Go ahead and fall asleep in math class...

There's a scene from the 1997 movie Good Will Hunting where Matt Damon's character ("Will Hunting"), a genius working as a janitor at MIT, solves a difficult math problem that was left by one of the math professors on a dry erase board as a challenge to his graduate students.  Will solves the problem anonymously, and when no one "fesses up" to having solved it, the professor leaves an even more difficult problem to solve.  He later catches Will working on the problem, and the rest of the movie focuses on how Will goes on to greater things.

Matt Damon and Ben Affleck wrote the screenplay to the movie (and won the Academy Award for Best Original Screenplay that year at the 70th Academy Awards), and the real life mathematician George Dantzig apparently served as inspiration for the scene discussed above (see also the video clip here).  Dantzig was an American mathematician who made significant contributions during his lifetime to industrial engineering, operations research, computer science, statistics, and a sub-branch of mathematics known as linear programming.  Apparently, when Dantzig was a graduate student at the University of California, Berkeley, his professor Jerzy Neyman posted two problems on the blackboard at the beginning of his class in 1939.  Dantzig arrived late and assumed (wrongly, as it turns out) that the problems were the homework assignment for the day.  Dantzig thought that the problems "seemed to be a little harder than usual" and handed in completed solutions for both a few days later.  Six weeks later, Professor Neyman told Dantzig that the "homework problems" were actually two of the most famous unsolved problems in statistics.  They submitted one of the problems for publication.  Dantzig recalled much later in a 1986 interview, "A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis."

Over the years, the story has been further embellished and has become an urban legend.  I recently saw a social media post telling a very similar story, though in this case, it's about a student at Columbia University who fell asleep during mathematics class.  As the story goes, when the student woke up at the end of class, he noticed the lecturer had written two problems on the whiteboard.  He thought that these were homework assignments, so he copied them down and went back to his dormitory.  He spent hours in the library researching the problems and trying to solve them both.  Eventually, he was able to solve one of the problems, even though it was very challenging.  It was only after asking if his professor was ever going to collect the homework assignment that he found out that they were two famous unsolved problems.  Together, the student and professor submitted four papers based upon the solution to one of the problems, and they are still displayed at the university today as evidence that we shouldn't listen to people who say that something is impossible and that we shouldn't be afraid to fail.  The story is further supposed to illustrate the power of positive thinking.

I am reminded of Audrey Hepburn's famous quote, "Nothing is impossible, the word itself says I'm possible."  Or Nelson Mandela, who said, "It always seems impossible until it's done."  Or Mary McLeod Bethune, who said, "Without faith, nothing is possible. With it, nothing is impossible."  Or dare I add (much to my mathematics teacher wife's chagrin), "Go ahead and fall asleep in math class...you never know what may come out of it."