I’ve written my own advice to students seeking a Ph.D. Here is Norbert Wiener’s, from 1954 (The Human Use of Human Beings, p.133-4):
Properly speaking, the artist, the writer, and the scientist should be moved by such an irresistible impulse to create that, even if they were not being paid for their work, they would be willing to pay to get the chance to do it. However, we are in a period in which forms have largely superseded educational content and one which is moving toward an ever-increasing thinness of educational content. It is now considered perhaps more a matter of social prestige to obtain a higher degree and follow what may be regarded as a cultural career, than a matter of any deep impulse.
I mean merely that if the thesis is not in fact such an overwhelming task, it should at least be in intention the gateway to vigorous creative work. Lord only knows there are enough problems yet to be solved, books to be written, and music to be composed! Yet for all but a very few, the path to these lies through the performance of perfunctory tasks which in nine cases out of ten have no compelling reason to be performed. Heaven save us from the first novels which are written because a young man desires the prestige of being a novelist rather than because he has something to say! Heaven save us likewise from the mathematical papers which are correct and elegant but without body or spirit. Heaven save us above all from the snobbery which not only admits the possibility of this thin and perfunctory work, but which cries out in a spirit of shrinking arrogance against the competition of vigor and ideas, wherever these may be found!
In other words, when there is communication without need for communication, merely so that someone may earn the social and intellectual prestige of becoming a priest of communication, the quality and communicative value of the message drop like a plummet…