Stanford's Maryam Mirzakhani wins Fields Medal Stanford Report, August 12, 2014 Stanford's Maryam Mirzakhani wins Fields Medal Maryam Mirzakhani is the first woman to ever win the Fields Medal – known as the "Nobel Prize of mathematics" – in recognition of her contributions to the understanding of the symmetry of curved surfaces. By Bjorn Carey Maryam Mirzakhani, a professor of mathematics at Stanford, has been awarded the 2014 Fields Medal, the most prestigious honor in mathematics. Mirzakhani is the first woman to win the prize, widely regarded as the "Nobel Prize of mathematics," since it was established in 1936. Courtesy of Maryam Mirzakhani Maryam Mirzakhani was awarded the Fields Medal for her sophisticated and highly original contributions to the fields of geometry and dynamical systems. "This is a great honor. I will be happy if it encourages young female scientists and mathematicians," Mirzakhani said.

"I am sure there will be many more women winning this kind of award in coming years." Officially known as the International Medal for Outstanding Discoveries in Mathematics, the Fields Medal will be presented by the International Mathematical Union on Aug. 13 at the International Congress of Mathematicians, held this year in Seoul, South Korea. Mirzakhani is the first Stanford recipient to win this honor since Paul Cohen in 1966. The award recognizes Mirzakhani's sophisticated and highly original contributions to the fields of geometry and dynamical systems, particularly in understanding the symmetry of curved surfaces, such as spheres, the surfaces of doughnuts and of hyperbolic objects. Although her work is considered "pure mathematics" and is mostly theoretical, it has implications for physics and quantum field theory. “On behalf of the entire Stanford community, I congratulate Maryam on this incredible recognition, the highest honor in her discipline, the first ever granted to a woman,” said Stanford President John Hennessy . "We are proud of her achievements, and of the work taking place in our math department and among our faculty. We hope it will serve as an inspiration to many aspiring mathematicians." 'Like solving a puzzle' Mirzakhani was born and raised in Tehran, Iran.

As a young girl she dreamed of becoming a writer. By high school, however, her affinity for solving mathematical problems and working on proofs had shifted her sights. "It is fun – it's like solving a puzzle or connecting the dots in a detective case," she said. "I felt that this was something I could do, and I wanted to pursue this path." Mirzakhani became known to the international math scene as a teenager, winning gold medals at both the 1994 and 1995 International Math Olympiads – she finished with a perfect score in the latter competition. Mathematicians who would later be her mentors and colleagues followed the mathematical proofs she developed as an undergraduate. After earning her bachelor's degree from Sharif University of Technology in 1999, she began work on her doctorate at Harvard University under the guidance of Fields Medal recipient Curtis McMullen. She possesses a remarkable fluency in a diverse range of mathematical techniques and disparate mathematical cultures – including algebra, calculus, complex analysis and hyperbolic geometry. By borrowing principles from several fields, she has brought a new level of understanding to an area of mathematics called low dimensional topology.

Mirzakhani's earliest work involved solving the decades-old problem of calculating the volumes of moduli spaces of curves on objects known as Riemann surfaces. These are geometric objects whose points each represent a different hyperbolic surface. These objects are mostly theoretical, but real-world examples include amoebae and doughnuts. She solved this by drawing a series of loops across their surfaces and calculating their lengths. "What's so special about Maryam, the thing that really separates her, is the originality in how she puts together these disparate pieces," said Steven Kerckhoff, a mathematics professor at Stanford and one of Mirzakhani's collaborators. "That was the case starting with her thesis work, which generated several papers in all the top journals. The novelty of her approach made it a real tour de force." Pure mathematics From 2004 to 2008, she was a Clay Mathematics Institute Research Fellow and an assistant professor at Princeton University. In 2008, she became a professor of mathematics at Stanford, where she lives with her husband and 3-year-old daughter. Mirzakhani's recent research further investigates the symmetry of surface geometry, particularly within theories regarding Teichmüller dynamics.

In general, her work can best be described as pure mathematics – research that investigates entirely abstract concepts of nature that might not have an immediately obvious application. "Oftentimes, research into these areas does have unexpected applications, but that isn't what motivates mathematicians like Maryam to pursue it. Rather, the motivation is to understand, as deeply as possible, these basic mathematical structures," said Ralph Cohen, a professor of mathematics and the senior associate dean for the natural sciences in Stanford's School of Humanities and Sciences. "Maryam's work really is an outstanding example of curiosity-driven research." The work, however, could have impacts concerning the theoretical physics of how the universe came to exist and, because it could inform quantum field theory, secondary applications to engineering and material science. Within mathematics, it has implications for the study of prime numbers and cryptography. Despite the breadth of applications of her work, Mirzakhani said she enjoys pure mathematics because of the elegance and longevity of the questions she studies. "I don't have any particular recipe," Mirzakhani said of her approach to developing new proofs. "It is the reason why doing research is challenging as well as attractive.

It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out." Editor's Note Maryam Mirzakhani will not be entertaining any interview requests at this time. Please send all media inquiries to Bjorn Carey, science information officer at the Stanford News Service. Ralph Cohen, a professor of mathematics and the senior associate dean for the natural sciences in Stanford's School of Humanities and Sciences, will be available for interviews. Arrangements can be made through Bjorn Carey, (650) 725-1944; bccarey@stanford.edu .

Maryam Mirzakhani Becomes First Woman To Win Prestigious Fields Medal | The Huffington Post Maryam Mirzakhani Becomes First Woman To Win Prestigious Fields Medal 08/13/2014 09:19 am ET | Updated Aug 13, 2014 1.4k Philip Ball Courtesy of Maryam Mirzakhani The International Mathematical Union (IMU) has revealed on its website the winners of the 2014 Fields medals, considered the highest honor in mathematics. The four young medallists — including Maryam Mirzakhani, the first female winner since the prizes were established in 1936 — have been selected for their contributions to topics ranging from dynamical systems to the geometry of numbers and the solution of equations of the type that describe many physical phenomena. The IMU had planned to publicly announce the names on 13 August in Seoul at the International Congress of Mathematicians , but — owing presumably to a technical glitch — the page with the announcement was already live on the organization's website in 12 August. The Wikipedia pages for the winners appeared to have been updated anonymously on the same day after 18:00 London time.

In addition to the medal itself, the Fields Institute, based in Toronto, awards each winner CAN$15,000 (US$13,700) in cash. The prizes are given to researchers aged 40 years or younger every four years. Although the prizes recognize outstanding achievement in the early stages of a career, they are also seen as an indicator of mathematicians to watch in the future. A native of Iran, Maryam Mirzakhani is at Stanford University in California. She won for her work on “the dynamics and geometry of Riemann surfaces and their moduli spaces.” “Perhaps Maryam's most important achievement is her work on dynamics,” says Curtis McMullen of Harvard University. Many natural problems in dynamics, such as the three-body problem of celestial mechanics (for example, interactions of the Sun, the Moon and Earth), have no exact mathematical solution. Mirzakhani found that in dynamical systems evolving in ways that twist and stretch their shape, the systems' trajectories “are tightly constrained to follow algebraic laws”, says McMullen.

He adds that Mirzakhani’s achievements “combine superb problem-solving ability, ambitious mathematical vision and fluency in many disciplines, which is unusual in the modern era, when considerable specialization is often required to reach the frontier”. The other three winners of the Fields Medals were: Artur Avila of the Institute of Mathematics of Jussieu in Paris, whose “profound contributions to dynamical systems theory have changed the face of the field”. Dynamical systems evolve over time, often in complex ways: they include celestial mechanics (the orbits of bodies in the Solar System); financial markets; the weather; and populations in ecosystems. Some of these systems exhibit chaotic behavior: their state at some future time cannot be predicted from their state at an earlier time, because imperceptible differences that exist now can cause big divergences later. Avila is a problem-solver who has worked on many aspects of this field. According to mathematician Étienne Ghys of the École Normale Supérieure in Lyon, France, “he didn’t just do one or two things, but has an incredible number of achievements”.

Avila has contributed in particular to complex one-dimensional dynamics — how a mathematical function with a single variable evolves when the solution is “fed back” into the function as the next value of the variable in an iterative process. This is how some fractal mathematical objects, such as the Mandelbrot set — a set of complex numbers for which a particular iterated equation does not approach infinity — are generated. Avila has also looked at the Schrödinger equation of unusual quantum systems, although Ghys attests that his motivation is more mathematical than physical. Manjul Bhargava of Princeton University in New Jersey, who “has developed powerful new methods in the geometry of numbers”. The geometry of numbers is a method for estimating how many points with integer coordinates (meaning their coordinates are whole numbers) are contained in a region of space of a given volume. “Bhargava has added a host of new techniques to this subject,” says Benedict Gross of Harvard University in Cambridge, Massachusetts.

“His style is completely original, and combines the three main areas of pure mathematics — algebra, geometry and analysis — in a beautiful way.” Gross says that one of Bhargava’s key results “gives an entirely new perspective on finding rational solutions [solutions that are ratios of integers] to cubic equations, a problem that goes back to the mathematics of antiquity”. Bhargava says that the award is “a source of encouragement and inspiration, hopefully also for my students, collaborators and colleagues”. Martin Hairer of the University of Warwick, UK, who “has made outstanding contributions to the theory of stochastic partial differential equations”. Partial differential equations (PDEs), which describe the evolution of quantities that depend on several different variables, crop up throughout science — from quantum physics to the propagation of heat. PDEs are stochastic if they include some element of randomness. By developing methods for systematically solving such equations, Hairer’s work “allows one to give a rigorous meaning to a bunch of stochastic PDEs”, says Ofer Zeitouni of the University of Minnesota in Minneapolis. The award is “an extraordinary recognition and I am very humbled by it”, says Hairer.

“It still doesn’t quite feel real, even though I’ve known about it for almost half a year now.” In addition to the Fields medals, the IMU awarded other prestigious prizes. These include: The Nevanlinna Prize for outstanding contributions in mathematical aspects of information sciences is awarded to Subhash Khot of New York University for his work contributing to the approximate solution of 'hard' optimization problems (those for which no reasonably fast algorithm exists that gives exact solutions), and in particular for identifying 'unique games'. Khot explains that the unique games problem can be considered to describe “a strange society” where people have unequal status but are happy if their own inequality doesn’t exceed some precise limit. The central problem is whether you can arrange people’s status to please everyone. He formulated a conjecture, now named after him and yet unproven, according to which even if such a state exists, it is impossible to find an algorithm that gets anywhere near it — one that makes people even a little bit happy. The value of the conjecture is that if it is hard to approximate the unique games problem in this way, then many other important ‘hard’ problems of this kind cannot be approximated well either.

This breadth of implication was not something that Khot foresaw at the outset of his work: “I was quite hesitant in the beginning even to propose the conjecture,” he says. Khot “has a rare ability to get to the heart of the issue very quickly,” says Sanjeev Arora of Princeton University. The Gauss Prize for research that has had an impact outside mathematics is awarded to Stanley Osher of the University of California at Los Angeles, who has developed techniques for image processing and animation that enable complex objects to be approximated realistically, and for blurred or indefinite objects to be more sharply defined. As well as being valuable in fluid dynamics and aeronautical design, Osher’s work has been widely used in computer graphics and animation for depicting complex objects such as flames. His work “combines deep mathematical concepts with intuition from applications to design highly efficient computational tools”, says Chi-Wang Shu of Brown University in Providence, Rhode Island. Ingrid Daubechies, the president of the IMU, and South Korean president Park Geun-hye is to hand out the awards at the congress on 13 August.

In contrast to the Nobel Prizes, in which the world finds out right after the winners do, in this case the winners were told months in advance under strict secrecy, says Daubechies. “I called them on the phone in March, and during the phone conversation sent them email to show that this was indeed official and not a hoax.” This story originally appeared in Nature News . Also on HuffPost: Maryam Mirzakhani: World's Top Mathematics Prize 'Fields Medal' Awarded to Woman for First Time Maryam Mirzakhani: World's Top Mathematics Prize 'Fields Medal' Awarded to Woman for First Time August 13, 2014 11:46 BST Iranian mathematician Maryam Mirzakhani is the first woman to be awarded the prestigious Fields MedalStandford University A woman has been awarded the world's most prestigious honour in mathematics for the first time since the award was established in 1936. Maryam Mirzakhani, a professor of mathematics at Stanford University in California, has been awarded the 2014 Fields Medal, widely regarded as the "Nobel Prize of mathematics".

Mirzakhani was awarded the prize for her sophisticated and highly original contributions to the fields of geometry and dynamical systems. The award will be presented by the International Mathematical Union at a ceremony in Seoul on Wednesday morning. "This is a great honour. I will be happy if it encourages young female scientists and mathematicians," Mirzakhani said. "I am sure there will be many more women winning this kind of award in coming years." Officially known as the International Medal for Outstanding Discoveries in Mathematics, the Fields Medal is worth around £8,000. It is awarded to exceptional talents under the age of 40 once every four years and between two and four prizes are announced each time. "On behalf of the entire Stanford community, I congratulate Maryam on this incredible recognition, the highest honour in her discipline, the first ever granted to a woman," said Stanford President John Hennessy. "We are proud of her achievements, and of the work taking place in our math department and among our faculty.

We hope it will serve as an inspiration to many aspiring mathematicians." The award recognises Mirzakhani's contributions to the fields of geometry and dynamical systems, particularly in understanding the symmetry of curved surfaces, such as spheres, the surfaces of doughnuts and of hyperbolic objects. Although her work is considered "pure mathematics" it has implications for physics and quantum field theory. "What's so special about Maryam, the thing that really separates her, is the originality in how she puts together these disparate pieces," said Steven Kerckhoff, a mathematics professor at Stanford and one of Mirzakhani's collaborators. "That was the case starting with her thesis work, which generated several papers in all the top journals. The novelty of her approach made it a real tour de force." Mirzakhani was born and raised in Tehran, Iran. As a young girl she dreamed of becoming a writer, but her affinity for solving mathematical problems and working on proofs had shifted her sights. "It is fun – it's like solving a puzzle or connecting the dots in a detective case," she said.

Mirzakhani became known to the international math scene as a teenager, winning gold medals at both the 1994 and 1995 International Math Olympiads. Three other researchers were named Fields Medal winners at the same ceremony in South Korea. The winners include Martin Hairer, 38, an Austrian based at Warwick University, Artur Avila, of the Institute of Mathematics of Jussieu in Paris, and Manjul Bhargava, a 40-year-old Canadian-American at Princeton University. Christiane Rousseau, vice president of the International Mathematics Union, told the Guardian: "It's an extraordinary moment. Marie-Curie had Nobel prizes in physics and chemistry at the beginning of the 20th century, but in mathematics this is the first time we have a woman winning the most prestigious prize.

This is a celebration for women." Related Iranian Maryam Mirzakhani first woman awarded the Fields Medal for mathematics - The Science Show - ABC Radio National (Australian Broadcasting Corporation) Iranian Maryam Mirzakhani first woman awarded the Fields Medal for mathematics Image: Maryam Mirzakhani (Stanford News) Iranian woman Maryam Mirzakhani is the first woman to win the Fields Medal, known as the Nobel Prize of mathematics, in recognition of her contributions to the understanding of the symmetry of curved surfaces. The Prize was established in 1936. Maryam Mirzakhani, a professor of mathematics at Stanford University in California. The award recognizes Mirzakhani's sophisticated and highly original contributions to the fields of geometry and dynamical systems, particularly in understanding the symmetry of curved surfaces, such as spheres, the surfaces of doughnuts and of hyperbolic objects. Although her work is pure mathematics and mostly theoretical, it has implications for physics and quantum field theory. what are these? Transcript Robyn Williams: We have a breakthrough this week. When I called Stephanie Pradier in Melbourne to tell us about the news, she'd been awake for two days working on the Australian synchrotron.

Nonetheless she agreed immediately to get to work, and here's her report on what's happened for the first time. Stephanie Pradier: The mathematics community is abuzz this week. History has been made, and if you had had a dollar on it, you'd be a trillionaire. For the first time a woman has won the Fields Medal, regarded as the Nobel Prize of mathematics. Maryam Mirzakhani of Stanford University, California, was one of four people awarded with this prestigious prize in the South Korean capital Seoul on Wednesday morning. The Fields Medal is awarded every four years to at most four people, who must be under the age of 40. In the annals of its 78-year history, 55 men have accepted this honour. Now, this is not Maryam's first of firsts. In 1995 she became the first Iranian student to achieve a perfect score in the International Mathematics Olympiad. This was her second gold medal at the international competition for high school students. In 1994 she dropped one point. Many of Maryam's recent comments to Quanta magazine reveal her attitude towards creating mathematics.

In the article she says she was lucky to be a teenager in Tehran as the Iran-Iraq war ended and things became more stable. This enabled her to attend a good high school where her principal instilled in her the confidence to reach for grandeur. Her mindset was very positive and upbeat. ‘You can do it, even though you'll be the first one. I think that has influenced my life quite a lot’, Maryam says. Maryam didn't always want to be a mathematician. Growing up she loved books and dreamt of being a writer. And in many ways she is living that dream. Mathematics research, Maryam says, is very similar to writing a novel. There are different characters, and you are getting to know them better. Things evolve, and then you look back at a character and it is completely different from your first impression. Maryam also admits to doing poorly in mathematics for a couple of years in middle school. She puts this down to not being interested in thinking about mathematics. Maryam believes that without being excited by it, mathematics can look pointless and cold. She said that the beauty of mathematics, the simple and elegant language reveals itself.

Maryam's PhD supervisor, Curtis McMullen from Harvard, says that she has a fearless ambition and a daring imagination, needed when you are tackling some of the most difficult problems in your field. This is what won her the Fields Medal, and what I hope is told to inspire lots more girls and young women to study mathematics. The gender imbalance in the field, while improving, is still rife. I know, I did a maths degree. In first year about a third of my peers were female. By my final year that fraction had fallen to a tenth. Christiane Rousseau, vice president of the International Mathematics Union, told the Guardian: 'It's an extraordinary moment. This is the first time in mathematics we have a woman winning the most prestigious prize. This is a celebration for women.' And I would agree. But it isn't just for women, it is a celebration for the entire community, a mathematical celebration with a story behind it, the story of a young girl growing up in Tehran, reading books, dreaming of characters and adventures and travelling the world, the story of a girl fascinated by the elegance and beauty held in a simple mathematical solution.

As Maryam so rightly puts it, the more time you spend on maths, the more excited you get by it. And as I said here on The Science Show a couple of weeks ago, if we teach our kids the history of mathematics and the stories behind our mathematicians, I reckon they would fall for numbers, fall for the romance and the magic that is clearly there, just below the silicon chip, just behind the mathematician's facade. So let's celebrate our mathematical heroes and heroines as this week we write a little mathematical history. Robyn Williams: Well, that was Stephanie Pradier in Melbourne. She's with the Australian Mathematical Sciences Institute and doing physics at the University of Melbourne. And now get some rest Stephanie! Fields Medal: Iranian Maryam Mirzakhani first woman to be awarded Nobel Prize of Maths | ABC Radio Australia Fields Medal: Iranian Maryam Mirzakhani first woman to be awarded Nobel Prize of Maths Fields Medal: Iranian Maryam Mirzakhani first woman to be awarded Nobel Prize of Maths Updated 13 August 2014, 22:55 AEST An Iranian-born mathematician has become the first woman to win a prestigious Fields Medal, widely viewed as the Nobel Prize of mathematics.

Maryam Mirzakhani (R) was given the top mathematics award by South Korean president Park Geun-Hye (L). (Credit: AFP) Maryam Mirzakhani, a Harvard-educated mathematician and professor at Stanford University in California, was one of four winners announced by the International Congress of Mathematicians (ICM) at its conference in Seoul. "This is a great honour. I will be happy if it encourages young female scientists and mathematicians," Professor Mirzakhani said. "I am sure there will be many more women winning this kind of award in coming years." The Fields Medal is given out every four years, often to multiple winners who should not be over 40 years of age. With no Nobel prize given for mathematics, the Fields Medal is regarded as the top global award for the discipline. The award recognised Professor Mirzakhani's sophisticated and highly original contributions to the fields of geometry and dynamical systems, particularly in understanding the symmetry of curved surfaces such as spheres. Although her work is considered "pure mathematics" and is mostly theoretical, it has implications for physics and quantum field theory, as well as for the study of prime numbers and cryptography.

"Fluent in a remarkably diverse range of mathematical techniques and disparate mathematical cultures, she embodies a rare combination of superb technical ability, bold ambition, far-reaching vision, and deep curiosity," the ICM said in a statement. Born and raised in Tehran, Professor Mirzakhani initially dreamed of becoming a writer, but by the time she started high school her affinity for solving mathematical problems and working on proofs had shifted her sights. "It is fun - it's like solving a puzzle or connecting the dots in a detective case," she said. "I felt that this was something I could do, and I wanted to pursue this path." She has previously won the 2009 Blumenthal Award for the Advancement of Research in Pure Mathematics and the 2013 Satter Prize of the American Mathematical Society. The other three winners this year were Artur Avila of France, Manjul Bhargava of Princeton University in New Jersey, and Martin Hairer of the University of Warwick in Britain. Professor Mirzakhani became known on the international mathematics scene as a teenager, winning gold medals at both the 1994 and 1995 International Math Olympiads - finishing with a perfect score in the latter competition.

In 2008, she became a professor of mathematics at Stanford, where she lives with her husband and three-year-old daughter. The medals were given out by South Korea's first woman president, Park Geun-Hye. "I congratulate all the winners, with special applause for Maryam Mirzakhani, whose drive and passion have made her the first woman to win a Fields Medal," Ms Park said. Stanford University president John Hennessy said: "On behalf of the entire Stanford community, I congratulate Maryam on this incredible recognition, the highest honour in her discipline, the first ever granted to a woman." AFP Meet the First Woman to Win Math’s Most Prestigious Prize | WIRED Time of Publication: 2:16 pm. 2:16 pm Meet the First Woman to Win Math’s Most Prestigious Prize As an 8-year-old, Maryam Mirzakhani used to tell herself stories about the exploits of a remarkable girl. Every night at bedtime, her heroine would become mayor, travel the world or fulfill some other grand destiny. Today, Mirzakhani — a 37-year-old mathematics professor at Stanford University — still writes elaborate stories in her mind.

The high ambitions haven’t changed, but the protagonists have: They are hyperbolic surfaces, moduli spaces and dynamical systems. In a way, she said, mathematics research feels like writing a novel. “There are different characters, and you are getting to know them better,” she said. “Things evolve, and then you look back at a character, and it’s completely different from your first impression.” This article is part of a five-part series on the 2014 Fields Medal and Nevanlinna Prize winners, reprinted with permission from Quanta Magazine , an editorially independent division of SimonsFoundation.org whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences. The Iranian mathematician follows her characters wherever they take her, along story lines that often take years to unfold. Petite but indomitable, Mirzakhani has a reputation among mathematicians for tackling the most difficult questions in her field with dogged persistence. “She has a fearless ambition when it comes to mathematics,” said Curtis McMullen of Harvard University, who was Mirzakhani’s doctoral adviser. With her low voice and steady, gray-blue eyes, Mirzakhani projects an unwavering self-confidence.

She has an equal tendency, however, toward humility. Asked to describe her contribution to a particular research problem, she laughed, hesitated and finally said: “To be honest, I don’t think I’ve had a very huge contribution.” And when an email arrived in February saying that she would receive what is widely regarded as the highest honor in mathematics — the Fields Medal, which was awarded August 13 at the International Congress of Mathematicians in Seoul, South Korea — she assumed that the account from which the email was sent had been hacked. Other mathematicians, however, describe Mirzakhani’s work in glowing terms. Her doctoral dissertation — about counting loops on surfaces that have “hyperbolic” geometry — was “truly spectacular,” said Alex Eskin , a mathematician at the University of Chicago who has collaborated with Mirzakhani. “It’s the kind of mathematics you immediately recognize belongs in a textbook.” And one of Mirzakhani’s more recent contributions — a monumental collaboration with Eskin about the dynamics of abstract surfaces connected to billiard tables — is “probably the theorem of the decade” in Mirzakhani’s highly competitive field, said Benson Farb , also a University of Chicago mathematician.

Tehran As a child growing up in Tehran, Mirzakhani had no intention of becoming a mathematician. Her chief goal was simply to read every book she could find. She also watched television biographies of famous women such as Marie Curie and Helen Keller, and later read “Lust for Life,” a novel about Vincent van Gogh. These stories instilled in her an undefined ambition to do something great with her life — become a writer, perhaps. Mirzakhani finished elementary school just as the Iran-Iraq war was drawing to a close and opportunities were opening up for motivated students. She took a placement test that secured her a spot at the Farzanegan middle school for girls in Tehran, which is administered by Iran’s National Organization for Development of Exceptional Talents. “I think I was the lucky generation,” she said. “I was a teenager when things got more stable.” Mirzakhani grew up in Iran and was at first more interested in reading and writing fiction than doing mathematics. Courtesy of Maryam Mirzakhani In her first week at the new school, she made a lifelong friend, Roya Beheshti , who is now a mathematics professor at Washington University in St. Louis.

As children, the two explored the bookstores that lined the crowded commercial street near their school. Browsing was discouraged, so they randomly chose books to buy. “Now, it sounds very strange,” Mirzakhani said. “But books were very cheap, so we would just buy them.” To her dismay, Mirzakhani did poorly in her mathematics class that year. Her math teacher didn’t think she was particularly talented, which undermined her confidence. At that age, “it’s so important what others see in you,” Mirzakhani said. “I lost my interest in math.” The following year, Mirzakhani had a more encouraging teacher, however, and her performance improved enormously. “Starting from the second year, she was a star,” Beheshti said. Mirzakhani went on to the Farzanegan high school for girls. There, she and Beheshti got hold of the questions from that year’s national competition to determine which high school students would go to the International Olympiad in Informatics, an annual programming competition for high school students. Mirzakhani and Beheshti worked on the problems for several days and managed to solve three out of six.

Even though students at the competition must complete the exam in three hours, Mirzakhani was excited to be able to do any problems at all. There are really many great female mathematicians doing great things Eager to discover what they were capable of in similar competitions, Mirzakhani and Beheshti went to the principal of their school and demanded that she arrange for math problem-solving classes like the ones being taught at the comparable high school for boys. “The principal of the school was a very strong character,” Mirzakhani recalled. “If we really wanted something, she would make it happen.” The principal was undeterred by the fact that Iran’s International Mathematical Olympiad team had never fielded a girl, Mirzakhani said. “Her mindset was very positive and upbeat — that ‘you can do it, even though you’ll be the first one,’ ” Mirzakhani said. “I think that has influenced my life quite a lot.” In 1994, when Mirzakhani was 17, she and Beheshti made the Iranian math Olympiad team. Mirzakhani’s score on the Olympiad test earned her a gold medal. The following year, she returned and achieved a perfect score.

Having entered the competitions to discover what she could do, Mirzakhani emerged with a deep love of mathematics. “You have to spend some energy and effort to see the beauty of math,” she said. Even today, said Anton Zorich of the Université Paris Diderot-Paris 7 in France, Mirzakhani gives “the impression of a 17-year-old girl who is absolutely excited by all the mathematics that happens around her.” Harvard Gold medals at the mathematical Olympiad don’t always translate into success in mathematics research, McMullen observed. “In these contests, someone has carefully crafted a problem with a clever solution, but in research, maybe the problem doesn’t have a solution at all.” Unlike many Olympiad high-scorers, he said, Mirzakhani “has the ability to generate her own vision.” After completing an undergraduate degree in mathematics at Sharif University in Tehran in 1999, Mirzakhani went to graduate school at Harvard University, where she started attending McMullen’s seminar. At first, she didn’t understand much of what he was talking about but was captivated by the beauty of the subject, hyperbolic geometry.

She started going to McMullen’s office and peppering him with questions, scribbling down notes in Farsi. “She had a sort of daring imagination,” recalled McMullen, a 1998 Fields medalist. “She would formulate in her mind an imaginary picture of what must be going on, then come to my office and describe it. At the end, she would turn to me and say, ‘Is it right?’ I was always very flattered that she thought I would know.” Mirzakhani with her parents during a visit to Isfahan, Iran. Courtesy of Maryam Mirzakhani Mirzakhani became fascinated with hyperbolic surfaces — doughnut-shaped surfaces with two or more holes that have a non-standard geometry which, roughly speaking, gives each point on the surface a saddle shape. Hyperbolic doughnuts can’t be constructed in ordinary space; they exist in an abstract sense, in which distances and angles are measured according to a particular set of equations. An imaginary creature living on a surface governed by such equations would experience each point as a saddle point.

It turns out that each many-holed doughnut can be given a hyperbolic structure in infinitely many ways — with fat doughnut rings, narrow ones, or any combination of the two. In the century and a half since such hyperbolic surfaces were discovered, they have become some of the central objects in geometry, with connections to many branches of mathematics and even physics. But when Mirzakhani started graduate school, some of the simplest questions about such surfaces were unanswered. One concerned straight lines, or “geodesics,” on a hyperbolic surface. Even a curved surface can have a notion of a “straight” line segment: it’s simply the shortest path between two points. On a hyperbolic surface, some geodesics are infinitely long, like straight lines in the plane, but others close up into a loop, like the great circles on a sphere. The number of closed geodesics of a given length on a hyperbolic surface grows exponentially as the length of the geodesics grows. Most of these geodesics cut across themselves many times before closing up smoothly, but a tiny proportion of them, called “simple” geodesics, never intersect themselves.

Simple geodesics are “the key object to unlocking the structure and geometry of the whole surface,” Farb said. She has these huge pieces of paper on the floor and spends hours and hours drawing what look to me like the same picture over and over Yet mathematicians couldn’t pin down just how many simple closed geodesics of a given length a hyperbolic surface can have. Among closed geodesic loops, the simple ones are “miracles that [effectively] happen zero percent of the time,” Farb said. For that reason, counting them accurately is incredibly difficult: “If you have a little bit of an error, you’ve missed it,” he said. In her doctoral thesis, completed in 2004, Mirzakhani answered this question, developing a formula for how the number of simple geodesics of length L grows as Lgets larger. Along the way, she built connections to two other major research questions, solving both. One concerned a formula for the volume of the so-called “moduli” space — the set of all possible hyperbolic structures on a given surface.

The other was a surprising new proof of an old conjecture proposed by the physicist Edward Witten of the Institute for Advanced Study in Princeton, N.J., about certain topological measurements of moduli spaces related to string theory. Witten’s conjecture is so difficult that the first mathematician to prove it — Maxim Kontsevich of the Institut des Hautes Études Scientifiques, near Paris — was awarded a Fields Medal in 1998 in part for that work. Farb said that solving each of these problems “would have been an event, and connecting them would have been an event.” Mirzakhani did both. Mirzakhani’s thesis resulted in three papers published in the three top journals of mathematics: Annals of Mathematics , Inventiones Mathematicae and Journal of the American Mathematical Society . The majority of mathematicians will never produce something as good, Farb said — “and that’s what she did in her thesis.” ‘A Titanic Work’ Mirzakhani likes to describe herself as slow. Unlike some mathematicians who solve problems with quicksilver brilliance, she gravitates toward deep problems that she can chew on for years.

“Months or years later, you see very different aspects” of a problem, she said. There are problems she has been thinking about for more than a decade. “And still there’s not much I can do about them,” she said. Mirzakhani doesn’t feel intimidated by mathematicians who knock down one problem after another. “I don’t get easily disappointed,” she said. “I’m quite confident, in some sense.” Her slow and steady approach also applies to other areas of her life. One day while she was a graduate student at Harvard, her future husband, then a graduate student at the Massachusetts Institute of Technology, learned this lesson about Mirzakhani when the two went for a run. “She’s very petite, and I was in good shape, so I thought I’d do well, and at first, I was ahead,” recalled Jan Vondrak , who is now a theoretical computer scientist at IBM Almaden Research Center in San Jose, Calif. “But she never slows down. After half an hour, I was done, but she was still running at the same pace.” As she thinks about mathematics, Mirzakhani constantly doodles, drawing surfaces and other images related to her research.

“She has these huge pieces of paper on the floor and spends hours and hours drawing what look to me like the same picture over and over,” Vondrak said, adding that papers and books are scattered haphazardly about her home office. “I have no idea how she can work like this, but it works out in the end,” he said. Perhaps, he speculates, that is because “the problems she is working on are so abstract and complicated, she can’t afford to make logical steps one by one but has to make big jumps.” Mirzakhani, who says she thinks about mathematics in pictures, often doodles her ideas on giant sheets of paper. Thomas Lin/Quanta Magazine Doodling helps her focus, Mirzakhani said. When thinking about a difficult math problem, “you don’t want to write down all the details,” she said. “But the process of drawing something helps you somehow to stay connected.” Mirzakhani said that her 3-year-old daughter, Anahita, often exclaims, “Oh, Mommy is painting again!” when she sees the mathematician drawing. “Maybe she thinks I’m a painter,” Mirzakhani said.

Mirzakhani’s research connects to many areas of mathematics, including differential geometry, complex analysis and dynamical systems. “I like crossing the imaginary boundaries people set up between different fields — it’s very refreshing,” she said. In her area of research, “there are lots of tools, and you don’t know which one would work,” she said. “It’s about being optimistic and trying to connect things.” Sometimes, the connections that Mirzakhani makes are mind-blowing, McMullen said. In 2006, for example, she tackled the problem of what happens to a hyperbolic surface when its geometry is deformed using a mechanism akin to a strike-slip earthquake. Before Mirzakhani’s work, “this problem was completely unapproachable,” McMullen said. But with a one-line proof, he said, “she constructed a bridge between this completely opaque theory and another theory that’s completely transparent.” In 2006, Mirzakhani began her fruitful collaboration with Eskin, who considers her one of his favorite collaborators. “She is very optimistic, and that’s infectious,” he said.

“When you work with her, you feel you have a much better chance of solving problems that at first seem hopeless.” After several projects together, Mirzakhani and Eskin decided to tackle one of the largest open problems in their field. It concerned the range of behaviors of a ball that is bouncing around a billiard table shaped like any polygon, provided the angles are a rational number of degrees. Billiards provides some of the simplest examples of dynamical systems — systems that evolve over time according to a given set of rules — but the behavior of the ball has proven unexpectedly hard to pin down. “Rational billiards got started a century ago, when some physicists were sitting around saying, ‘Let’s understand a billiard ball bouncing in a triangle,’ ” said Alex Wright , a postdoctoral researcher at Stanford. “Presumably, they thought they would be done in a week, but 100 years later, we’re still thinking about it.” Billiard Ball Trajectories If you place mirrors on the walls of a billiard table, a ball bouncing off a wall looks as if it is continuing to roll in a straight line in the looking-glass world.

Follow this straight path through one looking glass after another as the ball hits more walls, and after a finite number of reflections, you’ll be back in a billiard table world that has the exact same orientation as the original table. If you glue together the sides of this finite succession of billiard table worlds, you end up with a surface — a doughnut with two or more holes — that inherits a flat geometry from the billiard table (except at the handful of points that correspond to the corners of the table). Paths on the original billiard table correspond to straight lines on this surface, called a “translation” surface. Mathematicians have shown that understanding the “moduli space” of all translation surfaces is the key to understanding billiards. To study a long billiard ball trajectory, a useful approach is to imagine gradually deforming the billiard table by squishing it along the direction of the trajectory so that more of the ball’s path can be seen in a given amount of time. This transforms the original billiard table into a succession of new ones, moving the table around in what mathematicians call the “moduli” space consisting of all possible billiard tables with a given number of sides.

By transforming each billiard table into an abstract surface called a “translation surface,” mathematicians can analyze billiard dynamics by understanding the larger moduli space consisting of all translation surfaces. Researchers have shown that understanding the “orbit” of a particular translation surface as the squishing action moves it around in the moduli space helps in answering a host of questions about the original billiard table. On the face of it, this orbit might be an extremely complicated object — a fractal, for instance. In 2003, however, McMullen showed that this isn’t the case when the translation surface is a two-holed (“genus two”) doughnut: Every single orbit fills up either the entire space or some simple subset of the space called a submanifold. McMullen’s result was hailed as a huge advance. He recalled that before his paper was published, however, Mirzakhani — then still a graduate student — came to his office and asked, “Why did you just do genus two?” “That’s the kind of person she is,” he said.

“What she sees hints of, she wants to understand more clearly.” After years of work, in 2012 and 2013, Mirzakhani and Eskin, partly in collaboration with Amir Mohammadi of the University of Texas at Austin, succeeded in generalizing McMullen’s result to all doughnut surfaces with more than two holes. Their analysis is “a titanic work,” Zorich said, adding that its implications go far beyond billiards. The moduli space “has been intensively studied for the last 30 years,” he said, “but there’s still so much we don’t know about its geometry.” Mirzakhani and Eskin’s work is “the beginning of a new era,” said Wright, who spent months studying their 172-page paper . “It’s as if we were trying to log a redwood forest with a hatchet before, but now they’ve invented a chain saw,” he said. Their work has already been applied — for example, to the problem of understanding the sightlines of a security guard in a complex of mirrored rooms.

In Mirzakhani and Eskin’s paper, “under every layer of difficulty and ideas lay another, hidden beneath,” Wright wrote in an email. “By the time I got to the center, I was amazed at the machine they had built.” It was Mirzakhani’s optimism and tenacity that kept the pair going, Eskin said. “Sometimes there were setbacks, but she never panicked,” he said. Even Mirzakhani herself is amazed, in retrospect, that the two stuck with it. “If we knew things would be so complicated, I think we would have given up,” she said. Then she paused. “I don’t know; actually, I don’t know,” she said. “I don’t give up easily.” Next Chapter Mirzakhani is the first woman to win a Fields Medal. The gender imbalance in mathematics is long-standing and pervasive, and the Fields Medal, in particular, is ill-suited to the career arcs of many female mathematicians. It is restricted to mathematicians younger than 40, focusing on the very years during which many women dial back their careers to raise children. Mirzakhani feels certain, however, that there will be many more female Fields medalists in the future.

“There are really many great female mathematicians doing great things,” she said. In the meantime, while she feels greatly honored to have been awarded a Fields Medal, she has no desire to be the face of women in mathematics, she said. Her ambitious teenage self would have been overjoyed by the award, she said, but today, she is eager to deflect attention from her achievements so she can focus on research. Mirzakhani has big plans for the next chapters of her mathematical story. She has started working with Wright to try to develop a complete list of the kinds of sets that translation surface orbits can fill up. Such a classification would be a “magic wand” for understanding billiards and translation surfaces, Zorich has written . It’s no small task, but Mirzakhani has learned over the years to think big. “You have to ignore low-hanging fruit, which is a little tricky,” she said. “I’m not sure if it’s the best way of doing things, actually — you’re torturing yourself along the way.” But she enjoys it, she said. “Life isn’t supposed to be easy.” Thomas Lin contributed reporting from Stanford, Calif.

Fields Medals 2014: prizes for maths work that few of us can grasp | Science | The Guardian Mathematics Fields Medals 2014: prizes for maths work that few of us can grasp Don't worry if you don't understand the work of this year's winners. Nor do most of their university colleagues Maryam Mirzakhani, the first woman to win the Fields Medal maths prize in its history. Photograph: Stanford University Wednesday 13 August 2014 03.17 EDT First published on Wednesday 13 August 2014 03.17 EDT Share on Messenger Close When I interviewed the 2010 Fields medallist Cédric Villani a couple of years ago, I asked him how many people understood his work. "A few hundred people," he said, before clarifying that for some of his more abstract results the number would be even less. This year's four Fields Medal winners have similarly won the maths world's most celebrated honour for work that is most likely unfathomable to the great majority of their colleagues in universities around the world. Of course, there are levels of understanding.

According to Villani, nowadays it is only possible for a mathematician to have a general appreciation of about a third of what passes for contemporary mathematics, at the very maximum, and it is impossible for any one person to master more than a few per cent of it. The intellectual isolation of the modern mathematician is a result of the unique nature of the subject. Unlike the physical and human sciences, where theories can be rejected and improved on, a mathematical result is true for ever. The volume of proofs and theorems that have built on each other since the ancient Greeks is now so huge, and so diverse, that there is no choice but to specialise early on if you want to reach the highest level. Fields medallist Artur Avila. Photograph: /IMU It is also the case that many fields are so conceptually challenging that even the most brilliant minds can take years to understand them in any depth. Different areas of maths require different mathematical languages, which like real languages require time and practice in which to become fluent. The romantic idea of the maths genius as a solitary thinker is an outdated myth. Even though at the forefront of research are small groups with very narrow specialisms, maths is more and more a collaborative discipline.

Just like a football coach assembles players with different but complementary skills, mathematicians increasingly assemble thinkers with different skills and knowledge bases to collaborate on problems. Artur Avila, for example, has co-authored papers with about 30 colleagues around the world. His main area is dynamical systems, which concerns the behaviour of systems over time such as, say, a point moving around according to a mathematical rule. The award of the Fields Medal to Manjul Bhagarva is notable not only because he plays the tabla drum professionally in his spare time but also because of his novel use of computers in mathematical exploration. For a long time mathematicians tended to be rather dismissive about computers, but now they consider them an important tool. Martin Hairer, who has developed and sells his own Mac audio software, has said that programming helps develop mathematical intuition. Manjul Bhargava is awarded his Fields Medal by the South Korean president, Park Geun-hye. Photograph: Yonhap/AFP/Getty Images Bhargava's area is algebraic number theory, which mixes algebra with the study of the properties of numbers. Hairer is a specialist in differential equations, which are the type of equations first developed by Isaac Newton in order to describe planetary orbits.

Maryam Mirzakhani's field is possibly the most difficult to describe in the pages of a newspaper, but it links the following concepts: hyperbolic geometry, which is the geometry you get on saddle-shaped surfaces such as Pringle crisps; complex numbers, which are "numbers" that include a value for the square root of minus one; topology, which is the study of the properties of shapes that are unchanged when stretched or bent; and calculus, which is the study of change. The notes provided by the International Mathematical Union to describe her most important results say that together with her collaborators she "proved that complex geodesics and their closures in moduli space are in fact surprisingly regular, rather than irregular or fractal. It turns out that, while complex geodesics are transcendental objects defined in terms of analysis and differential geometry, their closures are algebraic objects defined in terms of polynomials and therefore have certain rigidity properties." Don't worry if you don't understand what this means. Neither do I, and I guarantee that most of those people at the International Congress of Mathematicians in Seoul don't fully understand it, either.

Maryam Mirzakhani, who was born and raised in Iran, has been awarded the highest honour a mathematician can attain Published: 12 Aug 2014 Fields Medal mathematics prize won by woman for first time in its history | Science | The Guardian Mathematics Fields Medal mathematics prize won by woman for first time in its history Maryam Mirzakhani, who was born and raised in Iran, has been awarded the highest honour a mathematician can attain Tuesday 12 August 2014 21.30 EDT First published on Tuesday 12 August 2014 21.30 EDT Close This article is 2 years old It will go down in history as the moment one of the last bastions of male dominance fell. A woman has won the world's most prestigious mathematics prize for the first time since the award was established nearly 80 years ago. Maryam Mirzakhani , an Iranian maths professor at Stanford University in California, was named the first female winner of the Fields Medal – often described as the Nobel prize for mathematics – at a ceremony in Seoul on Wednesday. The maths community has been abuzz with rumours for months that Mirzakhani was in line to win the prize.

To outsiders her work is esoteric, abstract and impenetrable. But to more qualified minds, she has a breathtaking scope, is technically superb and boldly ambitious. She describes the language of maths as full of "beauty and elegance". The prize, worth 15,000 Canadian dollars (£8,000), is awarded to exceptional talents under the age of 40 once every four years by the International Mathematical Union . Between two and four prizes are announced each time. Three other researchers were named Fields Medal winners at the same ceremony in South Korea. They included Martin Hairer , a 38-year-old Austrian based at Warwick University in the UK, Manjul Bhargava , a 40-year old Canadian-American at Princeton University in the US and Artur Avila , 35, a Brazilian-French researcher at the Institute of Mathematics of Jussieu in Paris. There have been 55 Fields medallists since the prize was first awarded in 1936, including this year's winners. The Russian mathematician Grigori Perelman refused the prize in 2006 for his proof of the Poincaré conjecture.

Mirzhakhani, 37, was among a number of women tipped for the prize in recent years and her success won immediate praise from fellow mathematicians. Christiane Rousseau , vice president of the International Mathematics Union, said: "It's an extraordinary moment. Marie-Curie had Nobel prizes in physics and chemistry at the beginning of the 20th century, but in mathematics this is the first time we have a woman winning the most prestigious prize there is. This is a celebration for women." "I am thrilled that this day has finally come," said Sir Tim Gowers , a Fields medallist and mathematician at Cambridge University. "Although women have contributed to mathematics at the highest level for a long time, this fact has not been visible to the general public. I hope that the existence of a female Fields medallist, who will surely be the first of many, will put to bed many myths about women and mathematics, and encourage more young women to think of mathematical research as a possible career." Born and raised in Iran, Mirzakhani completed a PhD at Harvard in 2004. Her path into mathematics was not a given, though. As a child, her passion was not for numbers, but literature.

Her school in Tehran was near a street full of bookshops and because browsing was not allowed, she ended up buying a lot of random books. "I dreamed of becoming a writer," she said in an interview for the Clay Mathematics Institute (CMI) in 2008. "I never thought I would pursue mathematics before my last year in high school." It was Mirzakhani's brother who first piqued her interest in science. He used to come home from school and talk over what he had learned. He told her the story of the German mathematician, Carl Friedrich Gauss , who displayed his precocious skills as a schoolboy when he worked out in seconds how to sum all the numbers from 1 to 100. (The answer is 5,050 and the trick is to look at pairs that add up to 101.) "That was the first time I enjoyed a beautiful solution, though I couldn't find it myself," she said. The seed that had been sown began to germinate, with help from her school principal, a strong-willed woman who made every effort to ensure her students had the same opportunities as the boys.

As a teenager, Mirzakhani took part in international maths olympiads and won gold medals in 1994 and in 1995. In the first, in Hong Kong, she dropped a single point. At the latter, in Toronto, she finished with a perfect score. Later, as a student at Sharif University, she befriended inspiring mathematicians and found that the more time she spent on the subject, the more excited she became. Then, at Harvard, she began to work with another Fields medallist, Curt McMullen , and became fascinated with how he made mathematics so simple and elegant. Most of the problems Mirzakhani works on involve geometric structures on surfaces and their deformations. She has a particular interest in hyperbolic planes, which can look like the edges of curly kale leaves, but may be easier to crochet than explain. According to a citation released by the International Mathematical Union, Mirzakhani won the prize for her "outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces". Hairer won for his "outstanding contributions to the theory of stochastic partial differential equations", which contain terms that are inherently random.

At school, he created audio software that he marketed as "the Swiss army knife of sound editing". Avila was honoured for his "profound contributions to dynamical systems". Bhargava won for "developing powerful new methods in the geometry of numbers", including elliptic curves used in cryptography. "The mathematics that has been the most applicable and important to society over the years has been the mathematics that scientists found while searching for beauty; and eventually all beautiful and elegant mathematics tends to find applications," said Bhargava. Mirzakhani declined an interview, but she told the CMI in 2008 that while maths was not for everyone, many students did not give it a real chance. She did poorly at maths for several years at school because she was not interested in the subject. "I can see that without being excited, mathematics can look pointless and cold. The beauty of mathematics only shows itself to more patient followers," she said. Speaking to the American Mathematical Society last year , she said the situation for women in maths was still far from ideal. "The social barriers for girls who are interested in mathematical sciences might not be lower now than they were when I grew up. And balancing career and family remains a big challenge.

It makes most women face difficult decisions which usually compromise their work," she said. Frances Kirwan at Oxford University, one of Britain's leading mathematicians, said: "Maths is a hugely rewarding subject, but sadly many children lose confidence very early and never reap those rewards. It has traditionally been regarded as a male preserve, though women are known to have contributed to its development for centuries – more than 16 centuries if we go back to Hypatia of Alexandria . "In recent years around 40% of UK undergraduates studying maths have been women, but that proportion declines very rapidly when we look at the numbers progressing to PhDs and beyond.

I hope that this award will inspire lots more girls and young women, in this country and around the world, to believe in their own abilities and aim to be the Fields medallists of the future." Indian-Origin Manjul Bhargava Wins 'Nobel Prize of Maths' Indian-Origin Manjul Bhargava Wins 'Nobel Prize of Maths' Diaspora | Press Trust of India | Updated: August 13, 2014 11:08 IST EMAIL COMMENTS File Photo: Indian-Origin Mathematician and Fields Medal Winner Manjul Bhargava New York: Two Indian-origin academicians have won prestigious global prizes in the field of mathematics with one of them being awarded the Fields Medal - known as the "Nobel Prize of mathematics". Manjul Bhargava won the Fields Medal while Subhash Khot won the Rolf Nevanlinna Prize, awarded by the International Mathematical Union (IMU), at the International Congress of Mathematicians 2014 held in Seoul. Manjul Bhargava, a professor of mathematics at Princeton University, was among the four winners who have been awarded the Fields Medal, given out every four years.

Iranian-born mathematician and Stanford University professor Maryam Mirzakhani became the first woman to win the Fields Medal this year. Mr Bhargava was awarded the Fields Medal for "developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves." According to the award citation, Mr Bhargava's work is "based both on a deep understanding of the representations of arithmetic groups and a unique blend of algebraic and analytic expertise." Subhash Khot was awarded the Nevanlinna Prize for his "prescient definition of the 'Unique Games' problem, and leading the effort to understand its complexity and its pivotal role in the study of efficient approximation of optimisation problems." His work has led to breakthroughs in algorithmic design and approximation hardness and to new exciting interactions between computational complexity, analysis and geometry. Mr Khot is a professor in the Computer Science Department at New York University's Courant Institute of Mathematical Sciences. He has a PhD from Princeton. Born in 1974 in Canada, Manjul Bhargava grew up in the US and also spent much time in India.

He received his PhD in 2001 from Princeton University and became a professor in 2003. Mr Bhargava's honours include the Merten Hasse Prize of the Mathematical Association of America (2003), the SASTRA Ramanujan Prize (2005), the Cole Prize in Number Theory of the American Mathematical Society (2008) and the Infosys Prize (2012). He was elected to the US National Academy of Sciences in 2013. The Fields Medals were started in 1936 and the Nevanlinna Prize in 1982. The Fields Medal is awarded on the occasion of the International Congress of Mathematicians to recognise outstanding mathematical achievement for existing work and for the promise of future achievement. The candidates in fray for the medal must be below the age of 40.

The Rolf Nevanlinna Prize is awarded once every four years at the International Congress of Mathematicians, for outstanding contributions in Mathematical Aspects of Information Sciences including all mathematical aspects of computer science, including complexity theory, logic of programming languages, analysis of algorithms, cryptography, computer vision, pattern recognition, information processing and modelling of intelligence as well as scientific computing and numerical analysis.

Question: In August 2014 Maryam Mirzakhani became the first woman to be awarded the Fields Medal. For work is which discipline is the Fields Medal awarded?
Answer: MATHEMATICS