Ann Varela: The Passing of a Beautiful Mathematical Mind (and Personality)

Aug 1, 2017 by

An Interview with Ann Varela: The Passing of a Beautiful Mathematical Mind (and Personality)

Michael F. Shaughnessy –

1) Ann, Marina Ratner, a world famous mathematical recently died- what is your immediate reaction?

I am saddened for her daughter’s and grandchildren’s loss, but at the same time, I am encouraged and delighted by her ability to achieve distinction at an age that is considered to be late in life.  After all, she was almost 50 when she was recognized for contributing to the field of mathematics in a significant way.

2) What do we know about her early childhood? (I know she was born in the Soviet Union).

Marina Ratner’s childhood began in Moscow, Russia.  She was raised in a Jewish family which would prove to be an obstacle for her career later in life.  Her parents were both college graduates.  Ratner’s father was a plant physiologist and professor, while her mother’s occupation was a chemist.  Ratner proclaimed her love and fascination for mathematics in the fifth grade.  She had a sense of satisfaction and accomplishment when solving challenging problems in algebra and geometry, as many of us in the field do.

Ratner continued to excel in mathematics during her high school years.  Supportive teachers gave her strength and encouragement to study mathematics in college.  Although she was only able to solve 10 out of 11 of her college oral entrance exam questions, Ratner was accepted and attended Moscow State University in 1956.  Fortuitously, for Ratner, this university had presently begun admitting Jewish students.  Her studies included primarily mathematics courses, physics and the mandatory Marxism and Communist Party history curriculum.  By 1961, Ratner earned her M.A. degree.

3) Apparently, she worked in the Soviet Union for a prominent Andrey Kolmogorov, who was a famous mathematician. I am wondering if this is the same person who developed what I have used in statistics- the Kolmogorov-Smirnov test.

Ratner was interested in probability theory and began working in Kolmogorov’s statistics group and taught in his school for exceptional high school students upon earning her master’s degree.

Andrey Kolmogorov and Nikolai Smirnov did indeed develop the K-S test used in statistics.  The K-S test is used to compare a sample with a reference probability distribution, or to compare two samples.  The Kolmogorov-Smirnov test can be adapted to indicate the fit of the distribution.  That is, how well it corresponds to a set of observations (measurements).  See Figure 1.

Figure 1

https://upload.wikimedia.org/wikipedia/commons/c/cf/KS_Example.png

The black arrow identifies the K-S Statistic.  The shorter the distance, the better the correspondence.

https://upload.wikimedia.org/wikipedia/commons/c/cf/KS_Example.png

4) She completed her doctorate in 1969. But later worked in Israel. Do we know how this came about?

According to Ratner’s Berkeley colleague, Alexandre Chorin, Ratner had a difficult time in Russia finding permanent employment and felt compelled to leaving the country.  Her religious background played a role in this unfortunate situation.  It was not until 1971 that Ratner and her daughter, Anna, were able to immigrate to Israel.  Although she was able to continue her mathematical research, Ratner was employed as a temporary lecturer and not allowed to obtain a tenured positon at the Hebrew University of Jerusalem.  Fortunately, in 1975, Ratner gained employment at the University of California, Berkeley.  After about six years had passed, she was at last a tenured professor in 1982.

5) Now, in general, MOST mathematicians do their best work when young, yet Dr. Ratner found recognition in midlife. What is she MOST known for?

Ratner’s foremost work was in the area of mathematical analysis and ergodic theory.  Ergodic theory is a branch of mathematics related to probability theory and statistics that originated in the study of thermodynamics.  A dominant interest of ergodic theory is the behavior of a dynamical system (a system in which a function defines the time dependence of a point in a geometrical space) when it is permitted to run for an extended period of time.  More specifically, Ratner was interested in studying motion that is constrained to follow very special directions in uniform spaces.  Ratner theorized that either an object will follow an identical path repeatedly, or it will have a chaotic path.  These compliant, predictable paths in the dynamical system are known as unipotent flows.  See Figure 2.

Figure 2

https://upload.wikimedia.org/wikipedia/commons/f/f7/Hamiltonian_flow_classical.gif

Click on the link to see the animation.

https://upload.wikimedia.org/wikipedia/commons/f/f7/Hamiltonian_flow_classical.gif

Despite the claim that her Theorem concerning motion of objects in dynamical systems (unipotent flows) is theoretical and broad in spectrum, it has numerous applications, especially in Number Theory.

6) Rufus Bowen, a scholar in his own right brought her to Berkeley, California, where apparently she taught mostly undergraduate. Any insights at to what transpired there?

Rufus Bowen studied dynamical systems at the University of California, Berkeley.  Since Ratner was also studying geometrical dynamical systems, the two engaged in a correspondence which ultimately led to Ratner’s employment on the Berkeley campus.  Apparently, Bowen had to convince his colleagues and the Berkeley administration to support his nomination for Ratner to join the UC faculty.

7) It is said that Etienne Ghys, a math scholar in France spent 6 months trying to understand her work- but when he met her, the story goes that he exclaimed that his reading of her work seemed to be a self- explanation or self-validation of her work. Your thoughts?

I suppose that if one cannot even convince oneself of a theory’s validity, it would certainly be impossible to convince others of its worth or truth.  I imagine that she wrote with much detail, explaining each and every step with critical points being emphasized, so as to convince herself of the theorem’s claim.  She most likely wrote with a similar style as how she taught.  In other words, she possessed a clear, concise style of writing to convey her ideas and theories with the utmost care, so as not to confuse the reader or student.

8) Apparently she worked alone (some mathematicians may need the solitude) and did not promote her own theories (maybe she was modest).  Any last thoughts on this great female mathematician?

It is evident that Marina Ratner loved mathematics and teaching.  She once said, “For me, mathematics is a part of Nature’s beauty and I am grateful for being able to see it.  Whatever mathematics I happen to teach, I love to communicate its beauty to my students.”  Ratner’s daughter, Anna, supported this claim by sharing how her mother truly cared about her students understanding course material and encouraging them to pursue careers involving mathematics.  She apparently influenced many young mathematicians to excel and succeed.

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