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!