Sir Michael Atiyah and Isadore Singer have been awarded the Abel Prize for their outstanding work in mathematics.
The UK and US researchers developed what is now referred to as the Atiyah-Singer theorem about 40 years ago.
It concerns the use of differential equations and has allowed physicists to develop new theories about the cosmos.
The honour, from the Norwegian Academy of Science and Letters, was set up to mark a field of scientific endeavour that is overlooked by the Nobel Prizes.
In its citation for the £480,000 prize, the academy said their theorem "is one of the great landmarks of 20th Century mathematics, influencing profoundly many of the most important later developments in topology, differential geometry and quantum field theory".
In the spotlight
Sir Michael, 75, works out of Edinburgh University, and Singer, 79, is attached to the Massachusetts Institute of Technology.
The rules of nature can be expressed by differential equations, which are mathematical formulae based on rates of change.
These formulae can have and indices, which in the Atiyah-Singer theorem can be calculated in terms of the geometry of the surrounding space.
The mathematicians' contribution is said to have given modern theoretical physics a new tool to describe the forces and particles at work in the Universe. So-called superstring theory, which seeks to unify scientific understanding of all forces and all matter, is said to have been a great beneficiary of the work.
"I am delighted to win this prize with Sir Michael," Professor Singer said. "The work we did broke barriers between different branches of mathematics and that's probably its most important aspect.
"It has also had serious applications in theoretical physics. But most of all I appreciate the attention mathematics will be getting. It's well-deserved because mathematics is so basic to science and engineering."
Sir Michael was president of the Royal Society, the UK's academy of science, in the early 1990s. The present president, Lord May, said: "Sir Michael's outstanding achievements as a Mathematician have been recognised through an enviable array of awards and medals.
"The Abel Prize, effectively the Nobel for Mathematics, places him, quite rightly, at the top of his field on the international stage."
The prize is named after the brilliant Norwegian mathematician Niels Henrik Abel, who died in 1829, and was created in 2002.
The first prize, awarded last year, went to French mathematician Jean-Pierre Serre for his role in shaping algebraic geometry and number theory.
This year's prize is to be presented by Norway's King Harald at a May 25 ceremony in Oslo.