What could you achieve if you didn’t know what was impossible? Mathematician George Dantzig found out as a graduate student at UC Berkeley in 1939. Walking into a class late one day, he saw two statistics problems on the blackboard. Assuming they were a homework assignment, Dantzig copied them down and spent several days working on them. They seemed more challenging than usual, but after a few days he came up with the solutions and handed his paper in.
That’s when he found out that his professor had written the problems on the board as examples of two of the most famous unsolved problems in the field of statistics. Dantzig’s solutions appeared in mathematical journals. One year later, when talking to his prof about possible subjects for his thesis, the professor told him to simply put the two problems in a binder and submit them as is.
The story has been retold many times as an example of positive thinking; a version of it was adapted for an opening scene in the movie Good Will Hunting.