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Everybody knows what Urban Legends are, right? Of course, they are … Legends, you know, except that  sometimes they have some truth in them. Like The Unsolvable Math Problem.

This legend is used as the setup of the plot in the 1997 movie Good Will Hunting. As well, one of the early scenes in the 1999 film Rushmore shows the main character daydreaming about solving the impossible question and winning approbation from all.

I think that everyone has dreamed about solving their company’s biggest financial problem and receiving a big check just in time to buy that new gadget. Or about finding the ingredient of that particular glue Stradivarius used on his violins and blow away all the world’s most famous violonists. I guess this urban legend about solving "unsolvable" math problems would come from time to time visiting maths or computer science students or professors etc.

Short version:

Student mistakes examples of unsolvable math problems for homework assignment and solves them. 

But it seems that this legend comes from a true fact:

One day, in 1939, George Bernard Dantzig, a doctoral candidate at the University of California, Berkeley, arrived late for a graduate-level statistics class and found two problems written on the board. Not knowing they were examples of "unsolvable" statistics problems, he mistook them for part of a homework assignment, jotted them down, and solved them. 

And the rest is … you know, Legend! The professor helped him publish the demonstrations and later he received recognition for his work. It’s interesting to see how, afterwards, the story passed into a Legend. A Lutheran Reverend had heard the story and asked the permision to include it into a book about thinking positively:

The moral of his sermon was this: If I had known that the problem were not homework but were in fact two famous unsolved problems in statistics, I probably would not have thought positively, would have become discouraged, and would never have solved them.

Read full article here, on the Urban Legends Reference Page.