I love this story about George Dantzig, the mathematician and professor, who made substantial contributions in multiple fields.
During his study in 1939, Dantzig solved two [open problems in statistics] due to a misunderstanding. Near the beginning of a class, Professor Spława-Neyman wrote two problems on the blackboard. Dantzig arrived late and assumed that they were a homework assignment. According to Dantzig, they “seemed to be a little harder than usual”, but a few days later he handed in completed solutions for both problems, still believing that they were an assignment that was overdue. Six weeks later, an excited Spława-Neyman eagerly told him that the “homework” problems he had solved were two of the most famous unsolved problems in statistics.
Wikipedia, retrieved January 13, 2026.
As we know now, he would go on to build a highly successful career in academia and as a mathematician. So it is easy to read this story as “young genius figures out mathematics problems that no one else had been able to solve” – or something to that effect.
Of course, he was so smart. But I think that misses the point and a much more helpful interpretation of that story.
He assumed he was dealing with homework problems, not unsolved research. There is a pretty important difference between those two.
Generally unsolved problems are reasonably unexpected in a homework context. This distinction matters in two significant ways.
If it is homework, then it is something that you do for practice and to deepen your understanding in a given subject. It may be difficult, but you assume it is doable. Your teacher will likely have a solution and could correct or guide you along the way.
In this particular story, Dantzig realized it was more difficult than usual, so doubled down and put in extra effort, assuming he had to just work harder. It is telling he apparently felt the need to apologize for the delay, when he handed in his work a few days later.
On the other hand, if you know that no one has actually solved a given problem, then it might be a formidable challenge indeed. How will you judge the odds of you being the one who gets there? Open research is almost by definition much, much more difficult than a homework problem, certainly not something you should expect to “solve” within a few days of work. This is deterring people from investing themselves in a way that homework is not.
Dantzig unknowingly miscategorized the difficulty of the problems at hand, allowing him to tackle open research as homework instead. Assuming there is a known solution can help you keep going, when you are struggling to find your way to the answer.