Answer by Michael Ishigaki:

There's a well-known account of George Dantzig, "the father of linear programming," during his time as a mathematics student at UC Berkeley. One day, Dantzig was running late to a class taught by the famous Jerzy Neyman. When he arrived, he saw three problems on the blackboard and scribbled them down as homework problems. After class, Dantzig began working on solving these three problems. He found two of the problems straightforward and easy, but one of the problems was particularly difficult. He struggled with that third problem until minutes before the homework assignment was due.Six weeks later, on a Sunday morning, Dantzig was woken up by the noise of someone banging on the door of his house. He opened the door and was surprised to see his professor, Jerzy Neyman, at the door holding a handful of papers. His excited professor said, "I've written an introduction to one of your papers! Read it so I can send it out right away for publication!"

As it turns out, two of the three problems on the blackboard were not homework problems, but famous unsolved problems in mathematical statistics. Without knowing it, Dantzig solved two unsolved statistics problems for homework.

Later on, when Dantzig was having difficulty finding a topic for his thesis, Neyman told him to just put his solutions to those two problems into a binder and that Neyman would accept the solutions as Dantzig's thesis.

Sources: George Dantzig , Dantzig Obituary , The Unsolvable Math Problem