Abel Prize: Dennis Sullivan, who is able to see abstract worlds in his mind, wins the Nobel Prize in Mathematics | to know

One day in 1966 an intellectual shipwreck occurred in the North Sea. American mathematician Dennis Sullivan I was on a ship bound for Scandinavia and took advantage of the time to try and solve a diabolical problem with pen and paper in a space of unimaginable eight dimensions. He was 25 years old and had an exceptionally bubbly brain, but he stumbled upon an unexpected result. in a fit, He threw his notebook into the sea, but immediately continued to think and persevere. This Wednesday, Sullivan, born in Port Huron 81 years ago, won the Abel Prize, was awarded 775,000 euros and considered the Nobel Prize in Mathematics.

This young researcher focused on topology, the branch of mathematics that studies the invariant properties of things that deform. In the classic example, a circular cake balloon can be crushed into many configurations, but it can never be spherical. Its fixed property is to have a hole. This is why mathematicians often joke that, for a topologist, cup and donuts They are similar. Sullivan, of the State University of New York at Stony Brook, is one of the best topologists of the last century. He excelled in classifying highly complex structures, in spaces of many dimensions.

Spanish mathematician Daniel Peralta met Sullivan at Stony Brook in 2014 and has been in touch with him ever since. “He is one of the few mathematicians who, within their mind, is able to see worlds that are, for most people, just a series of symbols. Peralta, of the Institute of Mathematical Sciences in Madrid, explains a mental image of things much more abstract than the most common geometric ones.

Dennis Sullivan is one of the few mathematicians who, within his mind, is able to see worlds that are, for most people, just a series of symbols.

Daniel Peralta, mathematician

The Norwegian Academy of Sciences and Letters, which awards the Abel Prize, emphasized in a statement that Sullivan repeatedly jumped between various branches of mathematics, such as algebra and geometry, building unprecedented bridges between them. As if the same talented musician plays electric guitar, harpsichord, oboe, flamenco cajon, ukulele and military trumpet. I made this jumble symphonies The math is unmistakable, Peralta emphasizes. “His way of understanding problems is very peculiar, very original, and he does not follow the usual paths,” the Spanish researcher praises.

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Sullivan revamped topology in his twenties and condensed his ideas into a research paper in June 1970, while researching at the Massachusetts Institute of Technology (MIT). He never published these papers, but his colleagues began to copy them and circulate them around the world, in copies increasingly difficult to read, but which preserved an aura of sacred text.

Known as the MIT notes It was finally published in 2005. British mathematician Andrew Ranicki Then he commented that those copies, alien to the official culture, were translated into Russian and published in the Soviet Union in 1975, as a kind of samizdat, Secret Editions of Works Prohibited by the Communist Dictatorship. “The translation did not include the jokes and other unimportant material that moved the English version,” Raneki said in a 2005 publication introduction.

Sullivan is also the author of the theory of laminated cycles, according to Daniel Peralta, who recalls his results regarding geodesic lines: the shortest path between two points on a curved surface. “The question is when mechanical motion optimizes distances, when it follows the shortest paths with respect to a given scale, which may not be the usual scale of space. Sullivan, with his theory, is able to describe these geodesic fields,” explains Peralta.

The Norwegian Academy lauds that the American mathematician “repeatedly changed the landscape of topology,” introducing new concepts. Sullivan wanders into abstract worlds, but the foundation asserts that tools for measuring the properties of deformable objects “have been of immeasurable value in all branches of mathematics and in other fields, with notable applications in physics, economics, and data science.”

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Peralta says Sullivan is a mathematician on the board who enjoys discussing ideas with colleagues with chalk in hand. Moreover, in recent years, it has faced great mathematical challenges to try to save human lives. In 2014, after winning Balzan Prize worth over €700,000, announced that it will put together a team of young researchers to fine-tune complex theoretical algorithms, in order to try to predict phenomena such as the behavior of hurricanes and the dispersal of pollutants by wind. “It’s remarkable and exciting that these problems are still mathematically intractable,” said Sullivan, who is still going strong more than half a century after putting his first ideas at sea.

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