Tag Archives: Mathematics

Mathematical Model Reveals the Patterns of How Innovations Arise

Innovation is one of the driving forces in our world. The constant creation of new ideas and their transformation into technologies and products forms a powerful cornerstone for 21st century society. Indeed, many universities and institutes, along with regions such as Silicon Valley, cultivate this process.

And yet the process of innovation is something of a mystery. A wide range of researchers have studied it, ranging from economists and anthropologists to evolutionary biologists and engineers. Their goal is to understand how innovation happens and the factors that drive it so that they can optimize conditions for future innovation.

This approach has had limited success, however. The rate at which innovations appear and disappear has been carefully measured. It follows a set of well-characterized patterns that scientists observe in many different circumstances. And yet, nobody has been able to explain how this pattern arises or why it governs innovation.

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In Noisy Equations, One Who Heard Music/Experts say Martin Hairer’s epic masterpiece in stochastic analysis “created a whole world.”


Martin Hairer’s masterwork is so fantastic, so fully baked and so far out of left field, one fellow mathematician declared, that the manuscript must have been downloaded into his brain by a more intelligent alien race.

Another compared the 180-page treatise to the “Lord of the Rings” trilogy because it “created a whole world.” Few could recall another time in modern history when such a magnificent theory had emerged predominantly from the mind of a single person.

As for the researchers who have striven for decades to fathom the strange equations addressed by his theory, “He’s taken them all to the cleaners,” said Terry Lyons, a mathematician at the University of Oxford in England.

The Tolkienesque paper, published online in the journal Inventiones Mathematicae in March, is only the latest and greatest in a series of feats by the 38-year-old Hairer, who has frequently stunned colleagues with the speed and creativity of his work. But if you were to take a seat next to Hairer at the pub near his home in Kenilworth, England, you might have a nice chat with him without ever suspecting the gangly, genial Austrian is one of the world’s most brilliant mathematicians.

“Martin likes to talk to people; people like to talk to him,” said his wife, the mathematician Xue-Mei Li. He is good-natured, knowledgeable and calm, she said — “and funny enough.”

Today, Hairer is one of four recipients of the 2014 Fields Medal, announced on the International Mathematical Union’s website and presented at the opening ceremony of the International Congress of Mathematicians in Seoul, South Korea. The Fields is widely viewed as the highest honor a mathematician can receive. Hairer, a professor at the University of Warwick in England, has been regarded since his late 20s as a leading figure in stochastic analysis, the branch of mathematics dealing with random processes like crystal growth and the spread of water in a napkin. Hairer’s colleagues particularly note his rare mathematical intuition, an ability to sense the way toward grand solutions and beautiful proofs.

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