Esteemed mathematicians Maryam Mirzakhani and Marina Ratner could not have been more different, and yet they both made iconic impacts on the mathematical world.

Dr. Ratner was a Soviet born Jewish woman who worked at the University of California, Berkeley. In her 50s, she produced her famous Ratner Theorems.

On the other hand, Dr. Mirzakhani was a successful mathematician from Tehran, Iran. She worked at Stanford University, and in 2014 at the age of just 37, she became the only woman to have won the prestigious Fields Medal, an award which honors excellence in her field.

During her early schooling, Dr. Mirzakhani became the first woman to represent Iran when she competed in a mathematical Olympiad. She gained international attention when she won gold medals in two international Olympiads. In one of the two competitions, she received a perfect score.

When Dr. Ratner was at the Moscow State University, she was a student of Yakov Sinai, who is well known for his contributions to dynamical systems. She was elected to the American Academy of Arts and Sciences in 1992, and was awarded the Ostrowski Prize in 1993, which awards outstanding achievements in pure mathematics.

New York Times writer Amie Wilkinson met Mirzakhani in 2004. Wilkinson said that Mirzakhani “…was finishing her Ph.D. at Harvard…Given her reputation, I expected to meet a fearless warrior with a single-minded focus. I was quite disarmed when the conversation turned to being a mathematician and a mother.”

The New York Times also noted that “Dr. Ratner’s theorems are some of the most important in the past half-century, but she never quite received the recognition she deserved. That is partly because her best work came late in her career, and partly because of how she worked — always alone, without collaborators or graduate students to spread her reputation.”

Dr. Mirzakhani has inspired countless women to pursue her field, and Dr. Ratner’s theorems have become broadly and surprisingly applicable for all throughout the field of mathematics.

As Wilkinson put it, “There are a surprising number of social pressures against becoming a mathematician. When you’re in the minority, it takes extra strength and toughness to persist. Dr. Ratner and Dr. Mirzakhani had both.”

Dr. Ratner died when she was 78 years old, and Dr. Mirzakhani passed away this past July.

Because of these women, the world of mathematics has changed supremely. Thanks to them, it has become less insurmountable for women to imagine themselves adding to these two women’s legacies.

Featured Image by Chris de Kok on Flickr

Attribution 2.0 Generic (CC BY 2.0)

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