, closed surface, such as a sphere, torus, or pretzel. These surfaces can be classified by the number of their "holes," a mathematical concept called genus. For instance, 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 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 they can be constructed from a finite number of solutions. In 1922, Louis Mordell conjectured that equations with fields of genus greater than one can have at most a finite number of rational solutions. For over 60 years, this conjecture stubbornly resisted all attempts at proof. It was considered unsolvable until Gerd Faltings surprised the scientific community with his proof at the age of 28. Since then, Mordell’s conjecture has been known as Faltings' theorem.
The equation an + bn = cn is of genus greater than 1 for n > 3, so it follows from Faltings' theorem that there can be at most a finite number of rational, and thus integer, solutions. This theorem was a decisive step in proving Fermat's Last Theorem. However, Faltings's result is much more general and has numerous other applications. Due to this and many other significant results, Gerd Faltings became a leading figure in arithmetic geometry.
