Sometimes it is good to check out old sci-fi movies that get into this like:
- Clara an indie sci-fi movie about a troubled PhD seeking an exoplanet for discovery in an international competition. The movie shows briefly the way real astronomers work using visualization and analytic tools like Matlab.
- 2012 a campy apocalyptic movie with every disaster known to man showcased
- Contact where the scientists and engineers debate the alien contact and instruction book.
- Cosmos indie movie where three engineers get a signal from outer space while working on a satellite problem
Another source would be YouTube videos of grad students chronicling their efforts to get their degree. Here's one from Univ of Idaho about the steps to a degree:
My brother went through the grad student mill where he was assigned a prof to work with who gave him a problem to work for a thesis. After a year or so, the professor became disinterested in the problem and he had trouble meeting with him but continued to plod onward.
It wasn't until a more senior professor questioned why this professor hadn't graduated any of his students in recent years. They then proceeded to get these students prepped and through the dissertation process and out the door. One of my brother's fellow students left in disgust after being sidelined by this same professor. This is what can happen.
In another case, I heard that a prolific grad student who was pumping out a lot of papers coauthored with his advisor was held back from getting his degree so he could continue to pump out more papers.
In a more famous case, a grad student came late to class and thought that the professor had written a homework problem on the board to be solved. He did it and handed it in a few months later the professor contacted him to say he had solved two previously unsolvable problems in statistics. The student was George Dantzig who went on to become a prominent PhD who developed the simplex algorithm.
https://en.wikipedia.org/wiki/George_Dantzig
and of course Snopes investigated the urban version of the story as well:
https://www.snopes.com/fact-check/the-unsolvable-math-problem/