I passed Gordon Fisher's note along to Alan Tucker (son of Al Tucker) who says that it's not quite what he heard (many times) from his father. I got his permission to pass along the following:
"Milnor was a freshman, but he was taking a junior-level survey course in geometry for math and non-math majors. The day before Thanksgiving, my dad ended the planned material early and, instead of starting the next topic with a vacation coming up, he decided to fill up the rest of class by presenting a very famous open question about the curvature of a knot, which Boursak conjectured to be at least 4pi. This is the problem that Milnor solved. My dad took it to people around the Princeton Math Dept and then showed to people at the Inst. for Advanced Study, including Chern who was visiting there that year. The rest is history."
At 7:08 PM -0500 2/25/04, Gordon Fisher wrote: >My memory, from the time when I (and Al Tucker and John Milnor) were >at Princeton is that Tucker taught a course in mathematics appreciation >for freshmen, in which Milnor was a freshman student. Near the end of >the course, in order to illustrate the fact that there are many unsolved >problem in mathematics, posed one, I think in knot theory. A little >while later, Milnor went up to Tucker and deferentially handed him a >solution, which (Milnor said) he supposed was wrong. However, when >Tucker looked at it, he found it was right, and arranged for it to be >published somewhere. I got this story from a fairly reliable witness, >namely Al Tucker. > >(Tucker once asked me to collaborate with him on writing up his >freshman course for possible publication, and I attended the course >one semester -- not the one Milnor attended, but a little later. However, >I declined Tucker's offer because my wife and I accepted an offer to go >to the University of Otago in New Zealand, which we accepted partly for >the adventure, and partly to put some distance between us and my wife's >mother.) > >Gordon Fisher