Thursday, November 22, 2007

George Dantzig- Mathematical Genius and Urban Legend Hero

Jack Dini, Livermore, CA

Imagine you’re a graduate student taking a mathematics course at the University of California, Berkeley. One day you oversleep and are late for class, so late that everyone has gone. However, there are two problems on the blackboard. You assume these are homework problems and you copy them down. The problems are harder than usual and it takes you quite a while to finish them. When finished, you take them to your professor to see if he still wants the work. He tells you to throw it on his desk and you do so reluctantly because the desk is covered with a heap of papers. You fear that your homework will be lost forever. About six weeks later, on a Sunday morning you are awakened by someone banging on your front door. It’s your math professor with papers in hand, all excited. “I’ve just written an introduction to one of your papers. Read it so I can send it our right away for publication.” You initially have no idea what he is talking about. It turns out the problems on the blackboard which you had solved thinking they were a homework assignment were, in fact, two famous previously unsolved problems in statistics. (1)

This sounds like an urban folklore legend, and some folks have promoted it as such. It’s also been used by ministers in sermons, most famously by the Reverend Robert Schuller of the Crystal Cathedral and television fame. Schuller embellished the story by claiming the problems were part of a final exam and that the high scorer in the test would get a job in the math department. (These were the depression years and jobs were very coveted and hard to come by). Schuller also reported that even Einstein had been unable to crack the problems. (2)

The story has also been used as the setup of the plot in the 1997 movie Good Will Hunting, as well as in one of the early scenes in the 1999 film Rushmore showing the main character daydreaming about solving the impossible question and winning approbation from all. (3)

Well, the young graduate student who solved the problems was George Dantzig. The unintended consequences of this action was that besides showing that it was possible to do the ‘impossible,’ the problems also led to his Ph.D. in statistics. When he was searching for a thesis topic, his advisor, Jerzy Newman, told him to wrap the two problems in a binder and he would accept them as his thesis. (1)

Dantzig went on to have an illustrious career in mathematics. He created the field of linear programming from his ‘simplex method,’ an algorithm for solving complex problems that revolutionized scientific computation. Here’s what the Stanford Magazine reported after his death in May 2005, “Combined with the calculating power of today’s computers, Dantzig’s algorithm is a tool that allows businesses and governments to identify optimal solutions to problems involving many variables. Linear programming applies to thousands of diverse applications—from pricing products, scheduling shipments and workers, assigning personnel, rotating crops and targeting weapons. Professor of management science and engineering Arthur R. Veinott, Jr. calls Dantzig’s simplex method the single most widely used algorithm originated in the last six decades.” (4) The iron and steel industry has used a Dantzig programming method to evaluate iron ores, explore the addition of coke ovens, and select products. The Federal Energy Administration is using his method to evaluate energy policy alternatives, and linear programming has also been used or suggested for controlling water and air pollution. (5)

His 1963 book, Linear Programming and Extensions, which explains his methods, is still in print 43 years later. He also co-wrote Compact City: A Plan for a Livable Urban Environment, and after retiring from Stanford in 1997, completed two volumes on linear programming and wrote a science fiction novel. In 1975, President Gerald Ford awarded him the National Medal of Science.

Besides his math legacy he leaves us with some key motivational help. Because no one had told him that it couldn’t be done, he did it. He probably would not have thought positively if he had known the two problems were famous unsolved works. A person is limited only by the thoughts that he or she chooses.

References

1.More Mathematical People, Donald J. Albers, Gerald L. Alexanderson and Constance Reid, Editors, (New York, Harcourt Brace Jovanovich, 1990), 67

2.The First Christian News, Volume 53, Issue 31, August 3, 2005

3.“Way Out Research on Obscure Topics,” Flat Rock.org; accessed December 18, 2005

4.“Math Whiz Transformed Resource Management,” Stanford Magazine, September/October 2005

5.“INFORMS Mourns Death of OR Pioneer George B. Dantzig,” www.newswise.com: accessed December 18, 2005

2 comments:

Aditya said...

(BTW, it's Jerzy Neyman, not Newman).

Scooter McGee said...

Mr Dini,

Any idea how I get a hold of your son Steve? Its been years!

Thanks

Scott Van Epps