Mathematicians Hillel Furstenberg and Gregory Margulis have jointly won the 2020 Abel prize for their pioneering use of methods from probability and dynamics in other mathematical fields such as group theory, number theory and combinatorics.
Furstenberg, at Hebrew University of Jerusalem in Israel, and Margulis, at Yale University, have never formally collaborated, but both invented similar 鈥�random walk鈥� techniques to study various mathematical objects. They share a 7.5 million Norwegian kroner (拢595,000) prize.
鈥淚 received this notice with total disbelief,鈥� said Furstenberg, when told he had won. 鈥淥ne never knows what the impact of one鈥檚 work will be.鈥�
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A random walk is a path consisting of a succession of random steps 鈥� for example, the route a person walking through a city would take if they flipped a coin at every crossing to decide whether to go left or right.
They can be useful for modelling a range of phenomena, such as variations in stock prices, the behaviour of gas molecules or the pattern of firing neurons. 鈥淧art of the beauty of mathematics is the way that ideas from different fields come together,鈥� said Furstenberg.
Furstenberg and Margulis have both shown how the behaviour of random walks reveals properties about the structure of mathematical objects such as groups, which are collections of objects linked together by particular rules. Random walks can help explore very large groups that might otherwise be difficult to study.
The Abel Committee awarded Furstenberg and Margulis the prize for the surprising connections their work has revealed between different mathematical fields.
鈥淭hey have demonstrated the ubiquity of probabilistic methods and the effectiveness of crossing boundaries between separate mathematical disciplines, such as the traditional dichotomy between pure and applied mathematics,鈥� said the chair of the Abel Committee, Hans Munthe-Kaas, when announcing the prize via live stream.
The Norwegian government established the Abel prize in 2002, on the 200th anniversary of the birth of mathematician Niels Henrik Abel.
Last year, the prize was awarded to Karen Uhlenbeck, the first female laureate. Other previous winners include Andrew Wiles for his proof of Fermat鈥檚 last theorem, and game theorist John Nash, of A Beautiful Mind fame.
