Replied to my post: He was ignorant of the fact that the problems were supposed to be impossible. So he at least assumed the problem where thought to be unsolveable.
As to the gap between homework and open questions in the field, it can be fairly small in mathematics when the course is on the cutting edge. The field of Statistics was a lot more open back then, and there are still plenty of subjects where the gap between cutting edge homework and original research is fairly small.
PS: I once had a teacher suggest I write something up as original research as an undergraduate. The circumstances where a little different but less than you might think. It was a lecture where he was describing an algorithm and I said “that’s seems slow why not do X” but the same basic concept.
I can think of one:
http://www.snopes.com/college/homework/unsolvable.asp?a
Replied to my post: He was ignorant of the fact that the problems were supposed to be impossible. So he at least assumed the problem where thought to be unsolveable.
As to the gap between homework and open questions in the field, it can be fairly small in mathematics when the course is on the cutting edge. The field of Statistics was a lot more open back then, and there are still plenty of subjects where the gap between cutting edge homework and original research is fairly small.
PS: I once had a teacher suggest I write something up as original research as an undergraduate. The circumstances where a little different but less than you might think. It was a lecture where he was describing an algorithm and I said “that’s seems slow why not do X” but the same basic concept.