Sunday, August 31, 2014

Back to School

I don’t know exactly when it happened, but we’ve come to make the journey of “going back to school” into the most miserable experience imaginable.  There once was a time when kids were enthusiastic about going to school or returning to school.  There was a real excitement about new shoes, bright new clothes, new book bags and pencils or pens.  There were fresh, unsullied booklets and binders.  We’d put paper bag or team sport covers on our books.  We looked forward to seeing friends who lived too far away to see during summer.  There was a certain joy about returning to class led by a favorite teacher. 

Parents participated in this “tone at the top.”  They’d use this time to teach us how to organize ourselves for the school. They’d coach us to polish our shoes and put them near the door. They’d run down first-day-of-school checklists: Did we have this? Did we pack that? Was our lunch or lunch money ready?

Today, every cartoon in our local paper broadcasts the imminent misery of going back to school.  Advertisers are conditioning our kids to counter the prospective misery by buying up and over-dressing to compensate for the tedium of school days ahead. As a consequence, why are we surprised that kids today act out that negativism in disruptive, aggressive, and sometimes bullying behaviors?

The prospect of a positive learning experience has been exchanged for this negative hype.  Misery loves company, so every mention of back to school becomes a downer.

If we want kids to be enthusiastic about their learning experiences at school, we will have to set the “tone at the top” and close down the negativity.  Going back to school needs to become, once again, an exciting, positive, productive learning experience.  

To Make the World a Better Place to Live In

When I was in the 7th grade, my father was commuting daily by train between our small town in Southern New Hampshire and his office in Boston, Massachusetts.  My mother would drive him to the station each morning and back home again each evening. Often I would “ride shotgun” with her when she drove to pick him up in the evening.

Many times he was joined in the evening by another townsman commuter.  We would drive him from the station to his home on the way to our home.  My father would take over the driving, my mother would take over the “shotgun” seat, and I would sit next to our fellow townsman who inevitably would try to engage me in conversation.

He was a man of routine, as were most men of that era.  He’d start the conversation with, “Well, what did you do today to make the world a better place to live in?” Heady stuff for someone who barely qualified as a teenager! I’d have to think about an answer each evening, just in case he’d be on the train with my father and just in case I’d get his query. 

“What did I do, today?” would be my first thought?  I’d have to review school, classes, gym, and play after school to inventory what, in fact, had occupied my time.  The real challenge was whether or not I did anything worth reporting that might match his higher standard.  “What would make the world a better place?”

He was pretty generous in his performance appraisals.  I could say “I watered the plants at school,” and he would respond enthusiastically, “That’s marvelous!” as if I’d just saved the Amazon forests.  I might say, “I feed the dogs” to which he’d respond, “Good work!” making me feel like a responsible adult.  I might have to search for a performance measure, but usually could find something to report in terms of a grade, project, or report at school.

All of which was his point, of course.  His job was to set out some expectations that only I could determine would be acceptable by the standards of “make the world a better place.”  I had to find the actions that I deemed worthy of mention to him in the back seat of our car.  He made me think about my efforts each day.  Were they worthy?

At the end of the evening, we would drop him off at his front door, where he inevitably would say the same parting words, “Thanks for the buggy ride!” And we’d go our separate ways.

His expectations were pure and simple, but they stayed with me for these many years. Even today I will ask myself if I’ve done anything that might make the world a little better place to live in.  That is a mindset for which I must thank our townsman commuter - our fellow buggy rider.

Friday, August 29, 2014

On Asking Questions

It was interesting to read that the 2014 Fields Medal winner, Maryam Mirzakhani, was sharp enough in college to pursue opportunities to attend the “informal seminars” offered by noted Harvard mathematician, Curtis McMullen (a Fields Medal winner in his own right, in 1998). Taking advantage of extemporaneous learning experiences like that is an example of the initiative that puts individuals such as Mirzakhani on track toward exceptional advancement.

Mirzakhani was much more than merely a bump on the log among the seminar audience.

She asked questions.

Probably, she asked many deep, penetrating, and interesting questions. Which was one of the reasons Professor McMullen became interested enough in her intellectual development to mentor her as a doctoral candidate.

How many times have we attended an event or given a presentation or webinar where the moderator invited the audience to join in the “Questions & Answers?”  And how many times have we encountered dead SILENCE?

Smart speakers and moderators know this phenomenon all too well.  They seed the audience with one or two prepared questions to ensure that the proper tone is set and that the dead air doesn’t infect everyone.  That silence is very frustrating to a presenter.  You ask yourself, “Why did I bother?”

The “Question & Answer” portion of a presentation can be as enriching as the speech itself, but only if the members of the audience generate intelligent, relevant, and interesting queries in the speaker’s domain of expertise.  The failure of the audience to step up and carry their share of the responsibility results in the waste of valuable intellectual resources.

The speaker’s knowledge is under-valued.  Speakers thrive on the exchange of productive ideas and constructive dialog.  By failing to engage the speaker, the audience is failing to tap that fountain of wisdom.

The audience potentially is an active learner, but only if members formulate an intelligent question worthy of a response.  If the audience cannot think of anything to add to this field of inquiry, then when would there be a more fertile chance for idea exchange in which individuals might participate.

What are the reasons (or, more accurately, the excuses) for the silence?

“I don’t want to appear stupid.”  Isn’t it reasonable to believe that an individual exhibits a measure of intelligence simply by seeking the wisdom of the speaker and attending the event in the first place?  Isn’t there just one basic question that might add value to this topic and evidence your smarts more than your stupid?  

“I wasn’t listening closely enough. The speaker may have answered the question in the presentation.” For shame! Next time, listen up!

“I hate to be first.” So, you aspire to be second? Or merely a follower?

“I’m afraid of speaking in public.” The average person is more afraid of speaking in public than dying.  So, are you in that audience because you are an average or an exceptional person?  There are many ways to overcome this anxiety.  The easiest way is to just start asking a few good questions in a public event when invited to do so.

“The speaker knows more than I do.” Right! That’s why the speaker is on the stage, while you are not.  But, you are there to learn.  So, start by identifying one small area or thought whereby the speaker could enlighten you by sharing his/her insight.

“I should have prepared a few questions in advance.” Right again.  You should have done some research about the individual and formulated one or two questions to show you have a little interest in this topic.

“I wish I had more time to ask more than just one question.”  Which question is the most important one right now?  If you cannot get that one question asked and answered, why would the speaker bother with any of the other questions?

“I’d really like a one-on-one opportunity to talk with this individual.” Do you have secrets you don’t want to share with other members of the audience?  Why would this presenter possibly be interested in participating in that one-on-one with you if you don’t have the courage to express your questions in the public forum?

Imagine, if you would, the loss of idea development that might have resulted if Maryam Mirzakhani had not engaged Curtis McMullen in a creative dialog where she thought carefully about and asked some really good questions of him – so good, in fact, that he helped her achieve her doctoral goals as an advisor. Asking good questions is a fundamental skill that we all must develop.

Oh, and one more thought:  the question, "Will the presentation slides be available?" is NOT a valid, information-gathering, intelligence-enhancing question.  We really can do better than that!

Wednesday, August 27, 2014

Outstanding Woman in Mathematics: Maryam Mirzakhani

On August 13, three amazing women stood together on the stage at the 2014 Seoul, Korea International Congress of Mathematicians (ICM). Maryam Mirzakhani was recognized with the Fields Medal, an award for “outstanding mathematical achievement for existing work and for the promise of future achievement” from the International Mathematical Union (IMU). The Fields Medal is given to an exceptional mathematician aged 40 years or younger.  Including this year, there have been 56 recipients, but Maryam Mirzakhani is the first woman so honored.  The IMU described Mirzakhani’s work in these glowing terms:

“Fluent in a remarkably diverse range of mathematical techniques and disparate mathematical cultures, she embodies a rare combination of superb te4chnical ability, bold ambition, far-reaching vision, and deep curiosity.”[i]

Her specialty is the geometry of hyperbolic surfaces and moduli spaces (a geometric space whose points represent some form of algebraic or geometric object). 

She described her own work in these terms:

“I like crossing the imaginary boundaries people set up between different fields – it’s very refreshing.  It’s about being optimistic and trying to connect things.”[ii]

The individuals who opened the congress and awarded Mirzakhani her medal (along with three others) were President Park Geun-hye (the first woman president of South Korea) and Ingrid Baroness Daubechies (the first woman president of the IMU and a noted Belgian physicist and mathematician in her own right). In 2000, Daubechies was the first woman to receive the National Academy of Sciences Award in Mathematics.

Biographical Background

Maryam Mirzakhani was born (May 1977) in Tehran, Iran. She was one of three children raised by supportive parents.  She read copiously about men and women role models, imagining herself  becoming a writer. Her parents placed her in Farzanegar high school, “a national organization for the development of exceptional talents,” yet her first math teacher failed to motivate her. It was her older brother who piqued her interest in science and math by showing her the mystery of Karl Friedrich Gauss’ method of adding numbers from 1 to 100 (consisting of a series of 50 pairs each adding up to 101, for a total of 5050).

In 1994, she and her close colleague and math partner at high school, Roya Beheshti (now Zavareh) became the first women to represent Iran in the International Mathematical Olympiad which was held in Hong Kong. Mirzakhani won the gold medal while Beheshti won the silver medal that year. In the Toronto competition in 1995, Mirzakhani received a perfect score.
In 1999, they both earned Bachelor of Science degrees in mathematics at the Sharif University of Technology in Tehran.  Beheshti Zavareh went on to earn her Ph.D. in Mathematics from MIT in 2003 and currently is an Associate Professor of Mathematics at Washington University in St. Louis, MO.[iii]

Mirzakhani was accepted at Harvard University where she studied hyperbolic surfaces.  Her doctoral advisor at Harvard was Curtis McMullen (a 1998 Fields Medal winner). Mirzakhani attended the informal seminars that McMullen organized, where she regularly asking him questions. She received her Ph.D. from Harvard in 2004. She was a Clay Mathematics Institute (Providence, RI) Research Fellow and assistant professor of mathematics at Princeton University (Princeton, NJ) from 2004 to 2008. She joined Stanford University’s Department of Mathematics as a Professor in September 2008.

In 2009, she was awarded the Blumenthal Award (from the American Mathematical Society) for “the advancement of research in pure mathematics.” In 2013, she received the Ruth Lyttie Satter Prize (from the American Mathematical Society), recognizing an outstanding contribution to mathematics research by a woman during the preceding six years. In 2014, she was given a Clay Research Award from the Clay Mathematics Institute awarded to Mirzakhani and Peter Scholze to recognize their achievements in mathematical research.

Mentors, in addition to McMullen at Harvard, include Alex Eskin, professor of mathematics and collaborator from the University of Chicago, and Steven Kerckhoff, professor of mathematics at Stanford.

She is married to Jan Vondrak, a theoretical computer scientist at IBM Almaden Research Center in San Jose, CA, and they have a 3 year old daughter, Anahita.

The Fields Medal

The Fields Medal was created in 1936 from a behest left to the IMU by John Charles Fields, a Canadian mathematician and researcher who died in 1932.  The Fields Medal is one of five scientific and mathematical awards granted every four years for unique contributions to the field of mathematics. Fields himself did not originally set an age limit but wrote that, “… while it was in recognition of work already done it was at the same time intended to be an encouragement for further achievement on the part of the recipient and a stimulus to renewed effort on the party of others.”

The award includes a small stipend of about $15,000 (Canadian). Originally, surplus funds from the 1924 ICM gathering were combined with funds from Fields estate to support two award recipients. An anonymous donor provided additional sums in 1966 which made it possible to award four Fields Medals at each four year gathering of the IMU.

The four other IMU prizes are: 
  • Gauss Prize - to honor scientists whose mathematical research has had an impact outside mathematics – either in technology, in business, or simply in people's everyday lives.
  • Chern Medal Award – the highest level of recognition for outstanding achievements in the field of mathematics
  • Rolf Nevalinna Prize – for outstanding contributions in mathematical aspects of information sciences
  • Leelavati Prize (at the ICM Closing Ceremony) recognizes outstanding public outreach work for mathematics


Maryam Mirzakhani will prove to be an enduring role model for young girls who consider the opportunities in math. Lessons from her experience echo those we have seen before:
  • Parents who encouraged her and created surroundings that fostered her intellectual ambitions
  • A brother who provided a counterbalance to an uninspiring math teacher
  • A close friend (Roya Bereshti Zaraneh) with similar interests to challenge and support her
  • Excellence of education
  • Mentors whose intellect she pursued and who counselled her progress
  • Collaborators who were proud to pursue like interests with her
  • Organizations that recognized the unique contributions of their members
  • An open mind, herself, enabling her to reach across the silos of expertise
  • And an open mind, as well, among all those who saw her innate talents.     

[i] “The Work of Maryam Mirzakhani” from the International Mathematical Union, August 2014 Press Release,
[ii] “A Tenacious Explorer of Abstract Surfaces” by Erica Klarreich, Quanta Magazine, August 12, 2014
[iii] For more information on Roya Beheshti Zavareh, see: