Will get pointed up but just smacks of passive-agressive argumental.
History, specifically in science and math is full of examples where people who actively sought to question the knowledge of more senior experts have made discoveries that advanced the knowledge of human-kind and have then been overlooked or ignored because they did not have the correct background. Institutions such as The Royal Society and The Geological Society where created exactly on this principle.
The idea that "you cannot question X because X is a learned man above your station" is what IMO destroys general interest in fields such as physics. You have to spend a career following the party line in the hope that one day you will be given enough rope to actually challenge anything.
How on earth would you put probability on something like that?
The existence of a black swan doesn't imply that swans are usually black.
A. "There are examples where newcomers to a field found a novel solution that senior experts have missed."
B. "It is often the ignorant who succeeds."
B does not follow from A. Not even in mathematics where people use to say that you have to prove yourself worthwhile by the age of 25 or it won't happen.
> You have to spend a career following the party line in the hope that ...
This is a slightly different discussion but IMHO in many fields (e.g. medicine) contemporary science has little to do with genious or insight but rather is an industrial effort ... and that _often_ isn't fun.
A lesson on logic from somebody who equates
"It's often the foolhardy and the ignorant that tackle problems that are supposedly impossible. And sometimes end up succeeding"
to
"It is often the ignorant who succeeds"
seems ironic to put it mildly.
The model of the atom that was popular before the current model. The model of the atom that was popular before that one. The model of the atom before..., ok you get the point.
If you'd like more, A Short History Of Everything by Bill Bryson is about 600 pages of examples.
From the page: "George Bernard Dantzig, a doctoral candidate at the University of California, Berkeley. ... George Dantzig (himself the son of a mathematician) received a Bachelor's degree from University of Maryland in 1936 and a Master's from the University of Michigan in 1937." Not exactly my definition of somebody ignorant.
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.
Please name some examples. How often is sometimes? What is their probability of success compared to that of domain experts?