"You can expect to make about USD 30,000 (before taxes) for the academic year."
Well that's a lie. NC State is $20k for a CS PhD Student, oh, and that's before you pay the $4k a year on student fees.
The article glosses over it, but you're paid dirt. And what sucks more, is you're paid good dirt, so all the other PhD departments look at your with their barely 10k stipends and think you're ungrateful for your poverty line wage.
Anecdotally, this seems like one of the reasons cs phds are rarely pursued by U.S. citizens.
Even if you love research, the programs will select for people who have good grades/institutions, who lack student debt, can invest 4 years at 20k/yr and survive, and are willing to turn down 6 figure jobs in industry.
Given this, it’s not a surprise that 79% of CS phd students in the US are international, where undergrad costs are often substantially lower.
> English is sufficient for getting a CS PhD in Europe.
Depends on the country and programme, but more and more so. Even France, traditionally not at all known for programmes at any level fully in English, has been making huge advancements in those areas, and there are full programmes in the Paris Saclay university hub entirely in English, exclusively to attract foreigners who don't speak French.
You have to also take into account the cost of living. I've lived in Zürich. It was almost literally twice what it costs me to live in New England, which is one of the most expensive parts of the US. So that 2x stipend will not get you 2x as far.
There are ways to increase your pay and doing summer work is one of those. However, the student fees portion of my comment still rings true. You'll be spending about $4k on student fees, $500 on parking. Depending on your martial status, number of kids, type of apartment, you will still be barely scraping by.
This may be in there and I just missed it, but I'll add if you are still an undergraduate (or high school student) and think you might later want a PhD, take a look at a few PhD programs and see if they have any non-obvious requirements that you had best take care of before you start their PhD program.
For example, when I was a high school student applying to Caltech's undergraduate program I took a look at the graduate school section of the catalog just to see what their math and physics PhD requirements were.
They had a language requirement for a math PhD. To get a PhD you had to either be fluent in one of French, German, or Russian, or you had to have a sufficient reading ability in two of those to read the current and historical math literature in those languages.
That kind of thing is much better to take care of in high school or as an undergraduate.
>They had a language requirement for a math PhD. To get a PhD you had to either be fluent in one of French, German, or Russian, or you had to have a sufficient reading ability in two of those to read the current and historical math literature in those languages.
This a thing of the past, from a time when people in the USSR still published things of note in Russian (the same for the other countries/languages your mentioned). Today everyone publishes in English and I don't of a single math department that still has that as a requirement.
I also don't know of any other such extracurricular requirements for any program (can't even imagine what it would be - community service???)
Those language requirements never never never mean fluency. They mean the ability to read an academic paper in that language, with a dictionary in hand, a skill you can develop for almost any language in a few months, more for languages with unusual writing systems
I think the most important thing to know about PhDs is that you get paid to get them. Personally, I didn’t understand how people could afford to stay in school so long. I regularly tell Uber drivers this just to spread the PhD ambition.
I think it’s important to note that it’s a little misleading to think of it as being paid to go to school. In most cases, especially past your first year and unless you’re on some special grant, you are paid because you are working for your advisor on his research projects. You have a boss telling you what to code and they will have a large say in what you’re working on.
Exactly. A lot of people unfamiliar with graduate school assume that it is like professional schools (law & medicine) where you actually have to pay (sometimes more than 100K all told for a degree over several years). Graduate stipends may be stingy, but at least you don't end up in debt from it.
> sometimes more than 100K all told for a degree over several years
Is it even possible to get a medical or law degree for less than 100k these days without rare scholarships and grants? Even a shorter 12 quarter program still runs around $11k a quarter. And even then the school can’t be bothered to pay for basic supplies and equipment you’re required to get, nor for the thousand-dollar licensing exams. And they still expect to get paid for that one quarter you go offsite to do unpaid work for some other provider to get real-world experience.
What a racket. (It’s probably obviously I’m peeved about a specific case :p)
Does it actually cover expenses? From what I read stipend does not even cover rent in expensive university towns. I could study on tropical island, be unemployed,
party every day and still have better disposable income.
My fiancee is getting her PhD in physical chemistry and is paid well enough to afford rent and food and the occasional nice thing.
It's actually just a little under the median household income for the area, so theoretically it's doable even with kids, though that speaks more to the level of poverty in Philadelphia.
I'm actually curious whether that is always the truth.
I've been in the industry for several years and made enough savings to cover my current lifestyle for a long time while also paying a significant stipent to a university.
Would it make sense to consider good PhDs where I wouldn't be able to get a salary, or are they always 100% scams?
In the sciences, if the advanced degree does not come with a stipend it is guaranteed to be a scam. Grants, which the advisor is expected to have, come with salaries for graduate students.
There are a couple of typos/incomplete sentences if you want to correct them. In section 1, “ Still, my opinion is heavily by my own environments, experiences, and beliefs.” I assume this should be heavily influenced by my own…
In 3.3, you mention “ The value of a standardized test is that it give sus some calibration.” Which appears to have a misplaced “s” after give.
Lastly, thank you for writing such a detailed post!
Thank you for these. I didn't think anyone would read it, but since I've been proven wrong, I actually ran a spell-checker. (-: Wouldn't have (and didn't) catch the first typo, though!
Interesting that he mentioned the $300,000 model...
Hypothetical question for US-based folks:
I wonder if there is a non-traditional path for people who can afford to research without the need for a stipend?
Technologists tend to be in the upper income brackets. For a lucky few, it's possible to achieve financial independence in their 40's. At that point conducting research may seem like an attractive intellectual pastime.
These hypothetical PhD students can sustain themselves for 4-6 years without a salary. I suppose there would still be some grant-seeking, depending on the scale of the research. Technically they could actually pay the university, becoming a funding source instead of a burden...
If someone had $2-$3 million in their retirement accounts, it seems strange to scratch and claw for $300k of research stipend funding.
Has anyone heard of such an arrangement? Is this a thing?
If you are financially independently wealthy, then you can just apply to the school and pay the full-rate tuition. Usually the way admission works is that you indicate a faculty advisor with whom you want to work. They will act as your mentor. I don't know of a situation where you would work alone, nor would you want to if you wanted to get the most out of your time there. So you would want to talk to that actual person you want to work with, and have a conversation about the fact that you can fund your own research. I imagine the funding process would have to go through the University. They get a cut of research funding, so they would want to funnel your funds through the same system set up for private grants, of which there are plenty.
So yeah, I don't see why you couldn't do this. You would just set up a private research grant with a faculty member and fund yourself with it.
That's an elaborate analysis of the considerations of getting a US Ph.D.
Gee, I got a Ph.D. in applied math; it could have been called computer science. But I never went through even 10% of that analysis. I didn't get accepted to Stanford, Berkeley, CMU, or MIT, but I didn't apply to any of them. But I did get accepted to Indiana University, Cornell, Princeton, Brown, and Johns Hopkins and went to one of those.
Why did I get accepted? In my application I showed that I had (a) a good ugrad pure math education, (b) a good career in applied math and computing with some good work results (samples), and (c) a lot of learning of applied math and computing since my ugrad education.
While I was a grad student, I regarded the courses as only vague suggestions. If I found the courses not well done or not much relevant to my interests, then I felt free just to ignore the courses. In the end, I had four courses that were good, one of which I already knew maybe 80% of the material (it totally pissed off the prof that I already knew so much of the material and effortlessly and unintentionally led the class on all the grading by wide margins). The other three courses were good and I learned some good stuff well.
Next were the Ph.D. qualifying exams: There were five exams, and I led the class on four of them. For three of the four, I led because of what I knew before I entered the program.
Next, what really got me on track, waxed the bottoms of my skis, to get my Ph.D. was that in one of the good courses I saw a problem, saw no solution in the literature, and in two weeks found a solid solution. Later I published the work. Any of the faculty members would have been proud to have published that work.
For the dissertation itself, I identified the problem and found an intuitive solution before entering grad school. Next, independently in my first summer, I converted the intuitive solution to solid math. Later in a few weeks I wrote and ran software that did well illustrating that my solution worked, was practical.
So, summary lesson: (i) Arrive well prepared, from ugrad school, work experience, independent study, whatever. (ii) As soon as possible, hopefully before entering grad school, independently get a research problem and make good progress on it. (iii) While in grad school, likely largely independently, hopefully find some little problem, find a solution, and publish that. (iv) Likely independently, finish the dissertation project, submit the written document, and stand for an oral exam. (v) Do expect never to pay any tuition, but don't expect any pay. Instead, have some money, a car, clothes, etc. from, say, savings from work before grad school. (vi) Don't expect much from the department -- don't expect good research projects, good hints for project solutions, etc. Instead, just work and produce good results almost completely independently.
One more piece of advice: For a Ph.D. in any of the STEM fields, start with a good background in pure and applied math, say, foundations, abstract algebra, linear algebra, and analysis. In particular, learn how to write math. Then outside of pure math departments, will likely be the local star in abilities in math. Then for research, mathematize some part of the STEM field.
No offense but your post is rambling and does not contain great advice for prospective phds. Most advisors I met during PhD were extremely generous with their time and their ideas, and their students would not have found appropriate problems and made rapid progress towards solutions without the intuition or help of their advisors. The story you tell about “2 week discoveries” and rapid independent progress is not the norm.
Right. What I described is "not the
norm". Are we supposed to consider only
what is "the norm"?
Instead of "the norm", I took the subject
to be essentially how to get a US computer
science Ph.D. and gave some ideas that
worked for me and are "not the norm".
Three points that might help:
(1) My suggestions about doing so much
independently can cut out a lot of
slogging through dangerous waters of
organizational behavior, competitions,
comparisons with other students, personal
relationships, department gossip, personal
image, etc.
I've seen a lot of people seriously hurt
in graduate school. In the program I was
in, I thought that the students were
beautifully qualified, but only about 1
out of 16 left with a Ph.D. In two words,
it was a blood bath. From the failure
rate, that program, and others I've seen,
made the Army Rangers and Navy SEALS
training programs look like fuzzy-bunny
play time. Nearly all my fellow students
were perfectly capable of doing good
research quite independently; their
problem was interactions with faculty and
the department on the way to doing good
research. Soooo, it can be helpful, if a
student can, to work so independently, if
only just to reduce possibly harmful
interactions with faculty.
"Seriously hurt": I've seen very capable,
dedicated people get seriously hurt,
sometimes for life, and sometimes DIE, as
in DEAD, from the damage. One who was
hurt was my brother. One that was badly
hurt was a physics prof I knew. I saw a
lot of profs that had been badly hurt and
developed really sick personalities. One
student who was hurt had been
Valedictorian, Summa Cum Laude, winner
of Woodrow Wilson and NSF fellowships,
astoundingly capable, totally dedicated,
and DEAD.
Let me put it to you this way: Sometimes
a university will have as their official
requirement for a Ph.D. dissertation "an
original contribution to knowledge worthy
of publication". Soooo, two options:
First option, do the work, write it up,
print it out, drop it on the desk of the
advisor, say you believe that the work is
publishable and you are ready to stand for
an oral exam. Second option, publish the
work and drop the dissertation on the desk
of the advisor with a copy of the letter
from the journal accepting the paper.
(2) At least at one time the Web site of
the math department at Princeton stated
(from memory) "No courses are offered for
preparation for the qualifying exams.
Graduate courses are introductions to
research by experts in their fields.
Students are expect to prepare for the
qualifying exams on their own. Students
should have some research project underway
in their first year.". Okay, that's
essentially what I did and got it done
before I saw Princeton's statement. So,
what I did was essentially "the norm" at
the Princeton math department.
(3) Fields of research vary. There is
math, computer science, the rest of the
STEM fields, the social sciences, the
humanities, the arts, biological/medical
research, and more. But here we are
talking about computer science and,
appropriately enough, I've tacked on some
math. So, in such work it is common for a
new Ph.D. to get an assistant professor
slot where they are expected to publish,
hopefully get research grants and publish,
get promoted, have successful graduate
students, and get promoted, etc. In all
of this, they are wanted to do good
research, good enough to win prizes, get
grants, give students a good start on
their careers. The "good research" is to
be at least "new, correct, and
significant". In nearly all of this work,
the prof has above him to look up to for
guidance only God; otherwise the prof is
working essentially "independently". Uh,
a suggestion then, along the lines of what
Princeton said and what I did, is to learn
to work heavily independently and to learn
that as soon as possible. Right, it's not
"the norm". In the program I was in, "the
norm" was 15 students out of 16 leaving
the university without a Ph.D. No doubt,
of those 15 students, interactions with
faculty were not always sweetness, smiles,
and good coffee and Vienna desserts.
For your "rambling", that sounds like I
was being graded in an English class! One
reason I got into math was that my correct
proofs could not be criticized as
"rambling" or anything else by any of the
teachers. Instead of "rambling", I just
described step by step what some of the
issues were and how I was successful.
What I wrote is MUCH shorter than the OP
-- one of my points was, and I started
with it, the OP was too long and
complicated. If you want to apply
"rambling", do that to the OP -- it
covered lots of stuff that is just too far
from what is crucial: What is crucial is
one word, research. Two words,
publishable research. Four words, prize
winning publishable research.
Ah, computer science has long regarded a
good algorithm as one with worst case
performance O(x^n) for any problem size x
and some positive integer n. Okay, this
definition was from Jack Edmonds. He left
the University of Maryland (UM) without
his Ph.D. Then he published some of his
work on networks. Then some of the
faculty at UM came to see Jack and assured
him that should he wish to stack some of
his papers and put a staple in one corner,
that would be accepted for a Ph.D.
Sooooo, Jack did his work independently.
For the "two weeks", that's just what it
took. I had and applied good preparation
for the problem. I found the problem in a
relatively advanced and well done course
-- soooo, it's not too surprising that the
problem was sitting there unsolved. It
was an old loose end in the subject, and I
tied it off. Some of what I did was a bit
surprising. But when get out to the edge
of a subject, there can be some problems
still left and relatively easy to solve --
it can help to have a good math
background, and that other people didn't
have such a good background is some of why
the problem was still unsolved. When get
out to the edge like that, not all the
remaining problems are ready for a Clay,
Turing, Abel, Nobel prize -- there can be
some little problems also.
My POINT was not that I solved a problem
in two weeks. Instead, my POINT was, as
part of how to get a Ph.D., if a grad
student can find some such doable problem
with a publishable solution, then finding
that solution can "wax their skis", cut
out department gossip, cut down any issues
of image or presentation of self before
the public, let the student "prove
themselves", etc. Or, to heck with the
research result; instead, do such a thing
to solve essentially POLITICAL problems.
Soooo, yes, part of getting a Ph.D. is to
do well enough on politics.
Bottom line: If a student can work
relatively independently as I described,
then that can ease getting a Ph.D. Right,
it's "not the norm".
Oh, CMU was mentioned: One of my
(official) dissertation advisors was later
President at CMU! He seemed to like my
work -- he had some of his other students
build on my dissertation!
Ah, one more piece of advice: Where to
find problems such as I did for my Ph.D.?
Sure, the usual way is to get a problem
from an advisor. Hmm .... Here is
another way, not "the norm": Get a
problem off campus, from the real world.
E.g., I don't know but I can guess that in
the server farms of some major
corporations, big banks, Google, Facebook,
Amazon, Microsoft, Cloudflare, the US DoD,
etc. they have some unsolved practical
problems, e.g., how to do well on
performance, reliability, security,
scalability, and cost all at the same
time. So, there, pick a problem, confirm
that the literature has no practical
solution, build a suitable mathematical
model, find an optimal solution, write
some software to confirm that the solution
is practical, and publish that. So, for
the criteria "new, correct, and
significant", the "significant" part can
come from the fact that some 10s of
millions of dollars are to be saved, or
reliability is greatly improved, or ....
For "new", you checked for that at the
beginning, and besides such server farms
have been growing so fast that it is
unlikely that they have good, old
solutions for all their problems. Also,
maybe go for a future problem assuming
some factors of 10 scale up; by the time
you get your work done, that future may be
the present! For "correct", that can be
mostly just about the math, and there can
establish correctness with mathematical
proofs. In short, that is what my Ph.D.
dissertation did -- so, it can work.
Also, surprising or not, commonly profs do
NOT really have feet on the ground, finger
tip feel, good knowledge of all
challenging practical computing
situations. So, should be able to find a
good problem to solve.
Is this advice "great"? Well, it was
"great" for me -- it worked, and I came
out undamaged. Also it's not "the norm"
which might be an advantage!
Readit News
Well that's a lie. NC State is $20k for a CS PhD Student, oh, and that's before you pay the $4k a year on student fees.
The article glosses over it, but you're paid dirt. And what sucks more, is you're paid good dirt, so all the other PhD departments look at your with their barely 10k stipends and think you're ungrateful for your poverty line wage.
Even if you love research, the programs will select for people who have good grades/institutions, who lack student debt, can invest 4 years at 20k/yr and survive, and are willing to turn down 6 figure jobs in industry.
Given this, it’s not a surprise that 79% of CS phd students in the US are international, where undergrad costs are often substantially lower.
http://nfap.com/wp-content/uploads/2017/10/The-Importance-of...
Two examples of many:
- https://imprs.is.mpg.de/
- https://ethz.ch/en/the-eth-zurich/working-teaching-and-resea...
Depends on the country and programme, but more and more so. Even France, traditionally not at all known for programmes at any level fully in English, has been making huge advancements in those areas, and there are full programmes in the Paris Saclay university hub entirely in English, exclusively to attract foreigners who don't speak French.
Source: currently applying to grad school
Better source: https://www.cmu.edu/stugov/gsa/Campus-Advocacy/Stipend-Repor...
Um, ok, ouch... jk :D
There are ways to increase your pay and doing summer work is one of those. However, the student fees portion of my comment still rings true. You'll be spending about $4k on student fees, $500 on parking. Depending on your martial status, number of kids, type of apartment, you will still be barely scraping by.
Source: All but dissertation
1) you don’t have to pay FICA taxes, which is a big deal.
2) you don’t have to pay tuition or taxes on the remission. That can be almost $30k per year before you reach candidacy.
For example, when I was a high school student applying to Caltech's undergraduate program I took a look at the graduate school section of the catalog just to see what their math and physics PhD requirements were.
They had a language requirement for a math PhD. To get a PhD you had to either be fluent in one of French, German, or Russian, or you had to have a sufficient reading ability in two of those to read the current and historical math literature in those languages.
That kind of thing is much better to take care of in high school or as an undergraduate.
This a thing of the past, from a time when people in the USSR still published things of note in Russian (the same for the other countries/languages your mentioned). Today everyone publishes in English and I don't of a single math department that still has that as a requirement.
I also don't know of any other such extracurricular requirements for any program (can't even imagine what it would be - community service???)
Go to language exam.
Ideally you're working on your own research project, not someone else's.
In any case, whatever the downsides, I’d wager that the majority of people don’t know that you get paid to get phds. I don’t think that is misleading.
Is it even possible to get a medical or law degree for less than 100k these days without rare scholarships and grants? Even a shorter 12 quarter program still runs around $11k a quarter. And even then the school can’t be bothered to pay for basic supplies and equipment you’re required to get, nor for the thousand-dollar licensing exams. And they still expect to get paid for that one quarter you go offsite to do unpaid work for some other provider to get real-world experience.
What a racket. (It’s probably obviously I’m peeved about a specific case :p)
It's actually just a little under the median household income for the area, so theoretically it's doable even with kids, though that speaks more to the level of poverty in Philadelphia.
I've been in the industry for several years and made enough savings to cover my current lifestyle for a long time while also paying a significant stipent to a university.
Would it make sense to consider good PhDs where I wouldn't be able to get a salary, or are they always 100% scams?
In 3.3, you mention “ The value of a standardized test is that it give sus some calibration.” Which appears to have a misplaced “s” after give.
Lastly, thank you for writing such a detailed post!
Hypothetical question for US-based folks: I wonder if there is a non-traditional path for people who can afford to research without the need for a stipend?
Technologists tend to be in the upper income brackets. For a lucky few, it's possible to achieve financial independence in their 40's. At that point conducting research may seem like an attractive intellectual pastime.
These hypothetical PhD students can sustain themselves for 4-6 years without a salary. I suppose there would still be some grant-seeking, depending on the scale of the research. Technically they could actually pay the university, becoming a funding source instead of a burden...
If someone had $2-$3 million in their retirement accounts, it seems strange to scratch and claw for $300k of research stipend funding.
Has anyone heard of such an arrangement? Is this a thing?
So yeah, I don't see why you couldn't do this. You would just set up a private research grant with a faculty member and fund yourself with it.
Gee, I got a Ph.D. in applied math; it could have been called computer science. But I never went through even 10% of that analysis. I didn't get accepted to Stanford, Berkeley, CMU, or MIT, but I didn't apply to any of them. But I did get accepted to Indiana University, Cornell, Princeton, Brown, and Johns Hopkins and went to one of those.
Why did I get accepted? In my application I showed that I had (a) a good ugrad pure math education, (b) a good career in applied math and computing with some good work results (samples), and (c) a lot of learning of applied math and computing since my ugrad education.
While I was a grad student, I regarded the courses as only vague suggestions. If I found the courses not well done or not much relevant to my interests, then I felt free just to ignore the courses. In the end, I had four courses that were good, one of which I already knew maybe 80% of the material (it totally pissed off the prof that I already knew so much of the material and effortlessly and unintentionally led the class on all the grading by wide margins). The other three courses were good and I learned some good stuff well.
Next were the Ph.D. qualifying exams: There were five exams, and I led the class on four of them. For three of the four, I led because of what I knew before I entered the program.
Next, what really got me on track, waxed the bottoms of my skis, to get my Ph.D. was that in one of the good courses I saw a problem, saw no solution in the literature, and in two weeks found a solid solution. Later I published the work. Any of the faculty members would have been proud to have published that work.
For the dissertation itself, I identified the problem and found an intuitive solution before entering grad school. Next, independently in my first summer, I converted the intuitive solution to solid math. Later in a few weeks I wrote and ran software that did well illustrating that my solution worked, was practical.
So, summary lesson: (i) Arrive well prepared, from ugrad school, work experience, independent study, whatever. (ii) As soon as possible, hopefully before entering grad school, independently get a research problem and make good progress on it. (iii) While in grad school, likely largely independently, hopefully find some little problem, find a solution, and publish that. (iv) Likely independently, finish the dissertation project, submit the written document, and stand for an oral exam. (v) Do expect never to pay any tuition, but don't expect any pay. Instead, have some money, a car, clothes, etc. from, say, savings from work before grad school. (vi) Don't expect much from the department -- don't expect good research projects, good hints for project solutions, etc. Instead, just work and produce good results almost completely independently.
One more piece of advice: For a Ph.D. in any of the STEM fields, start with a good background in pure and applied math, say, foundations, abstract algebra, linear algebra, and analysis. In particular, learn how to write math. Then outside of pure math departments, will likely be the local star in abilities in math. Then for research, mathematize some part of the STEM field.
Instead of "the norm", I took the subject to be essentially how to get a US computer science Ph.D. and gave some ideas that worked for me and are "not the norm".
Three points that might help:
(1) My suggestions about doing so much independently can cut out a lot of slogging through dangerous waters of organizational behavior, competitions, comparisons with other students, personal relationships, department gossip, personal image, etc.
I've seen a lot of people seriously hurt in graduate school. In the program I was in, I thought that the students were beautifully qualified, but only about 1 out of 16 left with a Ph.D. In two words, it was a blood bath. From the failure rate, that program, and others I've seen, made the Army Rangers and Navy SEALS training programs look like fuzzy-bunny play time. Nearly all my fellow students were perfectly capable of doing good research quite independently; their problem was interactions with faculty and the department on the way to doing good research. Soooo, it can be helpful, if a student can, to work so independently, if only just to reduce possibly harmful interactions with faculty.
"Seriously hurt": I've seen very capable, dedicated people get seriously hurt, sometimes for life, and sometimes DIE, as in DEAD, from the damage. One who was hurt was my brother. One that was badly hurt was a physics prof I knew. I saw a lot of profs that had been badly hurt and developed really sick personalities. One student who was hurt had been Valedictorian, Summa Cum Laude, winner of Woodrow Wilson and NSF fellowships, astoundingly capable, totally dedicated, and DEAD.
Let me put it to you this way: Sometimes a university will have as their official requirement for a Ph.D. dissertation "an original contribution to knowledge worthy of publication". Soooo, two options: First option, do the work, write it up, print it out, drop it on the desk of the advisor, say you believe that the work is publishable and you are ready to stand for an oral exam. Second option, publish the work and drop the dissertation on the desk of the advisor with a copy of the letter from the journal accepting the paper.
(2) At least at one time the Web site of the math department at Princeton stated (from memory) "No courses are offered for preparation for the qualifying exams. Graduate courses are introductions to research by experts in their fields. Students are expect to prepare for the qualifying exams on their own. Students should have some research project underway in their first year.". Okay, that's essentially what I did and got it done before I saw Princeton's statement. So, what I did was essentially "the norm" at the Princeton math department.
(3) Fields of research vary. There is math, computer science, the rest of the STEM fields, the social sciences, the humanities, the arts, biological/medical research, and more. But here we are talking about computer science and, appropriately enough, I've tacked on some math. So, in such work it is common for a new Ph.D. to get an assistant professor slot where they are expected to publish, hopefully get research grants and publish, get promoted, have successful graduate students, and get promoted, etc. In all of this, they are wanted to do good research, good enough to win prizes, get grants, give students a good start on their careers. The "good research" is to be at least "new, correct, and significant". In nearly all of this work, the prof has above him to look up to for guidance only God; otherwise the prof is working essentially "independently". Uh, a suggestion then, along the lines of what Princeton said and what I did, is to learn to work heavily independently and to learn that as soon as possible. Right, it's not "the norm". In the program I was in, "the norm" was 15 students out of 16 leaving the university without a Ph.D. No doubt, of those 15 students, interactions with faculty were not always sweetness, smiles, and good coffee and Vienna desserts.
For your "rambling", that sounds like I was being graded in an English class! One reason I got into math was that my correct proofs could not be criticized as "rambling" or anything else by any of the teachers. Instead of "rambling", I just described step by step what some of the issues were and how I was successful. What I wrote is MUCH shorter than the OP -- one of my points was, and I started with it, the OP was too long and complicated. If you want to apply "rambling", do that to the OP -- it covered lots of stuff that is just too far from what is crucial: What is crucial is one word, research. Two words, publishable research. Four words, prize winning publishable research.
Ah, computer science has long regarded a good algorithm as one with worst case performance O(x^n) for any problem size x and some positive integer n. Okay, this definition was from Jack Edmonds. He left the University of Maryland (UM) without his Ph.D. Then he published some of his work on networks. Then some of the faculty at UM came to see Jack and assured him that should he wish to stack some of his papers and put a staple in one corner, that would be accepted for a Ph.D. Sooooo, Jack did his work independently.
For the "two weeks", that's just what it took. I had and applied good preparation for the problem. I found the problem in a relatively advanced and well done course -- soooo, it's not too surprising that the problem was sitting there unsolved. It was an old loose end in the subject, and I tied it off. Some of what I did was a bit surprising. But when get out to the edge of a subject, there can be some problems still left and relatively easy to solve -- it can help to have a good math background, and that other people didn't have such a good background is some of why the problem was still unsolved. When get out to the edge like that, not all the remaining problems are ready for a Clay, Turing, Abel, Nobel prize -- there can be some little problems also.
My POINT was not that I solved a problem in two weeks. Instead, my POINT was, as part of how to get a Ph.D., if a grad student can find some such doable problem with a publishable solution, then finding that solution can "wax their skis", cut out department gossip, cut down any issues of image or presentation of self before the public, let the student "prove themselves", etc. Or, to heck with the research result; instead, do such a thing to solve essentially POLITICAL problems. Soooo, yes, part of getting a Ph.D. is to do well enough on politics.
Bottom line: If a student can work relatively independently as I described, then that can ease getting a Ph.D. Right, it's "not the norm".
Oh, CMU was mentioned: One of my (official) dissertation advisors was later President at CMU! He seemed to like my work -- he had some of his other students build on my dissertation!
Ah, one more piece of advice: Where to find problems such as I did for my Ph.D.? Sure, the usual way is to get a problem from an advisor. Hmm .... Here is another way, not "the norm": Get a problem off campus, from the real world. E.g., I don't know but I can guess that in the server farms of some major corporations, big banks, Google, Facebook, Amazon, Microsoft, Cloudflare, the US DoD, etc. they have some unsolved practical problems, e.g., how to do well on performance, reliability, security, scalability, and cost all at the same time. So, there, pick a problem, confirm that the literature has no practical solution, build a suitable mathematical model, find an optimal solution, write some software to confirm that the solution is practical, and publish that. So, for the criteria "new, correct, and significant", the "significant" part can come from the fact that some 10s of millions of dollars are to be saved, or reliability is greatly improved, or .... For "new", you checked for that at the beginning, and besides such server farms have been growing so fast that it is unlikely that they have good, old solutions for all their problems. Also, maybe go for a future problem assuming some factors of 10 scale up; by the time you get your work done, that future may be the present! For "correct", that can be mostly just about the math, and there can establish correctness with mathematical proofs. In short, that is what my Ph.D. dissertation did -- so, it can work. Also, surprising or not, commonly profs do NOT really have feet on the ground, finger tip feel, good knowledge of all challenging practical computing situations. So, should be able to find a good problem to solve.
Is this advice "great"? Well, it was "great" for me -- it worked, and I came out undamaged. Also it's not "the norm" which might be an advantage!
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