YAKOV SINAI, a professor of Maths at Princeton University since 1993, has just been awarded this year’s Abel Prize for his work on dynamical systems, ergodic theory and mathematical physics. The 6,000,000 Norwegian krone ($990,000) prize, given by the Norwegian Academy of Sciences and Letters, recognises excellence in the field of mathematics. Professor Sinai is being lauded for theories that blur the everyday distinction between "deterministic" and "random" behaviour in dynamical systems. Babbage has conducted some hasty homework to try and explain this in other terms.

A dynamical system is one whose state changes over time according to a fixed rule. Defining it means stating where it starts—the “initial position”—and how it evolves over time. If both are known exactly, then the entire future of the system is determined. Often, though, they are not, particularly when the dynamical system is real-world, for example the evolution of a colony’s population, the density of a chemical in a solution or the way the weather alters. Small changes to the initial conditions can pile up as the process plays out, meaning that eventually the outcome becomes unpredictable—even though no randomness is involved.

One approach to reducing this uncertainty would be to seek ever-greater accuracy in stating the initial positions. To use a cricketing analogy, imagine a batsman hitting a ball. In principle, the more you know about the speed with which the ball was travelling, the exact angle with which it struck the bat, and so on, the more precise the predictions you could make about where in the pitch it would end up.

But Professor Sinai found that a more fruitful approach would be to work backwards, allowing the dynamical system to play out over and over again, looking for patterns in the outcomes. He may or may not be a cricketing man: he illustrated his theories with the example of a billiard ball bouncing off the edge of a table.

A player strikes a ball with the aim of causing a series of collisions which result in the final ball being potted. The system is deterministic: if you know the position of every ball and the speed and angle of the cue at every strike, the outcome can be foreseen. But that is so unfeasible that it is more helpful to consider all possible outcomes, divide them into similar groups and calculate the probability of a given outcome landing in each of them. This may be done by computer modelling: running the dynamical system over and over again so as to build up a picture of the achievable end states—and how likely the outcome is to be in each group.

Born in Russia, Professor Sinai earned a doctorate in maths from Moscow State University in 1963. He has published over 250 research papers and several mathematical models are named after him: Sinai's billiards, Sinai's random walk, Sinai-Ruelle-Bowen measures, and Pirogov-Sinai theory. He will receive the Abel Prize from Norway’s Crown Prince at a ceremony on May 20th.