Why I left math

"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.

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...

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.

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...?

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).

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.

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.

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."

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.

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

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

Why is one case bad but the other good?

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.