
Why I left math - fogus
http://bentilly.blogspot.com/2009/11/why-i-left-math.html
======
anatoly
"These days mathematicians are divided into little cliques of perhaps a dozen
people who work on the same stuff. All of the papers you write get peer
reviewed by your clique. You then make a point of reading what your clique
produces and writing papers that cite theirs. Nobody outside the clique is
likely to pay much attention to, or be able to easily understand, work done
within the clique. Over time people do move between cliques, but this social
structure is ubiquitous. Anyone who can't accept it doesn't remain in
mathematics."

I think this is an exaggeration. Sure, much of mathematics and maybe most of
mathematics today works like this, but it's the exceptions, in accordance with
Sturgeon's Law, that are most interesting. The really good specialists tend to
transcend little cliques, and sometimes entire fields. There are plenty of
people who are respected outside the circle of their immediate coauthors,
everybody (for some definition of "everybody" that is anyhow wider than a
little clique) wants to read their papers, etc.

You could say that these are rare exceptions and >90% of working
mathematicians are producing highly specialized papers that are interesting to
maybe a dozen other people, that don't know much outside their narrow focus
and don't really care, and so on. And you'd be right. But in programming,
isn't it the case that >90% of programmers are chugging along in their Java or
C# shops, writing some enterprisey horror or an internal corporate
monstrosity, never caring enough to read Joel, nevermind Hacker News, or to
improve their knowledge of the language they're using everyday, nevermind
learn Haskell. The talented hackers are rare outliers. So what's different?

I do agree with some other thoughts in the article. Someone who wants to
dabble in many things has their work cut out in the academic math culture. I
left grad school because I couldn't hack a bloody-minded focus on working on
my thesis and doing nothing else. I had other reasons to suspect I won't be
staying around in academia. For one thing, I despise internal politics and
petty squabbling, and what I saw when I looked at the power structure and
battles more closely, being a graduate student, shocked and disgusted me. Even
more importantly, I had grave doubts about ever being able to do really
meaningful work rather than end up writing up small results in a little
clique. I doubted I had it in me to become an exception I talked about above.
I still regret not testing this more thoroughly by mustering the will-power to
shut down everything else, finish the damn thesis and get the damn degree,
even if I probably wouldn't end up in academia anyway.

------
tokenadult
Thanks very much for bringing up this subject, which has elicited several
interesting replies.

My favorite book recommendation on the subject of career paths for young
people considering pure mathematics:

[http://www.amazon.com/Mathematicians-Survival-Guide-
Graduate...](http://www.amazon.com/Mathematicians-Survival-Guide-Graduate-
Development/dp/082183455X)

My oldest son is a math-liker who has been exposed to the pure mathematics
research community through summer programs, and he (college-applying age) and
I are currently pondering whether becoming a math professor is a better fit
for him, or whether he will truly find paradise as a hacker starting a SaaS
business.

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roundsquare
I had a professor once who said something similar. He phrased it differently
though: in math people didn't want you to understand. Something about how it
made them feel smarter.

Amusingly, he's a top-notch theoretical computer scientist which is really a
kind of math (especially what he does). From this, I gathered that its really
the culture of the department, not the field that does this.

One possible counter argument which I'm not in a position to evaluate:
Theoretical CS is generally more grounded in "real" problems so maybe its
easier for people in other areas to understand...?

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zppx
The problem with mathematics is that it's very hard, it's not for everyone,
the common folk cannot understand it, and 99% of those who can will not be on
the level of a Felix Klein or Henri Poincaré. This is well exemplified in the
book "Indra's Pearls: The Vision of Felix Klein", even today it's hard to
trained mathematicians to visualize what Klein described. How many
mathematicians does the author of the post supposed there was at Göttingen for
just one Klein to come out of blue? To be answered just read the paper "Klein,
Hilbert, and the Gottingen Mathematical Tradition". I study applied math and
computational science at university, still an undergraduate, because I have
fun studying it, not to be a professional mathematician, I'm not smart enough
to be good in the area in which I study (Numerical Analysis and Applications,
Inverse Problems, Stochastic Processes and Scientific Computing), I'll
probably try be a experimental physicist if I chose to remain in academia or
will try to be a sysadmin (I already work as one in a part-time job).

~~~
WilliamLP
> 99% of those who can will not be on the level of a Felix Klein

We might be on the same plane though. (Sorry!)

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diiq
I am glad to know that this is true of people within the field. I've always
found mathematics a romantic subject, but the landscape is so broad I always
feel lost.

Well, maybe not 'glad' --- it's too bad that people are punished when they try
to be on more than one bleeding edge. But at least I feel like less of a
dunce.

~~~
tjarratt
While the landscape may be broad, it should be exciting that you can spend
your entire life studying one facet of a subject as deeply as you like and
there will still be an infinity of other truths you could have discovered.
Talk to colleagues studying other fields, even if you never have an amazing
cross-discipline breakthrough, it is nice to hear about other elements of
mathematics.

disclaimer: While I finished my degree in mathematics, I immediately entered
the field of programming, which was what I had intended to study.

------
pixcavator
The only way to succeed in grad school is to be single-mindedly focused on
mathematics. Not on being a "generalist", not about "cliques", tenure, etc.
This "meta-math" reasoning is a bad substitute for doing actual work. Clearly,
the guy is better off doing something else.

~~~
wtallis
Just because grad schools don't currently engender generalists doesn't mean
that they are a bad thing or less important. It's just harder to measure how
accomplished and brilliant a generalist is than it is to measure the
contribution of a researcher that has made significant progress in a specific
area. Generalism is only really well rewarded when it produces an unexpected
solution to or progress toward a solution of an open problem.

------
edw519
I left math for a totally different reason and I'm almost embarrassed to talk
about it. A little background...

I worked full time through college and graduated with less than $100 in the
bank. I had opportunities to go on to graduate school for either math or
business.

Every professor in our math department drove an older subcompact except the
department head who drove a Chevy Impala. Imagine, work your whole life, get
to the top of your field, and drive an Impala!

I had struggled too long to set myself up for more struggle. So I went on to
get my MBA, learned how to program, and have never had a lack of good quality,
high paying work. I'm a little embarrassed that I was so shallow back then,
but maybe my subconscious was trying to tell me something. I love math, but
I'm sure glad I made the choice I did.

At a recent math reunion, I felt right at home once again. I met a buddy who
graduated with me and continued on to become a tenured math professor at a
major university. I asked him how he felt about his choice. He told me, "I'll
never be rich, but I teach calculus for 8 hours per week 9 months per year, I
don't have to publish, and my wife and I have visited over 100 countries. Not
a bad life at all."

~~~
duh
> I'll never be rich

This seems like something of a false dichotomy to me. The professors at my
school (UCSD) in math, econ, and engineering were all industry consultants
and/or entrepreneurs and drove around in very nice cars like Porsches, Benzes,
Lexus etc. (I never saw their houses but a good many of them live in La
Jolla).

In fact, many of them were so busy with their 'extracurricular' activities
that they sometimes attempted (unsuccessfully) to schedule exams and lectures
at hours like 7am or 9pm.

The Chancellor drove a turbo porsche! I can only imagine what the faculty at a
school like Stanford is like...

It always seemed to me that being a professor _opened_ doors into industry,
instead of 'locking' you down.

~~~
hyperbovine
There's a noticeable gradient in car preferences as you go from northern to
southern California. At multiple points in my career at UC Berkeley, I saw
older model, unshowy American cars parked in the "NL" parking spots. (Guess
what NL stands for, hint not a country in Europe.) After I graduated and
started working in the Bay Area I met many people would could not have been
making <$200k driving normal everyday cars. The most extreme example would be
someone whom I knew for a fact was worth eight figures driving a Cadillac. It
was shiny and new but, really? A Caddy?

As I went to high school in LA, where it seems like 2/3 of the population over
20 is driving a late model BMW, this was something of a eye-opener: a lot of
rich people just aren't that into cars. That, and the whole conspicuous
consumption thing is a lot more en vogue in some places than in others. So to
answer your question, the faculty at Stanford probably drive a lot of Hondas.
(Someone chime in if I'm wrong, haven't been to the Farm in a while.)

~~~
duh
I have no idea what you're talking about, Silicon Valley and SF are filled to
the brim with expensive and exotic cars. Cruise around Atherton and Los Altos
hills or go to downtown PA or the nice parts of cupertino - Ferraris, Astons,
Porsches, BMW, Lexus, etc, etc. Even as far as Santa Cruz I have seen plenty
of people in their nice sports cars driving fast on 17 all the time.

This notion that "rich people aren't into cars" in northern california is
absolutely laughable. Sure there are MORE nice cars in LA, but that's only
because LA is a much larger metro area.

I've lived in both the bay and LA and I can tell that this game of "spot the
differences" that so many people play are observations based on selection and
confirmation bias. You're just looking for evidence that supports ideas you
already have.

In my opinion SF and LA are pretty much the exact same culturally. People from
SF just hate to admit it.

------
gchpaco
I'm not sure if I'm atypical, but I do remember having Hugh Woodin give a talk
about set theory that I, as a non-specialist (heck, as a computer scientist
moonlighting in math grad courses to keep my brain on!) could follow
reasonably easily. I still don't know what projective geometry is, but it
wasn't necessary to follow his argument.

~~~
abstractbill
There are some mathematicians who make big efforts to make their talks
accessible to a wider audience. Inexplicably, at least in the mathematics
department where I did my PhD, those kinds of talks were actually looked down
on by many people.

~~~
barry-cotter
Same reason most postmodernism and literary theory uses obscurantist language.
People value more what they had to work harder for, whether it's understanding
or a mug. Making something comprehensible to a broad audience doesn't do
anything for the people whose opinion really matters to you, your colleauges,
and it makes their work less prestigious by association, because its
theoretically comprehensible.

[Rant about Edward Said, and how he said some worthwhile stuff, then made it
virtually incomprehensible thought better of]

------
amichail
One could make the argument that cliques encourage more social interaction --
and subsequently more collaboration. This could be more beneficial overall for
the field.

~~~
timothychung
Good point.

I think the bottom line comes down to needs for cross-clique knowledge
sharing. The possibility for a change in culture is low if there is no
incentive for it.

------
amichail
Cliques in math are like social networking in startups: success partly depends
on your connections.

Why is one case bad but the other good?

~~~
abstractbill
The cliques in maths are different: They are much smaller (literally a dozen
or so people), and they really can't understand each other.

I agree with the article - it describes pretty well why I left pure
mathematics after my PhD and got a programming job.

------
borguk
I loved maths but life as a mathematician was very depressing. Another point I
would like to add is that there are very few mathematicians compared to
biologists. Actually, I am not very sure if it's true in the US and Europe but
it certainly is in India. The biggest of math conferences here have a 100 or
so people and so do the smallest of the biology ones.

