This is what happens when you hand math research to a physics major.

[Dishsoap]

Don't get me wrong, I'm all about research. I've been doing physics research for two years (not much, in the grand scheme of things), but I love it. I love programming which is mind-numbingly boring to most people, I love solving equations, I love being able to understand the universe around us. I enjoy giving presentations and answering questions, and overall I really think I have a passion for it.

So when an opening in a graph theory research group opened up, I jumped on board. I'm working with one of the best professors in the department, and I thought it would be really fun.

It's boring as heck.

I'm tired of spending hours drawing shapes, reading 50-page proofs of things, only to be able to find an Euler tour in a very specific case in a few years. I've never done any math research other than this, so I really just want to know: am I maybe just involved in the wrong group, or is this the nature of mathematics research?

In the meantime, I'm going to go draw some more shapes...

 

[Dembadon]

Have you tried research papers in another area? Here is a link to a paper by 3 of my professors:

FELL BUNDLES ASSOCIATED TO GROUPOID MORPHISMS

Not sure how familiar you are with groupoids or category theory, though. However, if you dislike proofs, you will not escape them no matter where you go in mathematics. Even in "applied" areas such as graph theory and combinatorics, proofs are required; without them research would be pointless.

 

[jbrussell93]

What kind of physics research were you doing before switching to math?

Just purely out of curiosity, if you liked it so much then why the switch?

 

[Dishsoap]

It's not that I dislike proofs at all, I just don't understand the point of spending 3-4 years proving something that has already been proven, just to make it "neater".

Also, I did not "switch", just picked this up in addition to physics. I work with a group which does work in quantum field theory. As an undergrad, the physics is way over my head, but I enjoy the brute force programming and learning things.

 

[jgens]

It's not that I dislike proofs at all, I just don't understand the point of spending 3-4 years proving something that has already been proven, just to make it "neater".

Dig through the literature sometime and find the original proofs for many of the basic results you learn in algebra and analysis. You might be surprised just how long and opaque some of the arguments are. Be glad someone decided to revisit older results and find more conceptual/neater proofs!

 

[homeomorphic]

I'm a math PhD who considered himself to be a physicist at heart, and as soon as I was exposed to a lot of the research-level stuff, I found a lot of it incredibly obscure and uninteresting. It gets to a point where there are very extravagant levels of abstraction and complication. So, on some level, I can relate, but I also wonder if you are looking at some of it in the wrong way. Personally, I am kind of fond of graph theory, and I see it as one of the less boring math subjects out there, though to some degree, it suffers from the same extreme over-formality and stuffiness of presentation as many other subjects.

Whether it's boring or not is pretty subjective. What I would say is that it's a pretty diverse subject, and you might find subjects more compelling. For a lot of it, you have to look at it in just the right way to see why it's interesting.

As I've said before, what I enjoy most about math is making things obvious to myself that were initially far from obvious. That might go some way towards explaining the point of coming up with better proofs of the same result. If you just view it as a way to establish a fact and forget why it's true, then who cares? But if you view it as a way to understand the fact, to know the why and intuition behind it, not just establish it, then it becomes crucial what proofs you use. So, it seems you are missing something fundamental to the appreciation of mathematics, though I do have some sympathy for resenting the lack of hands-on calculations, which is one thing that many mathematicians seem to neglect these days.

Some general criticisms I have of the state of the mathematical culture, particularly in regards to being boring:

1) They love to give incomprehensible talks. They need to come to their senses about this, ASAP. Here's a fun little opinion from Doron Zeilberger, a professor at Rutgers, who shares my opinion here:

http://www.math.rutgers.edu/~zeilberg/Opinion104.html

2) Their writing is too formal. Here is an article from a Fields Medalist, exposing some the issues here:

http://www.ams.org/journals/bull/1994-30-02/S0273-0979-1994-00502-6/S0273-0979-1994-00502-6.pdf

3) Not only is their writing too formal, but sometimes, their other forms of teaching as well (and even their thinking, as Thurston points out).

http://www.math.fsu.edu/~wxm/Arnold.htm

My favorite line from the whole article points out that it is impossible to understand an unmotivated definition. That's probably the number one thing that I see wrong with the way higher-level math is being taught these days.

4) Not enough thought is given to the purpose of what they are doing, including practical applications. Up to a point, math for math's sake is a worthy goal, but when you look at how hard mathematicians have to work, it seems as though many of their lives are just getting consumed by it, which completely defeats the purpose of enjoying math for its own sake. If the purpose is enjoyment, why would you drown your whole life in it? Moreover, drowning your whole life in it is almost a requirement for success, given the current competitive, rat-race conditions.Many mathematicians might try to insist that the writing needs to be so formal in order to be rigorous. This is quite obviously complete nonsense because adding additional intuitive commentary need not have any effect on the rigor.

There's some distinction between math as a subject and math as a research topic. As a subject to study, at the graduate level, I would disagree that it's boring, although the way it is presented is often very boring. It's not the subject's fault, though. It is the way it is presented.

Of the stuff that people do research on, however, 95% seems to be completely boring and obscure to me. Of course, that's fairly subjective, but I am not alone in my opinion. I quit math research, but I remember someone who continued with a postdoc saying that everything people are studying these days is ugly. Her husband, also a graduate student in algebraic geometry would have agreed. He quit research, too. In fact, 90% of us math PhDs quit research, and I'm willing to bet, in lot of cases, it doesn't have much to do with their lack of ability.

I think it's sort of out of control. Too much information out there, too many papers, too much pressure to publish, too much crap. We need precisely the sort of consolidation (better proofs, and more importantly, better explanations) you are objecting to to get it more under control. Who cares about producing billions of obscure results if no one can understand them?

 

[IGU]

I'm a math PhD who considered himself to be a physicist at heart...

http://www.math.fsu.edu/~wxm/Arnold.htm

...Who cares about producing billions of obscure results if no one can understand them?

So as a physicist at heart Arnold must really appeal to you. That's a great rant of his by the way -- thanks for the link to it. He advocates in favor of "development of correct Weltanschauung" -- indeed, shouldn't we all!

So, I'm curious, do you find such things as Polymath 8 boring and pointless? Do you think Arnold would?

 

[homeomorphic]

So, I'm curious, do you find such things as Polymath 8 boring and pointless? Do you think Arnold would?

It's hard to be absolute in my statements. It certainly seems to be a bit on the boring side to me, but that is in the eye of the beholder. Pointless is also hard to say. It's hard to rule out any particular bit of work as being pointless. Arnold and I would probably not agree on everything there. So, rather than point the finger at anything in particular that needs to be abandoned, my position is that we should shift the balance more in favor of applications, and not just applications, but motivation, even if it's purely mathematical motivation. Very few people bother to explain why their research is interesting and why we should care, even from a pure mathematician's point of view. The current situation is not very inviting to outsiders and newcomers, and when you consider that people are usually specialists, not even very inviting to anyone, except maybe the tiny little research groups working on very similar things. Most people seem to be talking past one another. It's a tower of babel.

My preference is definitely to focus on understanding more than establishing facts, but sometimes the facts come first and the understanding, later.

 

[homeomorphic]

Also, I should add that my point is that understanding is more valuable than brute facts that are not understood. However, there are circumstances where maybe all we can get is the facts. Maybe the 4-color theorem would be an example. So, I'm not saying that results that have proofs, but not understandable explanations are necessarily always worthless. Just that that are not worth as much, and there should be less focus on such things. Plus, it might not be the best use of people's time to read papers that are too technical to learn anything from, beyond pure verification of results.

 

[Hypersphere]

2) Their writing is too formal. Here is an article from a Fields Medalist, exposing some the issues here:

http://www.ams.org/journals/bull/1994-30-02/S0273-0979-1994-00502-6/S0273-0979-1994-00502-6.pdf

That was a great read! Thanks for posting the link.

Out of interest, is this state of affairs discussed often in the mathematics communities, or are people mostly happy/content with the way things are?

 

[homeomorphic]

Out of interest, is this state of affairs discussed often in the mathematics communities, or are people mostly happy/content with the way things are?

It's not the sort of thing I overheard professors talking about, but it does come up. Like here on mathoverflow:

http://mathoverflow.net/questions/153604/the-arnold-serre-debate

Here, they are pointing out how Arnold might have been a little too hard on Bourbaki because it was not so much their attention to write for teaching purposes (from what I've heard, though, some of his criticism is deserved).

Also, Thurston's article there was one of many responding to Jaffe and Quinn's, which he mentions at the beginning.

Here's a discussion started by Thurston, himself:

http://mathoverflow.net/questions/38639/thinking-and-explaining

My adviser made me use the overhead (and even suggested power-point), instead of a chalkboard, when I defended because I tend to be a bit slow when giving talks, but he mentioned how he doesn't like power-point, in much the same spirit as Zeilberger's opinion. He also said most people start with the most complicated case, but they ought to start with the simplest case.

I suspect it is easier to survive in the current mathematical climate if you are somewhat content with the situation. Arnold said in an interview that he had to "swim against the stream."

And it's a stream that you have to be pretty strong to swim against. Arnold became famous at age 19 for solving one of Hilbert's problems, so he was pretty strong. As for me, I wasn't strong enough, so I can only work outside of the stream.

There were always books being written here and there that try to explain math, rather than just formally present it (Visual Complex Analysis, all of Arnold's books, A Radical Approach to Real Analysis, to name a few).