Too Little, Too Late?

I had a birthday about a month ago, and with that birthday I entered a new decade.  I won’t reveal which decade, but let’s just say that my age is starting to really hit me.  I am not old, but I am not young either.  And this led to me reflecting on what I’ve done in my life.  There are so many things that I have accomplished, but there are so many things I still want to accomplish.  But am I now too far along to still achieve certain dreams?  If I look closely at the world of mathematics, the message seems to scream “Yes!”  After all, the top prize of mathematics, the Fields Medal (like a Nobel Prize for mathematics), is only awarded to people under the age of 40 years.  So, what does that mean?  Are the people who established the prize saying that mathematicians cannot possibly be noteworthy after reaching that particular age?  It sure feels that way.

But, just as I was experiencing a decline in hope, I thought about what some have done well past that point.  Take Yitang Zhang, for example.  A colleague shared the story of this quiet mathematician, who had a Ph.D. but struggled to get a university position.  His struggles were so stark that he spent time building sandwiches at Subway and sleeping in his car.  But, he never let his circumstances distract him from his work.  Tirelessly and silently, he plugged along in his research.  Then, he astounded the world of professional mathematicians with his discovery regarding the Twin Prime Conjecture.  (The Twin Prime Conjecture says that there are an infinite number of pairs of primes that differ by 2, such as 3 and 5 or 11 and 13.)

Zhang didn’t prove the conjecture outright, but he made huge progress in narrowing down how often prime pairs occur.  He didn’t show that there are infinite pairs with a difference of 2, but he did say that there are infinite pairs with a difference less than 70 million.  I know this doesn’t sound impressive at first, but he showed that we can start narrowing down pairs into infinity.  And this was the foundation needed by other mathematicians to build upon and narrow down the gap even further.  Suddenly, Zhang was a sensation!  It was not too late!  He prefers to avoid the limelight and continue working in the quiet, but he now has a prestigious university position and a place in mathematics history.  And this happened in his 50’s!  It is too late for a Fields Medal, which is a shame.  But it is not too late to achieve.  And that gives me hope.

Why do I need this hope?  Well, I am a teacher of many non-traditional students.  Adults come into my classrooms, hoping to reinvent themselves in later years.  Often, they are older than me.  And I am in awe of the sacrifices these people make to improve the lives of themselves and their families.  They are reaching for their dreams and achieving, not allowing age to stand in the way.  I watch my own students and draw inspiration from them.  But, I still wonder if I can do the same.  Is it possible in my chosen field?  And figures such as Yitang Zhang tell me that it is wholly possible and never too late.

*Recently, Quanta magazine highlighted the places that some top researchers visit to do their deepest thinking.  I particularly like Zhang’s location and dream of one day being there, too.

Yitang Zhang at the Beach in Santa Barbara



What if I told you that one of the top mathematicians of today makes discoveries in his field through valuable playtime?  It’s true!  And he is not the only one.  Just think about why children play.  For a child, playtime is work.  It is their way of figuring out how the world works as they grow up.  But why does it have to stop at adulthood?  It doesn’t, and it shouldn’t.  For someone such as number theorist Manjul Bhargava, playtime is his way of figuring out how the world works.  And he is very good at it!  In fact, he won a Fields Medal in 2014.  (A Fields Medal is only one of the highest honors a mathematician can receive, akin to a Nobel Prize.)

And how does he play?  For one, he is an artist.  He studies Sanskrit poetry and is an accomplished musician.  Both of these pursuits are rich in mathematics.  Did you know that Sanskrit poetry has the Fibonacci numbers?  I talked about Fibonacci numbers in the previous posts Flowers and Fibonacci and Fibonacci Fun.  Except, in India, the numbers in the famous sequence are called the Hemachandra numbers.

How else does he play?  His office at Princeton University is littered with mathematical toys such as Rubik’s Cubes, Zometools, and puzzles.  And what studies about Fibonacci/Hemachandra numbers would be complete without a collection of pine cones?  These toys are not fun and games.  But, maybe they really are?  Either way, Rubik’s cubes helped Bhargava to solve a 200-year-old number theory problem while he was still a graduate student at Princeton.  Talk about the power of play!

If you want to read more about this accomplished mathematician, check out the following article in Quanta magazine:   2014 Fields Medal and Nevanlinna Prize Winners Announced