dynamic geometry

Sorrow as Maryam Mirzakhani, the first woman to win mathematics' Fields Medal, dies aged 40

Maryam Mirzakhani, an Iranian-born mathematician who was the first woman to win the coveted Fields Medal, has died in a US hospital after a battle with cancer. She was 40.

Mirzakhani’ friend Firouz Naderi announced her death on Saturday on Instagram, and her relatives confirmed the death to the Mehr agency in Iran.

“A light was turned off today. It breaks my heart ….. gone far too soon,” wrote Naderi, a former director of Solar Systems Exploration at NASA.

“A genius? Yes. But also a daughter, a mother and a wife,” he added in a subsequent post.

Mirzakhani, a professor at Stanford University in California, died after the cancer she had been battling for four years spread to her bone marrow, Iranian media said.

In 2014 Mirzakhani won the Fields Medal, the equivalent of the Nobel Prize for Mathematics, which is awarded by the International Congress of Mathematicians.

Maryam Mirzakhani was the first woman to win the Fields Medal, the Nobel Prize for mathematics Credit: AFP PHOTO / The Seoul ICM 2014 / STRSTR/AFP/Getty Images

The award recognized her sophisticated and highly original contributions to the fields of geometry and dynamical systems, particularly in understanding the symmetry of curved surfaces such as spheres.

Born in 1977 and raised in Tehran, 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 when she won the Fields Medal.

“I felt that this was something I could do, and I wanted to pursue this path.”

Mirzakhani said she enjoyed pure mathematics because of the elegance and longevity of the questions she studies.

“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,” she added.

In 2008 she became a professor of mathematics at Stanford. She is survived by her husband and young daughter.

n Iran, President Hassan Rouhani said that Mirzakhani’s “doleful passing” has caused “great sorrow,” state media reported.

Rouhani praised the “unprecedented brilliance of this creative scientist and modest human being, who made Iran’s name resonate in the world’s scientific forums, (and) was a turning point in showing the great will of Iranian women and young people on the path towards reaching the peaks of glory…in various international arenas.”

Separately on Instagram, Iranian Foreign Minister Mohammad Javad Zarif said that Mirzakhani’s death is a cause for grief for all Iranians.

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Maryam Mirzakhani, first woman to win maths' Fields Medal, dies
Acclaimed Iranian mathematician Maryam Mirzakhani dies of breast cancer aged 40.

The 40-year-old Iranian, a professor at Stanford University, had breast cancer which had spread to her bones.

Nicknamed the “Nobel Prize for Mathematics”, the Fields Medal is only awarded every four years to between two and four mathematicians under 40.

It was given to Prof Mirzakhani in 2014 for her work on complex geometry and dynamical systems.

Iranian President Hassan Rouhani said Prof Mirzakhani’s death caused “great sorrow,” state media reported.

Foreign Minister Mohammad Javad Zarif said her death was a cause for grief for all Iranians.

“A light was turned off today. It breaks my heart… gone far too soon,” US-Iranian scientist Firouz Naderi posted on Instagram.

He added in a subsequent post: “A genius? Yes. But also a daughter, a mother and a wife.”

Prof Mirzakhani and her husband, Czech scientist Jan Vondrak, had one daughter.

Some social media users criticised Iranian officials for not using recent images of Prof Mirzakhani which showed her uncovered hair. Iranian women must cover their hair in line with a strict interpretation of Islamic law on modesty.

Iranian official media and politicians used older pictures in their social media tributes, which show her hair covered.

Stanford University President Marc Tessier-Lavigne described Prof Mirzakhani as “a brilliant mathematical theorist and also a humble person who accepted honours only with the hope that it might encourage others to follow her path”.

“Maryam is gone far too soon but her impact will live on for the thousands of women she inspired to pursue math and science,” he said.

“Her contributions as both a scholar and a role model are significant and enduring and she will be dearly missed here at Stanford and around the world.”

Born in 1977, Prof Mirzakhani was brought up in post-revolutionary Iran and won two gold medals in the International Mathematical Olympiad as a teenager.

She earned a PhD at Harvard University in 2004, and later worked at Princeton before securing a professorship at Stanford in 2008.

Her receipt of the Fields Medal three years ago ended a long wait for women in the mathematics community for the prize, first established in 1936.

Prof Mirzakhani was also the first Iranian to receive it.

The citation said she had made “striking and highly original contributions to geometry and dynamical systems” and that her most recent work constituted “a major advance”.

Prof Dame Frances Kirwan, a member of the medal selection committee from the University of Oxford, said at the time: “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.”

Maryam Mirzakhani

There are moments when we do not agree with what is happening around us… 

Maryam Mirzakhani (born May 3, 1977) is an Iranian-American mathematician and a professor of mathematics at Stanford University.

On 13 August 2014, Mirzakhani became both the first woman and the first Iranian honored with the Fields Medal, the most prestigious award in mathematics. The award committee cited her work in “the dynamics and geometry of Riemann surfaces and their moduli spaces”.

Her research topics include Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry.


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RIP Maryam - a monumental loss to humankind and all those in the math community.

A video profile of the 2014 Fields medalist Maryam Mirzakhani, whose monumental work draws deep connections between topology, geometry and dynamical systems.

Trailblazing maths genius who was first woman to win Fields Medal dies aged 40

The first woman to win the prestigious Fields Medal prize for mathematics, Maryam Mirzakhani, has died at the age of 40.

A professor at Stanford University in California, she had been fighting a four-year battle against breast cancer which had spread to her bone marrow, according to reports.

Born in Iran, she died in a US hospital, and was awarded the Fields Medal – considered the mathematics equivalent of the Nobel Prize – in 2014.

The award recognised her highly original work in the fields of geometry and dynamical systems, citing “her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces”.

Wisconsin professor Jordan Ellenberg described her research in a blog post at the time: “[Her] work expertly blends dynamics with geometry. Among other things, she studies billiards.

“But now, in a move very characteristic of modern mathematics, it gets kind of meta: She considers not just one billiard table, but the universe of all possible billiard tables.

“This isn’t the kind of thing you do to win at pool, but it’s the kind of thing you do to win a Fields Medal.”

Professor Mirzakhani graduated from the Sharif University of Technology in Tehran in 1999.

She went on to complete a PhD on hyperbolic surfaces – theoretical doughnut-like shapes – at Harvard in 2004.

Curtis McMullen, her doctoral adviser, had won the Field Medal himself in 1998.

She later collaborated with American mathematician Alex Eskin on research about the dynamics of abstract surfaces connected to billiard tables.

She doodled three-dimensional shapes constantly while she worked, and was known for her slow, measured approach to mathematical problems.

No other woman has won the prize, which is awarded every four years by the International Congress of Mathematicians to up to four mathematicians under 40, an age at which many women are re-entering the workplace after having children.

She was also the first Iranian to win a Fields Medal.

“The grievous passing of Maryam Mirzakhani, the eminent Iranian and world-renowned mathematician, is very much heartrending,” President Hassan Rouhani.

Growing up in Iran during the Iran-Iraq war, Professor Mirzakhani dreamed of becoming a writer and watched biographies of famous women like Marie Curie and Helen Keller.

She entered the Iranian International Mathematical Olympiad team at 17 in 1994, becoming the first girl to win a gold medal in 1994 and a perfect score the following year.

She had first taken an interest in maths when her older brother told her about how German mathematician Gauss discovered the formula for adding numbers from 1 to 100.

“It was the first time I enjoyed a beautiful solution,” she said in an interview given to the Clay Institute where she was a Research Fellow from 2004 to 2008.

“Of course, the most rewarding part is the ‘Aha’ moment, the excitement of discovery and enjoyment of understanding something new – the feeling of being on top of a hill and having a clear view. Most of the time, doing mathematics for me is like being on a long hike with no trail and no end in sight.”

Professor Mirzakhani is survived by her husband, an associate professor at Stanford University, and daughter Anahita.

Mathematician Maryam Mirzakhani is the first woman to win a Fields Medal. It had been an all-boys club since the prizes were established in 1936.

Mirzakhani, a native of Iran, is a professor at Stanford University. She won for her work on “the dynamics and geometry of Riemann surfaces and their moduli spaces.“

Here’s how Nature summed up her contributions:

“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”.


This is an exercise even I can do, so I’m sharing it with you. From Naive Lie Theory by John Stillwell


Elastic spheres can walk on water. Incited by public fascination and engineering application, water-skipping of rigid stones and spheres has received considerable study. While these objects can be coaxed to ricochet, elastic spheres demonstrate superior water-skipping ability, but little is known about the effect of large material compliance on water impact physics. Here we show that upon water impact, very compliant spheres naturally assume a disk-like geometry and dynamic orientation that are favourable for water-skipping. Experiments and numerical modelling reveal that the initial spherical shape evolves as elastic waves propagate through the material. We find that the skipping dynamics are governed by the wave propagation speed and by the ratio of material shear modulus to hydrodynamic pressure. With these insights, we explain why softer spheres skip more easily than stiffer ones. Our results advance understanding of fluid-elastic body interaction during water impact, which could benefit inflatable craft modelling and, more playfully, design of elastic aquatic toys.”