**PARIS** — Find the distribution of random paths on a directed graph. Of course, when you say it like that, such a problem will hardly excite the masses. But if you had managed to find this mysterious distribution, you would have obtained the PageRank algorithm. And if you have PageRank, you have Google, now the world's most valuable company, ahead of Apple.

What still was, 20 years ago, an obscure startup founded by two young Stanford students has become *the *undisputed symbol of the leading role played by mathematics in the modern economy in general, and in the digital economy in particular. "Digital has multiplied by 10, by 100, the impact power of mathematics," says Cédric Villani, director of the Henri Poincaré mathematics research Institute, and winner of the 2010 Fields medal, the highest honor in the field.

In the late 1980s, French mathematician Yves Meyer founded and developed the modern wavelet theory, opening up a new chapter in signal processing. A generation of brilliant young scientists followed in his footsteps; among them is Stéphane Mallat. It didn't take Mallat long to understand how wavelets could be useful in compressing high-definition images. This led to the creation of Let it Wave, one of the French gems of the 2000s. Unfortunately, the elites of the French economy weren't curious enough about mathematics, and Mallat had to sell his startup to a Silicon Valley-based company, Zoran Corporation, in 2008.

But Villani wants to believe that such a mistake wouldn't happen again. "Conceptions have evolved since then," he says. "There's been, without a doubt, a realization of the importance of mathematics in the digital economy."

This wake-up can be partly linked to a recent study on the socio-economic impact of mathematics in France, published in May 2015, which revealed, among other things, that math directly impacts 9% of jobs and 15% of the French GDP.

The coming of the digital age, illustrated by the influence of the Silicon Valley and the rise in power of the GAFA (Google, Apple, Facebook, Amazon), has shone fresh light on algorithms, a discipline that sits where math and computer science meet. But even more important has been the exponential growth in the actual quantity of digital data — the much talked about Big Data — that raises the influence of mathematics on the economy.

"We can see that the amount of data seems to follow a sort of 'new Moore's Law.' It's been doubling every two years, meaning that the human race has produced as much data over the past two years as during all the years before that — and that amount will again have doubled in two years' time," explains Villani. "But the question that's on the mind of every company's boss: How will this torrent of data help me better target and satisfy my customers, better adapt my products or services?"

Hence the strategic importance taken on by data mining and data scientists. Their role is to determine the set of parameters on which the real interest variables depend, to identify which of the existing correlations are just artifacts, etc. In other words, their job is to make a mountain of figures talk." It's no coincidence that the American company CareerCast, a job database site, ranked data scientist as the best job for 2016.

The French study on the socio-economic impact of mathematics also noted the importance of data mining by placing it in the top five list of the "major competency fields of mathematics" for the future of the economy, alongside signal and image analysis, modeling-simulation-optimization, high-performance computing and cryptography.

Long gone are the days when the best young mathematicians would choose to go into finance to develop more and more sophisticated products, the same ones that led to the subprime crisis of 2007-2008 and earned these mathematicians a thrashing in the media. "Finance is no longer the main hotbed for mathematicians," says Villani. He cites the example of modelling-simulation-optimization (MSO), where partial differential equations are used in all industries that have complex problems which must be modeled, such as fluid mechanics in aeronautics.

But the digital economy isn't the only sector being taken over by math and mathematicians. Health care is also getting increasingly math-heavy. Biology, which is particularly affected by the issue of Big Data, has long been employing bio-statisticians and specialists in mathematical modeling.

The advances enabled by this growing interweaving often take unexpected turns. At the last International Congress of Mathematicians in Seoul, in 2014, Frenchman Emmanuel Candès, now a professor at Stanford, mentioned an unexpected prospect of mathematical research. He explained to his peers that the so-called "sparsity" method, which is the core of the dozens of algorithms that enable Netflix and others to personalize their recommendations, could also be used to reduce the amount of time a patient needs to stay attached to a scanner, and therefore reduce the amount of radiation they're exposed to.

This is just one of many real-world examples of what mathematicians, for too long locked up in their ivory tower, can help provide to society.

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