Tuesday, December 27, 2011

39: A Statistical Legend

    You have probably heard the urban legend about the college student
who walks into a classroom late, solves the math problems on the
board thinking they are an assignment, and then finds out that the
lecture that day was on famous unsolved problems.  This story has
become a staple of lectures on positive thinking, and inspired a
subplot in the movie Good Will Hunting.  But the most surprising thing
about this urban legend is that it's based on a well-documented true
    The student involved was George Dantzig, a graduate student at
Berkeley in 1939.  He arrived late to a statistics class, and saw
several problems already on the board.  Assuming they were that week's
assignment, he copied them down.  It took him longer than usual to
solve them, so a few days later he sheepishly approached the busy
professor, Jerzy Neyman, and asked if he could turn in his homework
late.  The professor, not paying much attention, told him to leave the
homework on his desk.  Then a few days later, Neyman appeared, banging
on Dantzig's front door.  At that point he explained that the problems
had been famous unsolved problems in statistics, and he wanted to send
one of them out for publiction immediately!  He later accepted these
same solutions, written up a little more formally, as Dantzig's
Ph.D. thesis.
    The story passed from a curious anecdote into the realm of urban
legend after a chance encounter between Dantzig and evangelist Robert
Schuller of the Crystal Cathedral in Los Angeles.  Schuller liked the
story so much that, in addition to using it in motivational talks, he
published it in one of his books on the power of positive thinking.
The version in the books was badly distorted, moving Dantzig from a
grad student to an undergrad, and adding claims that Einstein had
attempted and failed to solve the same problems.  The anecdote began
to pop up regularly in Christian sermons across middle America.
    Dantzig quite went on to a very distinguished career, working at
the RAND corporation, Berekeley, and Stanford, and becoming known as
the father of Linear Programming.  Linear Programming is a method of
solving problems where there is a linear equation in multiple
variables with many solutions, but the solutions are constrained by a
set of inequality relations, so you want to try to find an optimal
result under the constraints.  A simple example might be in a factory
where you have constraints on the various amounts of resources that
can be used, a minimum required level of quality, and need to maximize
the number of units you produce.  This field of study was considered
so important that the U.S. government initially kept it a secret, due
to its potential reduction of costs and casualties to the army.   In
1975, Dantzig was awarded the National Medal of Science by
President  Ford. 
    So, what lessons can we draw from this story?  Well, Dantzig was
clearly a genius to start with, as his later career shows.  But his
experience is still relevant to the rest of us.  By approaching a
problem with the mindset that you should be able to solve it, rather
than starting out by thinking it's probably beyond your abilities, you
can significantly increase your odds of success.  I should probably
end the podcast now, before I start to sound like Oprah.
    And this has been your Math Mutation for today.

  • The Dantzig Urban Legend at Snopes
  • George Dantzig at Wikipedia
  • Linear Programming at Wikipedia
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