Just because someone does not know a solution to a given problem does not mean they think it's impossible. The teacher gave the problem as examples of something that seems solvable but nobody has a correct solution to. Then someone with a lot of domain knowledge spent some time and solved it. IMO, that’s says more about the value of domain knowledge than tenacity. It's not like they spent 20 years comming up with a solution.
PS: There are a lot of long standing math problems which people have spent vary little time trying to solve.
I don't get your point. There's a difference between an unsolved problem and an unsolvable one? That's obvious. It's also irrelevant to the story.
The relevant distinction is between coursework exercises and open problems in the field. That's a pretty big difference. When students complete their homework, they don't typically get woken up by phone calls from excited professors telling them to write their work up for publication immediately.
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.
Sorry, no. The probably was supposed to be solvable.
Once again, yet to be solved is not the same thing as assumed to be impossible. In the history of mankind nobody has solved a X^2 * (first thousand digits of PI) + (next thousand digits of PI) * X = 0. But, using modern techniques I don't think it would be that difficult. And if someone 50 years from now could find this post and decide to wast their time they might be the first person to solve a this 50 year old math problem etc.
This is one of the greatest stories ever. If it weren't true it would have to have been invented... but it is true.