Moving with efficiency

Beautiful minds attract big awards

How to move a heap of dirt from one place to another with the least amount of work

Two MSI mathematicians have solved an elusive 200-year-old mathematical puzzle that centres on the Monge-Ampere equation. Neil Trudinger and Xu-Jia Wang also won prestigious awards for their wider body of work on second order elliptic partial differential equations.

“The Monge-Ampere equation has widespread applications,” says Wang. “They include the optimisation of public transport systems, tracking the flow of blood through the body, working out the distribution of matter in the universe and tracing the flow of money in financial markets.”

The Monge problem is a special case of an optimal transportation problem, formulated in 1781 – how to move a heap of dirt from one place to another with the least amount of work.

“Our paper was attempting to simplify an old 1970s solution but, because of the flaws in the original, we were, in fact, solving it for the first time,” says Trudinger, a Fellow of the Australian Academy of Science and of the Royal Society of London. An American team also came up with a solution about the same time.

Trudinger has won the American Mathematical Society’s Leroy P. Steele Prize for Mathematical Exposition for his research monograph, Elliptic Partial Differential Equations of Second Order, co-authored with colleague, the late David Gilbarg.

Meanwhile, Wang, has won the prestigious 2007 Morningside Gold Medal of Mathematics from the International Congress of Chinese Mathematicians, an honour that ranks him alongside some of the world’s leading mathematicians. The theoretical mathematicians often don’t hear of new applications of their work until years after they have published it. In this case, due to the breadth of applications of the Monge-Ampere equations, Wang has already used some of their ideas for a new algorithm for antenna design.

Updated:  22 February 2018/Responsible Officer:  Director/Page Contact:  School Manager