The Hungarian-born researcher Peter Lax has collected the 2005 Abel Prize.
Professor Lax was awarded the prize on Tuesday in Oslo (Image: Knut Falch)
The £480,000 award is handed down by the Norwegian Academy of Science and Letters and supports a research field that is overlooked by the Nobel Prizes.
The 79-year-old mathematician is based at the Courant Institute of Mathematical Sciences in New York, US.
His work has provided new approaches to partial differential equations, which are used to describe non-linear systems such as the motion of gases.
Professor Lax was presented with the award by the Crown Prince Regent of Norway at Oslo University on Tuesday.
In the evening, the Norwegian government held a banquet at Akershus Castle in his honour.
Professor Lax grew up in Hungary but left with his parents and brother for the US in November 1941.
In 1945, he relocated to Los Alamos in New Mexico to join the Manhattan Project, the US effort to build an atomic bomb.
Lax was also a protégé of John von Neumann, one of the fathers of modern computing.
He received his PhD in 1949 from New York University and in 1951 began work at the mathematics institute founded by his thesis adviser Richard Courant.
"He has been an inspiration to me ever since I was a graduate," said Professor John Ball, of the University of Oxford, UK, who is president of the International Mathematical Union.
"Lax has a great talent. He finds unifying ideas which then set the framework for other mathematicians."
Linear differential equations, in which cause and effect are directly proportional, are reasonably well understood.
But the equations that arise in such fields as aerodynamics, meteorology and elasticity are nonlinear and much more complex - and their solutions are approximate at best.
Think of the shock waves that appear when an airplane breaks the sound barrier.
In the 1950s and 1960s, Professor Lax laid the foundations for the modern theory of nonlinear equations of this type (hyperbolic systems).
He constructed explicit solutions, identified classes of especially well-behaved systems, introduced an important notion of entropy, and, with US mathematician James Glimm, made a penetrating study of how solutions behave over a long period of time.
In addition, he introduced the widely used Lax-Friedrichs and Lax-Wendroff numerical schemes for computing solutions.
His work in this area was important for the further theoretical developments.
It has also been extraordinarily fruitful for practical applications, from weather prediction to airplane design.
Last year's Abel Prize was shared by Sir Michael Atiyah and Isadore Singer.