There's a tale about the math grad student who sees a problem on the blackboard and, thinking it was a homework problem, goes off and solves it getting a Ph.D. as a reward. It turns out there's some truth in the story.. this interview with George Dantzig.
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MP: How did it happen that you did your Ph.D. on a statistical topic w you took so few courses in statistics?
Dantzig: It happened because during my first year at Berkeley I arrived lat day at one of Neyman's classes. On the blackboard there were two problems assumed had been assigned for homework. I copied them down. A few days l apologized to Neyman for taking so long to do the homework?the pro seemed to be a little harder to do than usual. I asked him if he still wanted it. He told me to throw it on his desk. I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever. About six weeks later, one Sunday morning about eight o'clock, Anne and I were awakened by someone banging on our front door. It was Neyman. He rushed in with papers in hand, all excited: "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." For a minute I had no idea what he was talking about. To make a long story short, the problems on the blackboard that I had solved thinking they were homework were in fact two famous unsolved problems in statistics. That was the first inkling I had that there was anything special about them.
MP: But you had apologized to Neyman for taking so long to do them.
Dantzig: Well, there was no particular deadline, and you know how graduate students take their time. 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. The second of the two problems, however, was not published until after World War II. It happened this way. Around 1950 I received a letter from Abraham Wald enclosing the final galley proofs of a paper of his about to go to press in the Annals of Mathematical Statistics. Someone had just pointed out to him that the main result in his paper was the same as the second "homework" problem solved in my thesis. I wrote back suggesting that we publish jointly. He simply inserted my name as coauthor into the galley proof.
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a tip of the hat to Andrew