
How to do a PhD - efz1005
http://jameshaytonphd.com/the-10-commandments-for-phd-failure/
======
graycat
I've seen a lot of really good people get very badly hurt pursuing a Ph.D. I
did get a STEM field Ph.D. but didn't get hurt.

For a good and broad view of the problem, buried in D. Knuth's _The TeXBook_
is

"The traditional way is to put off all creative aspects until the last part of
graduate school. For seventeen or more years, a student is taught
examsmanship, then suddenly after passing enough exams in graduate school he's
told to do something original."

Yes, here Knuth identifies a significant challenge.

Compared with the OP, here's a very different and much more specific approach
that clearly makes a lot of sense and that worked well for me:

First, note carefully that for some work that can be called _research_ the
usual, nearly universal criteria are that the work be "new, correct, and
significant". Below, keep these three in mind.

Second, get a major in math, at least a good undergraduate major in pure and
applied math and hopefully enough more in pure and applied math for roughly a
Master's in math. Even if you don't care about the Master's degree, I do very
much recommend getting the math for a Master's degree.

Why pure math? The pure math gives you the crucial, central, foundational
tools of math, that is, many crucial prerequisites and, broadly, the ability
to state and prove theorems. E.g., you will learn how to write math, and that
alone will start to put you ahead, even of some high end professors.

What pure math? For your research likely mostly you will use the part of math
called _analysis_ but in your studies for more you will also want at least the
basics of abstract algebra and maybe differential geometry, combinatorics, and
maybe even some in foundations. In addition, if you have some reason to
believe you can get some value from algebraic topology or geometry, then, sure
study those.

Why applied math? Likely applied math will be closer to the math you will use
for your research. What applied math? Sure, e.g., statistics, numerical linear
algebra, ordinary differential equations, more in numerical techniques,
optimization, stochastic processes, etc.

Third, get your Ph.D. in some field of _engineering_ \-- computer science,
electronic engineering, mechanical engineering, civil engineering, operations
research, statistics, etc.

Three biggie points:

(1) In science and engineering, by far the most highly respected research is
that which _mathematizes_ the field. Good work here can help meet the
criterion of "significant".

(2) Work in math, well supported with theorems and proofs, is much more
difficult to criticize than work that is mostly just experimental or
empirical. Good work here can be help meet the criterion of "correct".

(3) The standard and severe weakness of the backgrounds of researchers in most
of science and in engineering is way too little in math. Thus, there are a lot
of good research problems they can't address. So, your good work here can be
help meet the criterion of "new".

So, with your background in math, on (1)-(3) you will have at least a good --
maybe even an overwhelmingly strong -- comparative, competitive advantage.

Another point if you care: Unless your family wants to donate $10+ million or
so, it is just super tough to get into an Ivy League university. But getting
in as a grad student is much easier -- e.g., I got accepted to Cornell, Brown,
and Princeton.

So, you should intend that your research be essentially math for that field of
engineering. Usually you will aim to use your math tools to solve a relatively
practical problem in that field of engineering, but you might use your math to
add to the basic _theory_ of that field; for some wild guesses, you might do
something in the theory of predators and prey in environmental engineering;
maybe you would have been the one who did Kalman filtering in electronic
engineering; maybe in mechanical engineering and continuum mechanics you will
make some nice theoretical contribution to materials science.

Why engineering instead of pure math or physical science? (1) Engineering has
no end of practical problems -- say, from outside of, and neglected by,
academics -- to be solved. So, if you pick, attack, and solve a problem
important in practice, then there is a good chance your work will meet the
criterion of "new", since the work is mathematical, "correct", and since the
problem was important in practice, "significant". (2) In pure math and
physical science, the range of candidate problems is much more narrow, e.g.,
in physics you can try to say what _dark energy_ is -- lots of luck doing
that.

So, right, for a research problem in some field of engineering, maybe pick a
practical problem that is considered important and that you found someplace,
maybe outside academics, maybe on a job, maybe a real job or maybe just a
summer job or an internship. I did that: I picked a problem I found at FedEx.

Then, it will be quite good for you to have the problem in mind when go for
your Ph.D. I had the problem and a good, first-cut, intuitive solution (worked
out on an airplane flight) before I entered my Ph.D. program. In my first
year, I took some advanced, relatively pure, not often taught, graduate math
coursework that gave me good math prerequisites to let me convert my intuitive
solution a solid math solution. So, in my first summer, in six weeks,
independently, alone in the library, I worked out the math, with theorems and
proofs, and walked out with a 50 page manuscript that was the original
research for my Ph.D. dissertation. I recommend doing such a thing.

Getting into research early is commonly considered good advice: E.g., IIRC,
the Princeton math department has said on their Web site that a student should
have some research underway in their first year. Even, better, have the core
research done before the second year -- which is what I did and, I believe, a
strong advantage in getting the Ph.D.

The math gave me another advantage: In a course, a problem was apparent -- a
tricky, deep question about the Kuhn-Tucker conditions. There was no answer in
the course, and I could find no answer in the library. So, I attacked the
problem -- the key was some pure math I had -- and found a surprisingly nice
solution, in two weeks. I wrote up my solution and got credit for a _reading
course_. But the work was publishable -- presto, bingo, at that university the
criteria for a Ph.D. dissertation was that the work be "an original
contribution to knowledge worthy of publication". Well, the best way to show
that some work is "worthy of publication" is to submit it for publication and
have it accepted. I did that. So, technically that work was enough for my
Ph.D. dissertation, a second one.

For that problem in the Kuhn-Tucker conditions and for my dissertation
research, I never had any real _faculty direction_. I recommend: Don't wait
for the faculty to provide a good problem or _direction_. Instead, on your own
as much as you can, at least if it is easy for you, and it was for me, pick a
good problem, do the research, get the work ready for publication, and,
hopefully, publish it. For a graduate student to have, early on, from largely
independent effort, some work worthy of publication makes essentially
everything else in the Ph.D. program and the start of a career much easier and
better.

Okay, how to do the research? Well, for me, the core, hard work of the
research was a little more involved but, really, not much more difficult than
the more difficult exercises in standard, advanced pure math texts.

The difference was, for research, in part need to keep in mind some view from
higher up, say, 50,000 feet down to 1000 feet and don't always be crawling
around on the ground with the lowest level details (which is common and
usually effective enough in solving exercises).

Next, guess: To find and prove a new result, first have to guess it. Sure,
make _educated guesses_ based on your solid background but also work just
intuitively. So build intuitive models and, as you learn more, revise the
models to make them more accurate.

E.g., during the work, is _A_ true? Well, it doesn't seem wrong right away
intuitively. But, if _A_ is true, then, hmm, _B_ is true. Could _B_ be true?
At least, first-cut, intuitively, naw, not a chance (this may be wrong, but
let that happen for now). So, likely _A_ is not true.

You can do a lot of this in your head without writing anything. And, even if
slowly, you will learn to do at least some derivations in your head.

Now, for _C_ , intuitively it looks true. So, try to prove _C_. Gee, the proof
doesn't work. Then observe: The proof doesn't make good use of all the
hypotheses of _C_ ; so, you've been trying to prove something more general
than _C_ and likely not true. Bummer. So look again at the hypotheses of _C_
and try to see how they are essential and how to exploit them.

So, continue in this way, maintaining a good view from above the ground level,
with lots of intuition and guessing and trying to prove some little things.

When you get a proof of a result that looks good, then write it up, carefully,
cleanly, put a date and title on the first page, put a staple in the UL corner
of the sheets, and toss it on a stack, continue on, maybe building on what you
have.

There is also Polya, _How to Solve It_.

From A. Wiles, the guy who solved Fermat's last theorem and just won the Abel
Prize, is

"Perhaps I could best describe my experience of doing mathematics in terms of
entering a dark mansion. You go into the first room and it's dark, completely
dark. You stumble around, bumping into the furniture. Gradually, you learn
where each piece of furniture is. And finally, after six months or so, you
find the light switch and turn it on. Suddenly it's all illuminated and you
can see exactly where you were. Then you go into the next dark room ..."

~~~
imranq
Really appreciate the insights here - I'd love to get your advice on my own
situation

I've already done a pure math (+business) undergrad from a mid-tier university
and have been working as a product manager at a financial services company for
3yrs post undergrad. I've been thinking of getting a PhD in an engineering
sub-discipline, but not sure how to go about doing it especially since I have
no research experience.

Do I:

(i) spend 1 year doing research with a professor nearby then apply (I live
close to a major research university)

(ii) apply now and hopefully my work experience can cover for research
experience

(iii) Rethink the whole PhD thing and get a professional degree like an MBA
(did well on GMAT)

(iv) Just continue to learn on the side and try to use my skills for
opportunities

\-----

Also two more questions if you don't mind:

How did you narrow your interests before applying for a PhD?

Is it possible to get a masters level pure math education through self study?
I've taken until PhD level measure theory.

~~~
graycat
> I've already done a pure math (+business) undergrad from a mid-tier
> university and have been working as a product manager at a financial
> services company for 3yrs post undergrad. I've been thinking of getting a
> PhD in an engineering sub-discipline, but not sure how to go about doing it
> especially since I have no research experience.

It would appear that you might pursue something in "financial engineering".

Since you are in the financial industry, you might ask around and grow a
network: E.g., ask person A; maybe can get them to suggest person B; tell
person B that person A recommended them and ask person B; etc. I.e., apply
social networking techniques. E.g., try to get to some people who can outline
some of what James Simons did. If you can, talk to Simons. Similarly for
various _quants_ and people who create algorithms and code for _automatic
trading_. Look into the programs in financial engineering at Princeton (E.
Cinlar), NYU (M. Avellaneda), Columbia (I. Karatzas), and CMU (S. Shreve).

If you want to get into some other field of engineering, then gather some
information, meet some people and get some input, and start to pick some
fields or one field.

> (i) spend 1 year doing research with a professor nearby then apply (I live
> close to a major research university)

Maybe. If you can find a good situation and like it, maybe, sure.

I have been suggesting that you start with your own problem and make some
progress on it, maybe with a little advice (once I got just three words), and
maybe then consider a professor as a official or unofficial mentor or
dissertation adviser.

> (ii) apply now and hopefully my work experience can cover for research
> experience

For a graduate program, in most fields, you are not expected to have
experience in research. So don't have to "cover for research experience".

> (iii) Rethink the whole PhD thing and get a professional degree like an MBA
> (did well on GMAT)

And, with that MBA, what will you do with it? Consulting? Try to work your way
up as a C-level guy? Try to do portfolio management or be a venture
capitalist?

I'm a former MBA prof -- typically an MBA is not very technical, but, now,
especially with some much in computing, being technical can be seen as an
advantage. Or, maybe the flip side is, soon all the work that the techies can
do will be done and what will be left is the non-technical work. Your guess.

As far as I can see, still need to hustle and/or be lucky to have a good
career.

Also, an MBA is expensive while a Ph.D. often costs $0.00 for tuition and
might provide a stipend.

> (iv) Just continue to learn on the side and try to use my skills for
> opportunities

That can be a short-term approach that can lead to a degree later.

If you sense that your background is not good enough to go for a degree, then,
sure.

A major cause of my success in grad school is the math I studied independently
between my Bachelor's and my Ph.D. program.

In particular, for a Ph.D., will likely have to pass qualifying exams, and you
will want to have enough preparation for a path to do that.

> How did you narrow your interests before applying for a PhD?

I attacked some practical problems with applied math and computing. I did
this, first, in work in US national security around DC.

> Is it possible to get a masters level pure math education through self
> study? I've taken until PhD level measure theory.

IIRC at one time the Web site of the math department at Princeton said that
the graduate courses were introductions to research by experts in their
fields, that no courses were offered for preparation for the qualifying exams,
and that students were expected to prepare via independent study. For this,
you will need a good undergraduate background.

There is some question how much a student or anyone should attempt via
independent study. As a researcher, a lot of independent study is usually just
part of the work, but there are seminars, etc. that can help.

Mostly I did well with independent study, but once in statistics I picked a
poor book and wasted some time. And, for some subjects, I did get and really
needed the good, mature overview of a good course -- else there are too many
places along the way where can waste time, get stuck, or go off on a tangent.
Also it can be good to be around good researchers and learn their attitudes
and approaches: E.g., often researchers go through new material surprisingly
quickly and, really, without the thorough mastery often implied as important
or even essential in high school and undergraduate school. E.g., in research,
for some new material are trying to make use of it, not get a high score on
some GRE exams.

~~~
imranq
Wow, thank you so much for the comprehensive response! This is the reason I
love HN. Will definitely take this advice to heart and apply it today.

Thanks!

------
ideonexus
_5\. Get to know the literature_

I'm not writing a thesis, but a book on teaching coding, and this one point is
really important. One of my chapters was on the cognitive benefits of writing
software code--which I assumed were great because of Seymor Papert
("Mindstorms") and Ted Nelson's ("Computer Lib/Dream Machines") glowing
enthusiasm for teaching kids how to code.

I started writing the chapter and had to get into the literature to find
references to support the idea that learning to code carried concrete
cognitive benefits. The research was extremely mixed, with one survey of the
literature being highly critical of Papert for assuming so many benefits when
the research was not finding that at all. I ended up having to stop everything
and just read papers for a week to understand what science really knew about
the subject. When I went back to rewrite my chapter, I had to temper my own
enthusiasm and add numerous qualifications and cautions about my claims
considering the evidence.

I'm happy for the experience as my thoughts on the subject are much more
highly nuanced now, but it was very disheartening at first.

~~~
ArkyBeagle
CS literature is uniformly abysmal.

~~~
kctess5
False.

------
jboggan
If you get the first one wrong the rest of the list will not matter at all.
The most important questions are, who will my advisor be? What is the
completion rate for graduate students under their care? What kind of personal
network does the advisor maintain and what kinds of roles do the graduating
PhDs go into?

I wish I had known to ask that sort of thing. My advisor typically kept a lab
of a dozen postdocs and a single PhD at any given time. I think in 25 years of
being a research professor with sizeable grants that advisor only graduated 4
doctoral students, and a rather distressing proportion of the postdocs left
not only academia but science after that lab.

I would also try to hang out with the current doctoral students and assess
their psychological well-being.

~~~
redraga
While this is completely valid advice, it might not be applicable with junior
faculty who may not have graduated many students. I chose my advisor (who was
as assistant professor at the time) based on the belief that I'll get to
publish aggressively since it's in both of our interests. But I had no way of
knowing how hard it would be to work with her. And I wasn't the only person
who felt this way; I saw my fellow group mates (all of us joined the group at
around the same time) and other collaborators express similar sentiments in
course of time. But since I'd already sunk in time, I decided to stick around.

I was able to successfully complete my PhD, but I took more time than
expected. Moreover, I was no way near as productive as I'd hoped to.

------
stared
I am after my PhD and I consider quality of this list being close to of a "be
creative" list.

That is, in principle all points make sense, but they are either truism, too
obvious, too vague or things that are out of control. (If I had read it before
starting my PhD it wouldn't have changed a thing).

Or maybe I am overly skeptical of simplistic life-advice? Is there any take-
home message that changed your way of acting?

~~~
jackcosgrove
Here is a piece of advice for CS graduate students: take a look at the Gartner
hype cycle. Here's the cycle from 2014:
[http://www.gartner.com/newsroom/id/2819918](http://www.gartner.com/newsroom/id/2819918).
Pick something far on the left side of the curve, and ride the hype.

~~~
Xcelerate
"Quantum computing" is ahead of "connected home"?

~~~
nmrm2
These curves are marketing material for an "advisory firm". Nothing more,
nothing less. The idea of the curbe is more important that the particular
points, and the points are often mis-placed. Also, lots of technologies jump
around randomly on the curve or move rapidly through some parts, etc.

------
rdlecler1
Definitely need to focus. I think most of us come into our PhDs thinking that
our research is going to change the world. For anyone doing highly theoretical
work we can be over ambitious. We try to bite off more than we can chew, and
then we're either paralyzed or we spend a good portion of our time back
peddling to simpler problems. If I could give one piece of advice. Start
simple. If possible replicate some of the earlier work because you may
discover that you're building on a lot of unreported assumptions. Aim for a
portfolio of small papers that together tell a larger story, rather than
trying to pack it all into on opus magnus.

~~~
amelius
> For anyone doing highly theoretical work we can be over ambitious.

I would say that this danger applies more to those doing practical (applied)
work. A practically oriented program will often have a clear goal, and preset
goals are often unattainable in research. By contrast, a student doing
theoretical work can always bend their goals when necessary.

~~~
ska
I think this contributes to why theoretical degrees take, on average, much
less time to complete in my experience.

------
henrik_w
Or, as in my case, don't do a PhD. I really thought I wanted to, but as it
turns out, I didn't:

[http://henrikwarne.com/2016/03/07/ph-d-or-professional-
progr...](http://henrikwarne.com/2016/03/07/ph-d-or-professional-programmer/)

------
scott_s
Be selfish.

Finishing a PhD is unlike completing a project in most other jobs. In most
other jobs, someone _needs_ what you're working on. Other people's investment
in the outcome is similar to your own. If you fail to complete your work,
others are likely to fail to complete their work. Consequently, incentives
(hopefully) line up, and infrastructure (hopefully) exists to support you,
with the recognition that your success is linked to group success.

Your PhD dissertation is not like this. Yes, your adviser _is_ invested in you
finishing - but not as nearly as much as you are. They will have other
students, and they can always work on their own. Your peers may be invested,
if they are working on another part of the project - but if you do not finish,
they will find a way to get on without you. Your university is invested in you
(quite literally, most of the time, with money), but again, not as nearly as
invested as you are: plenty of grad students never finish, and they will help
you, but schools also recognize that not all students finish.

The author has a good list, and I may read his book, but he's missing this
attitude that I felt I had to adopt. The person who cares most about you
finishing is you, and sometimes that means having to be selfish in order to
finish. That can take of the form of not engaging in as much service in your
department, or not providing some help on a project that is not part of your
dissertation.

I do think this attitude is unfortunate, but it is a natural result of the
requirement that a PhD dissertation represents work that the student _owns_. I
much more enjoy the research I have done in an industry research lab, where me
and my colleagues have collaborated equally. (Or equal-enough that in a grad
school context, no one person could claim ownership of the work for a
dissertation.) But, it's the system we have, and because of that, I think that
in order to finish, grad students have to - at least eventually - adopt a
selfish attitude.

Specifically, this "selfish attitude" means ruthless evaluating: will this
thing get me closer to graduation? If no, don't do it. (Obviously this only
applies to work. Having a life outside of grad school work is enormously
important.) In the beginning, I don't think one needs to have this attitude.
But as you approach completion, I think one needs to start thinking this way.

------
rubidium
While it has a bit of snark to it, certainly conveys the point of "This is
your PhD. No one is going to hold your hand. Get it done."

The people who drop out of PhD programs usually are plenty smart enough, they
just don't know how to make things happen.

Then again, some people seem content and happy to do 8 years of PhD studies
followed by 10 more of meandering post-docs. Bummer is when they're surprised
that no one wants to make them a professor.

~~~
ska

        The people who drop out of PhD programs usually are plenty smart enough, they just don't know how to make things happen.
    

Vast oversimplification. I've watched people leave Ph.D programs for a wide
array of reasons. Any attempt at binary classification on this is foolhardy.

~~~
static_noise
Clone a person ten times and send them to ten different positions, they will
all fail for different reasons. Luck is as big a factor as is talent and
diligence.

------
cranium
While the article is interesting, I find it quite confusing to read with its
paragraphs once ironic once advisory...

------
cwmma
11 commandments ...

