"for introducing powerful tools in arithmetic geometry and resolving long-standing diophantine conjectures of Mordell and Lang"

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Historical mathematical riddles at the heart of the Abel Prize

Towering figure
Gerd Faltings is a towering figure in arithmetic geometry. His ideas and results have reshaped the field. Not only did he settle major long-standing conjectures, but he also established 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.

Diophantine equations
One of the oldest and most central parts of mathematics is solving equations using only integers (a whole number which is either positive, negative or zero). These problems are called diophantine equations. One example is given by the Pythagorean theorem (x²+y²=z²). This equation has infinitely many solutions that are integers.  Two simple examples are 3²+4²=5², or 9+16=25, and , or . Diophantine equations are at the core of Gerd Faltings’ work within arithmetic geometry.

Historical mathematical mysteries
A diophantine problem known as the Mordell conjecture (1922) had fascinated the mathematical world for 60 years. This conjecture says that a wide class of equations can only have finitely many rational solutions. Faltings did not start out with the goal to solve the conjecture but hoped something interesting would come out of the work. Suddenly cracking this riddle that had puzzled the mathematical world for so long, made him famous overnight in 1983. The proof amazed the experts. Thus, the Mordell conjecture became Faltings’ theorem.

In the following decades new problems were solved like mathematical pearls on a string for Faltings.

In 1989, another mathematician, Paul Vojta, found an alternative solution to the Mordell conjecture. Inspired by this, Faltings developed a new tool, known as Faltings’ product theorem. Using this tool, he cracked another enduring mathematical conundrum – the Mordell-Lang conjecture. This is also one of his great achievements.

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Gerd Faltings - Abel Prize Laureate 2026. Photo: Peter Badge/Typos1/The Abel Prize

Early years
Gerd Faltings was born in 1954 in West Germany. In secondary school he won a national prize for mathematics, and after his Ph.D. he spent a year as a research fellow at Harvard. “My first goal was to get tenure, so I could make a living out of mathematics”, Faltings said in 2024.

 At the age of 28, in 1982, he became a full professor at the University of Wuppertal, Germany. The following year he proved the Mordell conjecture and thus turned it into Faltings’ theorem.

While working at Wuppertal, he met fellow mathematician Angelika Tschimmel. The couple married in 1984. Sadly, Angelika passed away in 2011. In 1985 Faltings took up a full professorship at Princeton University, where their two daughters were born. He also was a visiting scholar at the Institute for Advanced Study in Princeton, New Jersey on several occasions.

Faltings and his family moved back to Germany in 1994, and he took a post at the Max Planck Institute for Mathematics in Bonn. Being a director there gave Faltings exceptional freedom to pursue his research. As one of the most prominent mathematicians in Germany, he attracted a lot of talent, and the institute in Bonn became a worldwide centre for arithmetic algebraic geometry.

Today, an emeritus director at the Max Planck since 2023, Faltings continues his research. “I’m still doing maths, but I don’t have to go to administrative meetings”, Faltings said in a previous interview.

Awards and honours
2026 – The Abel Prize
2024 – Pour le Mérite
2017 – Cantor Medal
2015 – Shaw Prize
2014 - King Faisal International Prize
2010 - Heinz Gumin Prize
2008 – von Staudt Prize
1996 – Leibniz Prize
1988 – Guggenheim Fellowship
1986, 1994 - ICM Speaker
1986 – Fields Medal
1983 – Dannie Heineman Prize

Member of

• North Rhine-Westphalian Academy of Sciences, Humanities and the Arts
• Deutsche Akademie der Naturforscher Leopoldina
• Berlin-Brandenburgische Academie der Wissenschaften
• Academia Europaea
• The Göttingen Academy of Sciences and Humanities
• The Royal Society (UK)
• National Academy of Sciences (US)
• The Norwegian Academy of Science and Letters