
Was a PhD necessary to solve outstanding math problems? - reedwolf
https://www.greaterwrong.com/posts/p7uv4Ekhf8utFKBxa/was-a-phd-necessary-to-solve-outstanding-math-problems
======
bo1024
The article seems to treat a PhD merely as a credential - maybe assuming that
a person would be equally capable with or without it. Why? The whole point of
a PhD in math is to learn to do effective research in math and there are
almost no substitutes. This seems like being surprised that so many
professional violinists took violin lessons. (I admit my bias here but still.)

~~~
hn_throwaway_99
The same mindset occurs a lot in the software engineering world, and I think
it's somewhat baffling and potentially dangerous. I find software engineering
quite _difficult_ , and I am relatively intelligent, studied computer science
at top universities, and have decades of experience where I learned a ton. So
I'm all for coding bootcamps, but we wouldn't expect someone who went to a
violin bootcamp for 3 or 4 months to be able to play in an orchestra, but I
don't think that's the standard message coming from these coding bootcamps
(understandable, they have a biased motivation) or from higher ups in the tech
industry at large (more problematic IMO).

~~~
ludamad
"scratch the surface of programming, which nonetheless equips you for real
world jobs" could possibly be fair to say about a bootcamp. It certainly
filled a certain demand, although one has to wonder if better software won't
just eat 4 month configuration++ bootcamps

~~~
seibelj
I think a better use of coding boot camps would be to go deep in a very
specific DSL. Like learn how to do Salesforce or Excel programming deeply. A
lot of companies actually need this to improve processes, and restricted
environments reduce the cognitive load a novice needs to become productive.

------
strikelaserclaw
If u were gifted at math and wanted to do it all the time, would you a) get
paid for doing it with peers while getting a PhD or b) work a job as a janitor
to support yourself while doing math. With the amount of depth modern math
has, i think to achieve results you need to be able to do it full time, so
getting a PhD seems to be the most logical route for aspiring mathematicians.
Not to mention that most pure math don't have much practical application at
the moment, you certainly would not convince your manager in industry to let
you solve random problems just for the sake of solving it.

~~~
formercoder
There’s probably a middle ground given how little phds are paid. Consult as a
software engineer for 1/3 time, make double janitor comp, 2/3 time on
research.

~~~
varjag
It never ends at 1/3 time.

~~~
andrewstuart2
I feel like at 1/3 time you'd spend most or all of it catching up on what
happened in the 2/3 of the week you missed. Unless you're not on a team.

------
prionassembly
I dropped from grad school with a Master's degree in applied math, and vowed
to keep studying for the rest of my life.

It's really hard to study "real maths" on your own. It's harder to understand
materials without the aid of someone who has already deep-dove and built some
intuitions, metaphors and visual schemas. More critically, it's very hard to
know if you're doing proofs correctly without feedback.

------
DanBC
The article is missing mathematicians who do not publicize their results.
These would mainly be mathematicians working for agencies like GCHQ, NSA, etc.

If you want to work on certain math problems, don't mind working for the
government, and don't care about being published you can get good jobs with
these kinds of agencies.

~~~
black_puppydog
* and don't care about _why_ these results will go unpublished

~~~
i_am_proteus
Or you are comfortable with why they will go unpublished.

~~~
black_puppydog
of course, or that

------
fizixer
PhD is not strictly necessary, but the process and training that results in a
PhD degree is.

Case in point, Freeman Dyson, brilliant mathematician/math-physicist, never
got a PhD degree, but did research work all his life. Note, he was deeply
embedded in the research community, and pretty much everyone he collaborated
with, was a PhD or eventually got a PhD (meaning he went through the motions
just like other researchers).

Final note, the process and training required to be able to conduct research
is massively undernurtured, i.e., in my opinion, most PhD graduates are barely
an iota better-trained than MS graduates these days. This is getting
increasingly true as world population grows, and PhD diplomas get handed out
willy nilly (a topic I could go on at for hours). In short, Sturgeon's law is
in full swing.

~~~
leereeves
> PhD is not strictly necessary, but the process and training that results in
> a PhD degree is.

I was just about to post the same. I just finished a master's in math (in
fact, with additional coursework in physics and statistics I've almost
completed two master's) and I don't feel ready to tackle outstanding math
problems.

And the PhD students I knew were receiving a lot of help from their mentors as
they learned how to tackle outstanding problems.

There's just so much to learn to contribute to research math these days, it's
hard to imagine anyone learning it all on their own.

------
LudwigNagasena
This doesn’t prove that PhD is needed. This just proves that people prefer to
get paid.

~~~
black_puppydog
The author clearly articulated that it is needed in _practical_ terms. That
is, empirically (according to their small sample) people who don't do a PhD
don't feature in the list of notable maths achievements.

~~~
LudwigNagasena
Why then did he only mention money once in passing? Sounds like a very
practical concern to me.

------
jokoon
There's a difference between a degree and an education.

The problem is how we consider the destination (the degree), to be a proof of
competence and knowledge, while it's really the journey (the education) which
actually matters. That's why degrees should be abolished, and a certificate of
education be given to the student as long as he/she is present.

School should not act as a social filter. As long as you go to school and go
to classes, and shows motivation to learn, it's enough. There are no proper
ways to evaluate how a student really learned and absorbed the knowledge that
was given. There are many students who love the knowledge, but cannot accept
scholasticism, the competition, the selection and the filtering. It often ends
up being about "belonging to a group", and honestly it was never the goal of
education.

It's up to companies to really check if someone if competent and has the
knowledge, it's not the job of universities. Higher education is an enormous
source of inequality, and an immense social barrier.

It's really easy for people with degrees to disagree with this, I can only
answer with survival bias.

~~~
quickthrower2
I have a degree, and I agree with you. At least for software engineering.

What there could be is a standardised test, that is a national or
international standard, not linked to a uni. Learn to program and do the test
and that is your credential. Maybe it costs $200 or something.

That way you can skip uni, self teach but be able to show you can code without
employers needing to find novel ways to evaluate.

Just spitballing!

~~~
injb
Ultimately if you standardize something, people will gamify it. The point of
employers finding novel ways to evaluate candidates is to win that game and
beat the average. Good for them! It can't/shouldn't be otherwise (imo).

~~~
tprice7
They aren't mutually exclusive approaches, e.g. the standardized test could be
used just to get past the initial resume filter.

------
nottorp
If you're interested enough to do math research, you're likely to get a PhD in
mathematics because it's, well, full time math research?

------
YeGoblynQueenne
>> How many mathematical, biological, and physical discoveries would never
have been made, if it weren’t for robotics (invented by someone with no higher
education) and cheap compute (provided by the business sector)?

Who does the article mean, by "robotics (invented by someone with no higher
education)"? Wikipedia tells me that _[in] 1948, Norbert Wiener formulated the
principles of cybernetics, the basis of practical robotics_ [1], but Wiener
had a PhD from Harvard [2] and certainly much education, at all levels.

The wikipedia article on robotics has a number of other names of people who
contributed in various ways to robotics from ancient to modern times, but I'm
not sure who fits the article's description. Did Heron of Alexandria have a
"higher education", sensu stricto?

____________

[1]
[https://en.wikipedia.org/wiki/Robotics](https://en.wikipedia.org/wiki/Robotics)

[2]
[https://en.wikipedia.org/wiki/Norbert_Wiener](https://en.wikipedia.org/wiki/Norbert_Wiener)

~~~
eindiran
It's really unclear who they could mean. A few of the people in the History of
Robotics Wikipedia article[0] didn't have PhDs[1], but seemingly all of them
had some higher education. Maybe they are referring to someone who wrote
fiction about the idea of robots before robotics really existed: Karel Čapek
(who came up with the word "robot") had a PhD though[2]. Perhaps it refers to
L. Frank Baum, as he appears to have had no higher education[3].

[0]
[https://en.wikipedia.org/wiki/History_of_robots](https://en.wikipedia.org/wiki/History_of_robots)

[1] See William Grey Walter for example:
[https://en.wikipedia.org/wiki/William_Grey_Walter](https://en.wikipedia.org/wiki/William_Grey_Walter)

[2]
[https://en.wikipedia.org/wiki/Karel_%C4%8Capek](https://en.wikipedia.org/wiki/Karel_%C4%8Capek)

[3]
[https://en.wikipedia.org/wiki/L._Frank_Baum#Childhood_and_ea...](https://en.wikipedia.org/wiki/L._Frank_Baum#Childhood_and_early_life)

------
graycat
Hint, quiet, don't let this out, a Ph.D. is not really a _knowledge_ degree
but a _research_ degree. From that degree on, in blunt terms, everyone knows
that no one can carry the whole library around between their ears and so no
longer much cares what you know but cares what you can create!

There can be and are some exceptions, but overwhelmingly successful research
in math requires the background of a Ph.D. for (1) finding a suitable problem
and (2) having the knowledge to attack it. And it helps to be in a relatively
good school so that will get relatively good versions of (1) and (2).

But with everything in good shape, apparently there is one more challenge --
being successful in the actual research. For a hint at this challenge, 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.

That is, the research is work that is suddenly different, maybe for some
people quite different and challenging, than all the academic work before.
E.g., there are cases where a student made A's and was the darling of all the
teachers from kindergarten through college but in all that time never
encountered anything like having new ideas. Bad such cases can lead to stress,
loss of self-esteem, crippled ability to work, more stress, burn out, clinical
depression, and ... suicide. No joke.

For me, part of what helps in research is some _qualified respect_ for some of
the existing material. So, I look at what is there as needing improvement and
try to do that. If look at the existing material as some nearly perfect
construction, then maybe won't feel confident should or could improve on it!

One thing rarely taught in math is the importance of intuition: It is needed
to do well at guessing, guess a suitable problem, broad outlines of a
solution, attack, tools, etc. Good guessing is important since that's most of
what there is to do, and good intuition helps with good guessing. Sure, when
the results are obtained and in clean form with polished proofs, there can be
little or no view of the sources, the intuition.

There can be some question about how good some Ph.D. research is: The
professors don't want to grant Ph.D. degrees for poor research but don't
really know how to ensure good work, indeed, for either the students or
sometimes themselves. So one _standard_ that can remove some possibly painful
ambiguity is that the Ph.D. research should be "an original contribution to
knowledge worthy of publication" with the usual standards for publication
being "new, correct, and significant". If a student does some research and the
professors question if it is publishable, then the student can settle the
issue in an objective way -- try to publish the work.

E.g., computer science is concerned with _computational time complexity_ ,
i.e., _good_ algorithms where _good_ means running time that grows no faster
than some polynomial in the size of input data for the problem (rough
statement -- more details in the famous

Michael R. Garey and David S. Johnson, _Computers and Intractability: A Guide
to the Theory of NP-Completeness_ , ISBN 0-7167-1045-5, W. H. Freeman, San
Francisco, 1979.

and more recent sources).

IIRC that polynomial criterion came from J. Edmonds. More IIRC, he left his
Ph.D. program early and did and published some of his work on networks.
Eventually a committee of his former professors came to him and said that
should he stack his publications and put a staple in one corner, that stack
would be accepted as his Ph.D. dissertation and he would get his Ph.D.

~~~
mcguire
There is also (3): individual guidance and instruction on how to solve that
sort of problem.

~~~
graycat
Yes. I considered saying something like your (3) but thought that in the
interest of simplicity and brevity (a joke!) my

(2) having the knowledge to attack it.

would be enough.

------
jitendrac
From what I believe, many of the old days Mathematicians were given PhD by
various institutes after they got famous. Not all had PhD, but most of good
one got it after being recognized. Also don't forget many people of that time
did not publicize their work.

------
Joof
I'd agree with the hypothesis that a PhD let's you hang out and get paid to do
a lot of math. My brain is pretty spent from writing code -- I don't have time
to spend doing more math.

------
adamsea
It also depends on the person, no?

------
mcguire
" _A PhD is less important for doing groundbreaking applied engineering and
entrepreneurial work, especially in tech._ "

I'm just going to sit here and ponder "groundbreaking entrepreneurial work"
for a while. Is it like "financial innovation?"

Anyway, I'll also point to Matt Might's illustrated guide:
[http://matt.might.net/articles/phd-school-in-
pictures/](http://matt.might.net/articles/phd-school-in-pictures/)

