Hyderabad: Stanley J. Osher, is not your stereotypical mathematician—serious-looking, immersed in abstraction. Having co-founded three companies in 22 years, based largely on his own research, Osher is a mathematician and an entrepreneur, who, in a plenary lecture on 25 August, is going to tell the 3,000-plus mathematicians gathered at the International Congress of Mathematicians (ICM) in Hyderabad how “fast” algorithms are going to rock the world.
Osher, whose firms Cognitech Inc., Luminescent Inc., and Level Set Systems Inc. are all solving real world problems, says it’s an “incredible time for mathematicians”. His and others’ work in “level set” theorems, which enable capturing moving images into math models, have led to applications that were unthinkable before.
“The whole industry of graphics in movies is using these algorithms,” says Osher, director of applied mathematics at the University of California in Los Angeles. Titanic was the last movie to use old-fashioned technology of simplified physical models. The special effects of the recent 3D movie Avatar owe their brilliance to level-set algorithms, he adds.
Osher’s message to mathematicians isn’t formulaic: fast algorithms can analyse data in a variety of sectors, from better medical imaging with reduced radiation dosage to spectral imaging in military applications.
In the financial world, quants have already shown what analytics can do. Now, say experts, it’s other businesses, from advertising to banking, that are increasingly relying on math to understand consumer behaviour.
This year’s Rolf Nevanlinna Prize winner Daniel Spielman of Yale University, whose interest lies at the intersection of computer science and mathematics, has also designed “fast” algorithms. His work on “error correcting codes” (ECC), which leads to better ways of transmitting and storing digital information, led his colleagues to set up a company called Digital Fountain Inc.
In a medium where even a speck of dust can wipe out thousands of bits of data, says Spielman, ECC ensures safety by adding redundancy.
What Osher and Spielman epitomize is the applied side of mathematics, a discipline, which mathematician Sujatha Ramdorai at the Tata Institute of Fundamental Research in Mumbai, says is “totally missing from the Indian mathematics community, focused as it is on pure math”.
“We need to have these new fields, at the interface of economics, social sciences and biology,” says Ramdorai.
Incidentally, even applying mathematics to studying human behaviour or financial market hasn’t caught the imagination of mathematicians in India. It’s a branch of science that Alberto A. Pinto’s research, to be presented at ICM, represents very well. Work by Pinto, a mathematician at the University of Porto, Portugal, shows how models can simulate group behaviour—a tool that can help authorities to track social deviants, and, say, prevent a riot or a terrorist attack.
Another of Pinto’s models looks at stock market indices and provides a “probability distribution of market returns”. The genesis of this model lies in the probability distribution found in the natural world, such as in sunspots or in river heights, which Pinto found to be same as in stock market indices.
Math today has direct applications and the Indian community needs figureheads such as Osher, Spielman or Pinto, says Ramdorai. “I think the (new) Indian Institutes of Science Education and Research are the best places to start such disciplines,” she adds and as a former member of the National Knowledge Commission, she has recommended this to the government.
As mathematicians get their hands on flows of data, using algorithms to model people as shoppers, voters and workers, many, if not most, experts gathered in Hyderabad say it’s a great time to be a math graduate. Osher refers to a recent survey in the US, published in The Wall Street Journal, where mathematicians ranked the highest in terms of job satisfaction.
Mathematician G. Rangarajan of the Indian Institute of Science says not a week passes by when he doesn’t get a call from some financial services firm looking for math postgraduates or doctorates. “We just need to get more students and faculty in math,” he adds.
So much for applied math and the way it’s hitched to business. But can math ever solve the larger question of consciousness? Or, model human evolution?
Stanislav Smirnov, one of the winners of 2010 Fields Medal, says it is conceivable to think mathematicians can model evolution: earlier, biologists constructed the tree of life by hand, now they use computation.
However, it’s in the understanding of another puzzling problem—human consciousness—that mathematicians seem to give up.
“It’s beyond our wildest dreams. Since there’s no way of detecting or defining it (consciousness), it remains beyond the scope of math,” says Spielman.
But Smirnov doesn’t seem to have given up entirely and wonders “if there’s an abstract explanation” for consciousness. “(An) abstract explanation means you can apply mathematics,” he says.