Mathematicians have used pictures to solve equations ever since Pythagoras cooked up his famous theorem, but it wasn't until the 20th century that the deep links between shapes and sums really came into their own with the blossoming of algebraic geometry.
Now Pierre Deligne of the Institute for Advanced Study in Princeton, New Jersey, who played a crucial role in linking algebraic geometry to other areas of mathematics, has won the $1 million Abel prize, awarded by the Norwegian Academy of Science and Letters.
"I was very surprised," he said following the announcement. "I feel this money belongs to mathematics more than me, but I have no idea how to use it in a way that is useful for mathematics."
Algebraic geometry turns out to have connections to important problems such as Fermat's Last Theorem. Deligne is best known for using it to prove the last, and most fiendish, of the Weil conjectures, a series of four statements proposed in 1949 by André Weil.
The statements concerned polynomial equations, for example, x² - y² = 3. Such equations would normally have an infinite number of solutions, but Weil was interested in the problem of how to solve this kind of equation within number systems that have only a limited number of values, known as finite fields.
Shape-shifting trick
He suggested that the number of possible solutions in each finite field could be described by counting particular points on a related shape, which is done using another equation called a zeta function. (A similar equation is believed to help count the prime numbers, though whether it does is a famous unsolved problem called the Riemann hypothesis, itself worth $1 million to anyone that solves it).
Weil made four statements about the zeta function: proving these true was a way to confirm that the zeta function was indeed the correct way to tackle polynomial equations within finite fields.
The next decade or so saw proofs of three of the statements, but the last and most difficult remained. Mathematicians knew that finding something called a cohomology, a kind of classification system for distinguishing similar shapes, would crack the problem, but showing that a particular comohology was the one needed to probe Weil's remaining conjecture was tricky.
Deligne was finally able to do so in 1974, winning him the Fields medal in 1978 – another prestigious award that is only given to mathematicians under the age of 40, every four years.
"That completed one of the big stories of 20th-century mathematics," says Timothy Gowers of the University of Cambridge, who gave a presentation about Deligne's work following the Abel prize announcement and called him "one of the absolute all-time greats".
The proof of the last Weil conjecture, along with much of Deligne's other work, provided mathematicians with important tools in algebraic geometry that are still yielding important results. Ngô Bảo Châu, who won the Fields medal in 2010 relied on Deligne's tools to prove an important result linking elements of algebra with number theory. "His name pops up all over the place," says Gowers.
Coverage of other recent Abel prizewinners:
2012: Pattern master wins million dollar mathematics prize
2011: Exotic sphere discoverer wins mathematical Nobel
2010: Prizewinning math could reveal hidden patterns in primes
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Mirrored photo of Pierre Deligne in 2005 

The  awarded Belgian mathematician Pierre Deligne with  of 2013 for his contributions toward shaping . The award includes a 6 million  (1,026,000, 793,000) prize. , a mathematician from , announced the award in Oslo yesterday.

The Academy gave the award to Deligne for "seminal contributions to algebraic geometry and for their transformative impact on number theory, representation theory, and related fields".

For example, in 1974, Pierre Deligne did a mathematical proof of fourth , one of properties of . This concept is related to analysis of the  and the currently unsolved . During the proof of the Weil conjecture, a concept of  l-adic  was introduced.

Pierre Deligne said, "The nice thing about mathematics is doing mathematics. The prizes come in addition".