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Topic: Stanford's Maryam Mirzakhani wins Fields Medal
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Jerry P. Becker

Posts: 16,532
Registered: 12/3/04
Stanford's Maryam Mirzakhani wins Fields Medal
Posted: Jul 21, 2017 5:01 PM
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NOTE: As reported earlier in a posting, Prof.
Maryam Mirzakhani passed away July 14, 2017 after
a long battle with cancer. Mirzakhani was 40
years old. What follows is an article regarding
Prof. Mirzakhani and the honor of being awarded
the Fields Medal, the "Nobel Prize of
Mathematics" last year. An article that was
posted earlier regarding her death is given at
http://news.stanford.edu/2017/07/15/maryam-mirzakhani-stanford-mathematician-and-fields-medal-winner-dies/

*******************************
From Stanford News, August 12, 2014. SEE
http://news.stanford.edu/news/2014/august/fields-medal-mirzakhani-081214.html
*******************************
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.

"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.
---------------------------------
SIDEBAR PHOTO: Maryam Mirzakhani was awarded the
Fields Medal for her sophisticated and highly
original contributions to the fields of geometry
and dynamical systems. Courtesy of Maryam
Mirzakhani
---------------------------------
Media Contact -- Bjorn Carey, Stanford News
Service: (650) 725-1944, bccarey@stanford.edu
*****************************************
--
Jerry P. Becker
Department of Curriculum & Instruction
College of Education and Human Services
Southern Illinois University Carbondale
625 Wham Drive / MC 4610
Carbondale, Illinois 62901



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