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Why maths matters

Artur Avila, a Brazilian based in France; Martin Hairer, an Austrian based in Great Britain; Manjul Bhargava, a Canadian and Maryam Mirzakhani, an Iranian, both based in the US. The four mathematicians awarded the Fields Medal last week could be cited by advocates for open immigration policies. But they have also set new precedents. Mr Avila is the first Latin American recipient. Ms Mirzakhani is the first woman, and the first Iranian. Mr Bhargava is of course, being joyously feted as the first “desi” – even if he is not, technically, Indian.

The Fields, officially the International Medal for Outstanding Discoveries in Mathematics, is given every four years by the International Mathematical Union. The endowment by Canadian mathematician John Charles Field is modest, and the cash award amounts only to Canadian $ 15,000. There is also the stipulation that a recipient must be under the age of 40 on January 1 of the year the award is handed out, to encourage further work. This is in spite of the fact that, in general, mathematicians tend to do their best work long before middle age. Alfred Nobel was more interested in practical applications, which is why he did not endow a maths prize. The Fields is usually seen as the equivalent in terms of prestige. In fact, no matter how “abstract” pure mathematics seems, it tends to find practical applications, sooner or later. That’s because mathematical logic underpins all natural phenomena and processes. Mr Bhargava, for example, has already caused multiple headaches to cryptographers because his work provides much new insight into the underpinning of cryptographic methods. Ms Mirzakhani’s explorations of Riemann geometries could conceivably lead to a new understanding of the energy levels of nuclear particles. Mr Hairer’s work in stochastic differential equations may be key to a better understanding of financial derivatives – as well as in the construction of heat-shields for spacecraft. Mr Avila’s work in chaos theory has applications in the modelling of climate change and of epidemics.

Mr Bhargava is not the only desi mathematician to win recent recognition. Subhash Khot, another Indian based in the US, won the Rolf Nevanlinna Prize, at the same IMU conference. Mr Khot was awarded for his “prescient definition of the ‘Unique Games’ problem”. His work finds application in judging the probable computational complexity of certain types of problems. India has an ancient, if unstructured tradition, of mathematical research. It started with the famed discovery of the zero, which could be more properly described as the development of a positional number system. Down the centuries, Indian mathematicians have discovered many interesting theorems. They investigated the properties of numbers, discovered some infinite series, solved difficult problems in spherical trigonometry and also did some integral calculus. And, of course, the peerless genius of Srinivasa Ramanujan stunned Cambridge in the early 20th century as he generated a stream of incredible results.

A string of recent prizes and awards designed to reward pure maths research indicates that the world is coming to understand how important this is. In India, the Infosys Foundation has an award and the Shanmugha Arts Science Technology Research Academy (SASTRA) from Ramanujan’s hometown of Kumbakonam makes the Ramanujan Award (Mr Bhargava is a recipient of both). Norway offers the Abel Prize. The Clay Mathematics Institute of Cambridge, Massachusetts, has million-dollar awards for the solution of seven specified “Millennium problems”. (Mr Bhargava and Ms Mirzakhani are potential front-runners to solve at least two of those.) The Russian entrepreneur Yury Milner has teamed up with Mark Zuckerberg and Sergei Brin for the new “Fundamental Mathematics” prize of $ 3 million, to be awarded from 2015. These new incentives will hopefully inspire more children to consider pure research as a career. The world depends on technology – and technology depends on maths. What is more, maths that seems utterly obscure and abstract can suddenly become essential. Nurturing the gifted and giving them an atmosphere conducive to pure research could turn out to be mission-critical for civilisation.

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