Reacción a "The Abel Prize, the ‘Nobel Prize’ of mathematics, has been awarded to Gerd Faltings for his work on Diophantine equations"

Gerd Faltings is one of the most influential mathematicians of the last 50 years. He has resolved numerous long-standing conjectures, such as Tate’s conjecture for abelian varieties, Shafarevich’s conjecture, Mordell’s conjecture and the Mordell–Lang conjecture. At the time, the proofs presented by Faltings surprised experts with their vision and technical skill, and opened up new avenues of research.

He received the Fields Medal in 1986 for his proof of the Mordell conjecture and has also received many other prizes and honours, such as the Shaw Prize in 2015 and the Cantor Medal in 2017.

But, in addition to proving impressive conjectures, Gerd Faltings has introduced numerous new techniques into what we know as arithmetic geometry, a discipline at the intersection of algebraic geometry and number theory. For example, his monograph Degeneration of Abelian Varieties, written jointly with Ching-Li Chai, is still widely used by numerous researchers, more than 30 years after its publication. He has also been a pioneer in fields such as Arakelov theory and p-adic Hodge theory.

The variety of topics on which Faltings has worked and made significant contributions is striking. As he himself states in his research profile as a member of the European Academy, Gerd Faltings researches “whatever he finds interesting”.

It can be said that Faltings’ ideas and work have shaped what we now know as arithmetic geometry. I believe that the awarding of the Abel Prize to Gerd Faltings is more than deserved and is a recognition of his talent and work.