Professor Carleson said he was humbled by the news of his win
Swedish mathematician Lennart Carleson has been named as the winner of the 2006 Abel Prize for outstanding work in the field of mathematics.
The prize is worth about £520,000, and credits a discipline overlooked by the Nobel Prizes.
The honour recognises Professor Carleson's work in harmonic analysis, particularly for his proof of the convergence of the Fourier series.
The prize is awarded by the Norwegian Academy of Science and Letters.
'Ahead of the crowd'
Professor Carleson told the BBC News website that he felt grateful and humble on receiving the news, announced on Thursday in Oslo.
"There are so many good people that could have been chosen, so I feel very lucky," he said.
He will be presented with his prize by the King of Norway at an award ceremony on 23 May.
The international Abel Committee, which decided on the winner, said: "Carleson is always far ahead of the crowd. He concentrates on only the most difficult and deep problems.
"Once these are solved, he lets others invade the kingdom he has discovered, and he moves on to even wilder and more remote domains of science."
The Abel Committee said that his work on the Fourier series was of particular significance.
In 1807, the French mathematician Jean Baptiste Fourier began the branch of mathematics known as harmonic analysis when he discovered that natural phenomena of a periodic nature, such as electric currents or sound waves, could be described as the sum of simple mathematical building blocks - oscillating sine or cosine waves.
Periodic phenomena can be broken down into sine waves
For example, the sound from a trumpet can be shown graphically as a complicated wave, but Fourier's work suggested it could also be broken down into lots of simple sine or cosine waves.
Mathematicians had speculated that any periodic natural phenomenon could be simplified in this way.
But for 150 years the approach remained unproven, until in 1966 Professor Carleson published a paper which showed that Fourier's idea held true for all such examples.
Professor Carleson has carried out extensive work in harmonic analysis, and has also worked on dynamic systems, a branch of mathematics that uses models to describe how large systems, such as financial markets or meteorological phenomena, change over time.
Professor Marcus du Sautoy, a mathematician at Oxford University, UK, said Professor Carleson had made great contributions to the field.
"Not only has he solved a great unsolved problem, but he has created tools that we are now all using in our mathematics," he said.
"I think that's really what marks him out as a great mathematician."
The 6m Norwegian Kroner ($900,000) prize was established in 2002, and is named after the brilliant Norwegian mathematician Niels Henrik Abel.
Last year's prize was awarded to Peter Lax for his work on partial differential equations.