Stresses of a Ph.D. program? Yup. (1) My wife was high school Valedictorian and in college Summa Cum Laude, Phi Beta Kappa, and Woodrow Wilson and NSF Fellow.

Stresses of a Ph.D. program? Yup. (1) My wife was high school Valedictorian and in college Summa Cum Laude, Phi Beta Kappa, and Woodrow Wilson and NSF Fellow. For her Ph.D., she did fine in her coursework. But starting research, she struggled terribly: For her, the research itself was easy. Her problem was that, unlike coursework, what was good, good enough, too good, what was really wanted, the realities of research, were totally unclear leaving her terrified of doing something wrong. The stuff of professors being not helpful, giving poor advice, finally being too critical was real and devastating. She struggled on with the anxiety, right, causing depression. That actually hurt her speed for which she got criticism, the first ever in her academic work, and more stress and depression and finally real clinical depression. She was in severe clinical depression the day she got her Ph.D. She never recovered. She was visiting her family farm trying to recover, and she was missing. Her body was found in a lake. Yes, the OP is correct: Grad school can be a very destructive place. (2) As a high school senior, I took the SAT twice and got over 750 both times. At my high end, college preparatory, high school, of 1, 2, 3 on the Math SAT, I was #2. So, eventually it became clear I had some math talent. Well, I figured out I had some math talent in the 9th grade -- I ignored the class and taught myself from the book and then made As on the tests. I continued that way in high school math classes. The extreme case was plane geometry -- I loved the subject. The teacher was the nastiest teacher I ever had, so I slept in her class and refused to admit doing any homework. But in fact, I solved every nontrivial problem in the text, including the more difficult supplementary ones. On the state test, I was #2 in the class; #1 was the guy who later beat me by a little on the SAT Math. I was a horrible student. Why? In grade school, my brother was ahead of me and a good student. The teachers kept saying, "Oh you are Joe's [not his real name] brother!". Well, from that start, anything I could do would be lower than expectations. Moreover, I was a boy; all the teachers were women; I had no social insight on how to please those women; my handwriting was awful; ...; and I just gave up trying to please the teachers. The teachers talked to each other so much that I was labeled as a bad student with a new teacher before I even started her class. That's why I was a horrible student -- in grade school, for me to please the teachers seemed just hopeless. Well, that poor student approach continued in college: I nearly ignored every subject but math and physics, was a math major, largely taught myself, did some more advanced reading independently outside of class, took a reading course from a high end, pure math text where I did all the talking, lectures and exercises, and a prof just listened, and did write a math honors paper. Then I worked for a while in applied math and computing on US national security problems and later at FedEx. Learned a lot of math, job related and also just good pure math. Then I went to grad school. I already knew about enough for the qualifying exams. But I still preferred to work directly from some of the best texts. Class time was mostly just writing exercise copying from the board. The real learning was studying the text or class notes. Eventually I saw a problem not solved in class; I didn't find a solution in various relevant texts or the more famous relevant papers in the library so took a "reading course" to investigate, maybe just write an expository paper, on the problem. Well, it was a fun problem. I had some ideas and worked them out sitting with my wife on our bed while she watched TV. Some of my ideas were good, and I turned them into solid theorems and proofs. In two weeks, I was done. Fast reading course! The credit I got was the last I needed for an MS. But it was clear that what I'd done was publishable. Later I did publish in JOTA. One prof walked up to me in the hall and said "I heard about your theorem: It says that for Brownian motion ...." Right. So, with that work, original, publishable, done with no faculty direction, presto, bingo, I had a halo. Before grad school, I'd seen a problem. On an airplane flight I worked out an intuitive solution. Some coursework in my first grad school year gave me enough pure math background to turn my intuitive solution into solid math, and I did that independently in my first summer; walked out of the library with a 50 page manuscript. That was the original research for my dissertation. Later I wrote some illustrative software, polished my math, and that was it: There was no real faculty direction. I stood for an oral exam defense and got my Ph.D. Lessons: (1) For a Ph.D., the three most important things are research, research, and research. If get some good research done early on, then can have a halo and solid shield against criticism. (2) It helps a lot to be able to be a poor student in courses. This way you are used to criticism and don't take it seriously. Also you don't wear yourself out trying to get a Ph.D. just from working hard in the courses or pleasing the profs teaching the courses. Bluntly, can't get a Ph.D. just from doing well in courses. Indeed, at the high end grad school I went to, officially there was no coursework requirement for a Ph.D. Instead, the main requirement was just research -- "An original contribution to knowledge worthy of publication.". So, (A) I didn't burn myself out doing coursework. If I didn't like a course or thought it wouldn't do much for me, then I didn't do much in the course or just walked out. (B) But I DID work hard learning the good material, and for that worked much as I had, largely independently, as I'd done back to the 9th grade. (3) Work independently. Don't ask or expect the faculty to do much or anything to suggest problems, references, or approaches to solutions. Find your own problem, maybe even before going to grad school. Start research on your problem ASAP, in some sense in your first year or first summer. Before you and the school agree you are working on your dissertation, have it essentially all done, all but maybe some illustrative software and some polishing of the work, e.g., maybe more references. (4) For financial support, expect free tuition but no stipend. Have your own source of food, clothing, shelter, etc. (5) Stay close to math so that don't have to do lab work for some prof or for your research. (6) Pick a practical problem, get a good applied math solution building on mostly some pure math, and call the work engineering. The usual criteria for research are that the work be "new, correct, and significant." Well, can get the "significant" part from the importance of the real problem. Can get the "new" part from the particular math, somewhat new, for the new solution to the new particular practical problem. The new, practical problem can stimulate and justify some new math that otherwise might not be regarded as of value or interest. For "correct", have the core of the work theorems and proofs which are seen to be correct. So, where my wife wore herself out trying to get praise from the profs, I was willing to be a poor student and largely f'get about trying to get praise. Where my wife wore herself out trying to wonder if her research was good enough, I tried to do good research as I understood it and also that looked good enough for the criterion of "worthy of publication". Looking for praise, my wife was reluctant to do something original. I was ready to do something original whether I would get praise or not. Indeed, back in plane geometry, I'd taken a problem from outside of class, found a solution, after school showed that nasty teacher, and she said "You can't do that". Later I discovered that she was wrong and I'd reinvented a classic technique similitude and shown her. I didn't believe her. If are going to work with things that are new, realize that will likely get a lot of people, hopefully not quite everyone, saying that the work is not good. What I did can sound like Ph.D. hacking. Well, not really: IIRC, at least at one time the Web site of the Princeton math department just stated: (1) No courses are given for preparation for the qualifying exams. Students are expected to prepare for the qualifying exams on their own. (2) Courses are introductions to research taught by experts in their fields. (3) Students should have some research work in progress as soon as possible, hopefully in their first year. Well, that's basically what I did: I was already nearly prepared for the qualifying exams before I got there. I had a research problem started before I got there. The courses I worked hard on were good for my background and for my research. The course where I got the problem that led to my paper in JOTA was advanced enough that I could see a good unsolved problem.