Mathematician Gerd Faltings has won the 2026 Abel Prize for solving a 60-year-old mystery

Gerd Faltings he won the 2026 Abel Prize, considered the Nobel Prize of mathematics, for the ground-breaking proof that took mathematics by storm in 1983. His contributions helped to establish one of the most important branches of modern mathematics, arithmetic geometry.

The crowning achievement of Faltings, who also won the prestigious Fields Medal in 1986 for the same work, was proving Mordell’s conjecture, a long-standing theorem first proposed by Louis Mordell in 1922 that states that increasingly complicated equations produce fewer solutions.

Faltings, who is based at the Max Planck Institute for Mathematics in Germany, says he was “honored” to learn of the news, but reserved about the impact of his achievements. “Someone said about climbing Mount Everest it’s because it’s there and it was a problem,” Faltings says. “I solved it [the Mordell conjecture]but ultimately it doesn’t allow us to cure cancer or Alzheimer’s, it just increases our knowledge of things.”

Mordell’s conjecture concerns Diophantine equations, a broad category that includes famous equations such as a² + b² = c² from the Pythagorean theorem and aⁿ + bⁿ = cⁿ, which is at the heart of Fermat’s famous last theorem. Mordell wanted to understand which of these Diophantine equations in their more general form have infinitely many solutions and which have only a finite number.

If these equations are rewritten in complex numbers, a kind of 2-dimensional number, and then plotted as surfaces such as spheres or donuts, Mordell’s view was that the number of holes the surface contains determines how many solutions there are. Mordell guessed that for surfaces that have more holes than a donut, there will always be only a finite number of rational solutions, which are solutions using either integers or fractions, but he couldn’t prove it.

When Faltings finally proved Mordell’s hunch more than six decades later, it surprised mathematicians not only by the result, but also by how he came up with it. His proof brought together ideas from seemingly disparate mathematical disciplines such as geometry and arithmetic. “It’s very short, it’s like a miracle,” he says Akshay Venkatesh at the Princeton Institute for Advanced Study. “It’s this document of only 18 pages and it jumps intricately between different techniques and different intuitions.”

Faltings attributes his success to being comfortable with uncertainty and taking risks on ideas that may not be proven but that he suspects might work. “Sometimes I get ahead of people who try to do everything right away, but sometimes I’m also abstract,” Faltings says.

“One of the impressive things about his argument is that it covers so much and the pieces have to fit together,” says Venkatesh. “You wonder, how could he have had the confidence to go into this without knowing yet how the pieces fit together?”

Many of the conjectures that Faltings solved and the tools he developed as part of his Mordell proof formed the basis of some of the greatest areas of mathematical research today, such as p-adic Hodge theory, which examines the connections between the curves of a shape and its structure, but uses number systems quite different from our own. He also directly influenced a landmark development in modern mathematicssuch as paving the way for Andrew Wiles’ proof of Fermat’s Last Theorem and mentoring Shinichi Mochizuki, the Japanese mathematician who controversially claims to have proved the abc conjecture.

Faltings says he had no intention of working on such high-impact issues. “My idea was that I shouldn’t look at what can make me famous and rich, but I try to find things that I like,” Faltings says. “Because when you’re working on things you like, it’s more fun.”

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