after finishing many long, seemingly impossible, problem sets by narrow margins you start losing your wits and wondering what would happen if you were actually working on the hardest problems in physics without knowing it. and whether you would figure them out by virtue of having no idea how hard they are. this story answers this question, and that answer is a resounding yes.
in 1939 george bernard dantzig, a math grad student, came late to class and mistook two unproven equations written on the board for the homework assignment. obviously, in accordence with the rules of the humorous anecdote, he proved them. here is the story in his own words (college mathematics journal, 1986):
it happened because during my first year at berkeley i arrived late one day at one of [jerzy] neyman's classes. on the blackboard there were two problems that i assumed had been assigned for homework. i copied them down. a few days later i apologized to neyman for taking so long to do the homework — the problems seemed to be a little harder 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, [my wife] 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.
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.