Category: News from Academies in the Nordics and the Baltics

The Norwegian Academy of Science and Letters has decided
to award the Abel Prize for 2026 to Gerd Faltings of the
Max Planck Institute for Mathematics, Bonn, Germany
“for introducing powerful tools in arithmetic geometry and resolving long-standing diophantine conjectures of Mordell and Lang.”

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. 

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.

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

The Norwegian Academy of Science and Letters has decided to award the Abel Prize 2025 to Professor Masaki Kashiwara at Research Institute for Mathematical Sciences (RIMS), Kyoto University, Japan, and Kyoto University Institute for Advanced Study (KUIAS), Kyoto University, Japan.

Masaki Kashiwara has during more than half a century in mathematics opened the door to a new mathematical field. He has built bridges and created tools. He has proven astonishing theorems with methods no one had imagined. He has been a true mathematical visionary.

Like Niels Henrik Abel (1802-1829) himself, Masaki Kashiwara (b.1947) showed excellence already when very young. He remembers his love of algebra being kindled at school by a problem called Tsurukamezan, about calculating the numbers of cranes and turtles, respectively, from knowing the total numbers of heads and legs. He loved being able to generalise a method to solve any problem. From there on he has continued to find new approaches and create new methods to solve mathematical problems throughout his astonishing mathematical life.

At the University of Tokyo, he first encountered his mentor Mikio Sato (1928–2023), by enrolling for his senior year seminar. Sato had founded a new field – algebraic analysis – and in 1970 Kashiwara completed his Master’s thesis under his supervision. This thesis established the foundations of D-Module Theory, a new basis for studying systems of linear differential equations with algebraic analysis, when Kashiwara was just 23. For the next 25 years this thesis remained only available in Japanese, but it continued to have such great impact and influence, that it was eventually translated to English.

Broad spectrum of mathematics

With his Master’s thesis as a starting point, Kashiwara continued his remarkable mathematical career with new and groundbreaking discoveries and solutions. His numerous achievements have exerted great influence on various fields of mathematics and contributed strongly to their development. Over the years many mathematicians have been inspired through Kashiwara’s ideas.

While still a graduate student, Kashiwara travelled to France with Sato and fellow mathematician Takahiro Kawai, where he met his lifelong collaborator, Pierre Schapira. After completing his Ph.D. at Kyoto University in 1974, Kashiwara was appointed Associate Professor at Nagoya University. In 1977 he went as a researcher to MIT, before returning to Japan in 1978, where he has remained ever since at the Research Institute for Mathematical Sciences (RIMS), Kyoto University. He became Professor Emeritus following his retirement in 2010 and has continued his research as Project Professor at RIMS. He has also served as Program-Specific Professor since 2019 at the Kyoto University Institute for Advanced Study (KUIAS), specially established as a hub for the world’s most advanced research.

Read more at the official Abel Prize page. 

The Finnish Academy of Science and Letters has published a handbook for researchers on science-for-policy.

Pathways to Impact: Researcher’s Handbook on Science-for-Policy is a new handbook published by the Finnish Academy of Science and Letters. It provides strategic tools for strengthening the impact of research in policy-making. It answers questions such as: how is research knowledge transferred to policy-makers? And when is the right time to engage in a policy process?

The handbook can be downloaded from the Finnish Academy website.

“High-quality, multidisciplinary research knowledge is needed to support policy-makers in addressing interconnected societal challenges. Recognising that researchers already face a lot of pressures in their academic work, we wanted to produce a handbook that would make societal impact work more accessible and approachable for researchers. Indeed, we aim to encourage and motivate researchers to engage in societal impact work”, explains knowledge broker Linda Lammensalo.

“The handbook aims to assist researchers in different stages of their careers to excel in their impact work.”

The handbook, for example, outlines different stages of policy-making, with a focus on the Finnish national context. It also includes practical tips from the Finnish Prime Minister’s Office in responding to policy-makers’ knowledge requests. It contains interactive tools to practice and reflect on one’s own experiences and expertise, as well as concrete examples from other researchers who have already engaged in impact work.

According to Lammensalo, the handbook can give researchers a good starting point for their impact work.

“We hope that the handbook will inspire researchers to discover new pathways for increasing the impact of their research.”