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Wednesday, August 13, 2014

What Did Maryam Mirzakhani Achieve?

The late scientist Maryam Mirzakhani, formerly a professor of mathematics at Stanford University in the United States, became the first woman to receive the highly prestigious Fields Medal. She earned her undergraduate degree at Sharif University of Technology and later completed her doctorate at Harvard University.

The original article describes the work for which she became renowned in broad terms as research connected with Riemannian geometry. It explains that Riemannian geometry is an important and widely used branch of differential geometry founded in the nineteenth century by Bernhard Riemann and that geometry of curved spaces plays an important role in Einstein's general theory of relativity and its description of curved space and time.

The article notes that the subject is mathematically complex and gives, as an intuitive illustration of non-Euclidean geometry, the possibility of a triangle whose angles add to more than 180 degrees.

The author then speculates enthusiastically about the possible long-term importance of Mirzakhani's mathematical discoveries for future scientists seeking deeper understanding of the structure of space and time, including problems then occupying astronomers such as dark matter and dark energy. The article imagines that ideas regarded today as science fiction might someday become commonplace and that Mirzakhani could be remembered as a pioneering figure whose work helped make such advances possible.