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MATHEMATICIANS MARINA Ratner and Maryam Mirzakhani passed away within a week of each other, on July 7 and July 14, 2017, respectively. That they were successful women in a predominately man’s profession is noteworthy. That they both had specialities in dynamical systems, the particular branch of mathematics of my own studies, is significant to me. Last, they represented both example and counterexample of the folk legend that mathematicians perform their significant achievements when they are young.
Indeed, Maryam Mirzahhani, a Fields Medal winner in 2014, died at age 40 of cancer. Marina Ratner, who did her most significant work after age 50, died at 78 of cardiac arrest.
Maryam Mirzakhani was born in Tehran, Iran, in 1977. Iran and Iraq were at war during her childhood, but “I think I was the lucky generation,” she said later, “because I was a teenager when things became more stable.”
In high school, Mirzakhani was a member of the Iranian team at the International Mathematical Olympiad. She won a gold medal there in 1994, and another gold medal the next year.
Her undergraduate studies were at Sharif University of Technology in Tehran; her graduate work at Harvard culminated in a Ph.D. in 2004. Mirzakhani taught at Princeton before moving to Stanford in 2008.
In 2014, Mirzakhani was awarded a Fields Medal, considered the mathematical counterpart to a Nobel Prize. Unlike the latter, though, the Fields Medal is awarded to mathematicians who are under the age of 40. Mirzakhani was the first woman, and the first Iranian, to be so honored.
Mirzakhani’s speciality of dynamical systems can be thought of as a blend of dynamics and topology, the latter, a study of geometric properties preserved under continuous deformation. As one example, Mirzakhani imagined billiard balls bouncing around on pool tables with increasingly complex shapes and even higher dimensions. She described this in a video produced by Quanta Magazine.
Marina Ratner was born in Moscow in 1938, the daughter of scientists. She graduated from Moscow State University in 1961. Ratner worked for four years as assistant to Andrey Kolmogorov, a prominent Russian mathematician, before attending grad school at Moscow State. She got her doctorate there in 1969 (coincidentally the same year I got mine).
Ratner wished to emigrate to Israel, but the Soviet Union initially preferred that she teach at Moscow’s High Technical Engineering School. In 1971, she and her daughter were able to emigrate to Israel where she lectured at Jerusalem’s Hebrew University.
Ratner was not particularly known as a research mathematician until she turned 50. Her speciality evolved into a blend of dynamics and number theory. In fact, Ratner’s work is seen as fundamental to the research of Maryam Mirzakhani and Elon Lindenstrauss, both of whom won Fields Medals in 2014.
Ratner was a tenured professor at the University of California, Berkeley, an institution she joined in 1975. As noted by The New York Times, “At Berkeley, she earned high marks as a teacher of undergraduates but was thesis advisor to only one doctoral student.”
A colleague once remarked that her mathematical papers were written not for other mathematicians, but mainly to convince herself that the theorems were correct. Dr. Ratner is said to have replied, “Yes! Exactly! You understood why and how I write mathematics.”
Maryam Mizakhani’s “painting” and Ratner’s internally focused thinking are two wonderfully individual ways in which mathematics can be performed. Bless them both. ds
© Dennis Simanaitis, SimanaitisSays.com, 2017