How to Read and Understand PhD Papers in Math/Physics

[Fellowroot]

I am currently reading this paper.

http://arxiv.org/pdf/1401.2670v1.pdf

Because I am interested in knot theory and here are my impressions.

Why are these papers so difficult to read? It almost seems as if it really is a completely foreign language as if its not already a foreign language to begin with. I can read a textbook just fine, but this is way harder. I can hardly even understand any of it to be honest and I am wanting to purse a Phd in math or physics and am serious about it.

Where are the diagrams and pictures? How do I even begin to know what's going on in this paper.

It feels as if the person who wrote it is so smart that nobody else can even understand what they wrote about.

I know that you have to be at an expert level on the subject to read these papers, but good grief.

Anybody have any advice on how to get to this level of being able to read and understand other people's papers?

Thanks.

 

[SteamKing]

PhD papers are generally written for other PhDs to read; they are not intended for the generalist/non-specialized reading audience.

The dirty secret about textbooks, even college level texts, is that they are being written more and more at the level of what used to be high school texts. The texts themselves are so ponderously huge because they include much more illustration and whatnot than they used to. Of course, while the content of textbooks is constantly shrinking, the price for the book marches ever upward.

 

[FactChecker]

A large part of PhD work is learning how to write a research paper for other experts in the field. It is a learned skill to know what to include and what to omit. Math PhD theses are written for researchers in that field. An expert in the field will want the most brief explanation of the results as possible -- no introductory material needed. But the material will still have to include everything necessary to be rigorous. If every paper was written like a textbook, the contents of a person's file cabinet would take up several rooms and looking for the new results in papers would take 10 times as long.

 

[Spinnor]

If interested in the paper you might also be interested in the authors talk here,



More pictures at least.

Attack the problem from every angle you can.

 

[Mmm_Pasta]

You will get used to the language in your field after reading several articles, working on research and whatnot. These papers aren't meant to be pedagogical unless it is about teaching. If they were written like textbooks, then it would take a while to look for the things you need in the paper.

 

[cgk]

I did not look into this concrete paper, but the problem OP describes is quite prevalent over many fields.

Additionally to the possibly missing expertise of the readers, I think a major problem is that many writers of science papers are simply not good at writing, because they never learned it deliberately. The following paper gives much useful advice on writing:
Gopen & Swan - "The science of scientific writing" (http://engineering.missouri.edu/civil/files/science-of-writing.pdf
Nevertheless, all of this advice is quite basic and fundamental (at east in retrospect). But how many papers do you see which violate it in fundamental ways?

 

[mal4mac]

-- no introductory material needed.

And that includes no references to introductory material! This is why you have a PhD supervisor. At best, he will know exactly what introductory material to point you to. At worst, he'll be able to give you the sort of advice given in this thread!

An UG picking up a research paper is like a hill climber being dropped on the summit of Everest. He's likely to look down and think, "How did anyone climb this thing? Only superman could do it. How do I get down!?" But, of course, many quite ordinary folk do get up and down. It just needs a lot of training, practice, equipment, sherpas, ... (But, remember, a few die in the attempt. No one said it was easy. .)

 

[homeomorphic]

Personally, I question the way people are communicating with each other in these fields. I have a PhD in topology and I am casually familiar with that subject. It would take me forever to read that paper. That's one of the reasons why I quit.

One of the clues is that written material tends to be secondary. You might profit from reading Thurston's classic essay, here:

http://arxiv.org/abs/math/9404236

Anyway, a lot of times professors will try to make knot theory look like this cute subject where you play with bits of string, but I'm not so sure that's what it's really like, a lot of the time. Some of it is. I found a lot of modern math is pretty out there for me.

I don't think it's necessary for every paper to be so obtuse. Try reading one of John Baez's papers, for example. I wish people would write more papers like he does and less like that knot theory one. If you want good knot theory papers, though, I'd recommend checking out Bar Natan's papers. Not all of them are that bad. Just stay away from Heegard-Floer.

But you might take this as an early warning sign that knot theory might not be for you. I thought I was like a pure mathematician with an applied bent, but when I found out how over-complicated modern math is, I started to realize I am actually extremely applied in my motivations. I can't just go on and on like that without producing something of more concrete value. You might find the same thing. I didn't trouble myself too much with papers because I figured I would just get there eventually, but I got the PhD, and I didn't really get there. Most of the papers are still pretty obtuse to me, although there are a few that I can understand if I really sit down and wrack my brain over them. But even one of them could take a very considerable time for me to digest, still. I don't think I'm not as smart as the other guys, or if so, I'm only a little bit dumber than they are. My profs in undergrad thought I was really hot stuff and I passed my quals without too much trouble, did about average in graduate classes and everything. I still don't get topology, though.

I mean, it's not as if it's 100% BS that they are just making up. If you travel the very long path leading to Heegard-Floer theory, you'll see that it originated in some interesting gauge-theory ideas. I could explain some of the ideas to you by analogies with math that you've probably already studied. And that goes back to Thurston's point that the written stuff is secondary. Those papers aren't really written for human beings. In order to really understand any of that stuff, the best thing is just to talk to people and have them explain it to you. And mathematicians often do that. Even the pros might not understand every paper. They might just throw up their hands and say, I can't make heads or tails of this, so maybe I'll call up so and so and see if they can explain it to me or even invite them over to give a talk about it.

 

[homeomorphic]

Oh, and by the way, my adviser, who is one of the top people in his field, complained on at least one occasion about papers that were unreadable. So, it's definitely the case that some people have issues when it comes to writing papers that are meant for a human audience, rather than some weird math cyborg.

 

[porcupine137]

I am currently reading this paper.

http://arxiv.org/pdf/1401.2670v1.pdf

Because I am interested in knot theory and here are my impressions.

Why are these papers so difficult to read? It almost seems as if it really is a completely foreign language as if its not already a foreign language to begin with. I can read a textbook just fine, but this is way harder. I can hardly even understand any of it to be honest and I am wanting to purse a Phd in math or physics and am serious about it.

Where are the diagrams and pictures? How do I even begin to know what's going on in this paper.

It feels as if the person who wrote it is so smart that nobody else can even understand what they wrote about.

I know that you have to be at an expert level on the subject to read these papers, but good grief.

Anybody have any advice on how to get to this level of being able to read and understand other people's papers?

Thanks.

One thing to keep in mind is that most of the books you read are background and intro material while those papers are cutting edge and probing into very specific little bits of sub, sub-fields, often you need to already know everything in all the books from intro to advanced at the least. Of course, it depends upon the paper.

Sometimes new stuff is not well understood and those who create are not always the best at explaining things in the most straightforward fashion or may not truly deeply understand things themselves (look at how confusing some older texts make things- of course it's also true that some older texts like K&K seem a lot nicer than stuff like University Physics and the like, but in many cases it can take years or decades for papers and books to put things in the clearest terms).

Some of the papers on the archive are like diving 1 mile deep using snorkling gear if you look before having a really strong backyard. SOme are so obtuse and/or advanced that even expert might struggle. It depends.

 

[pasmith]

Research papers are aimed at experts. They report new results, assuming the basic results with which experts are expected to be familiar. They can't rehash all the basic results; there simply is not sufficient space (for the same reason there are often no diagrams).

Trying to learn a new area of mathematics by reading journal articles is an exercise in frustration and reference chasing until you come across the paper where the basic results were first reported.

Works which are aimed at nonexperts are textbooks and monographs, in which an expert has sorted out the wheat from the chaff and presented the basic results in a clear, logical order with perhaps some motivation (and some diagrams, because the cost of preparing diagrams and the space required for printing them is worthwhile for books, but not always for journals). If it's a textbook the author will also have provided exercises so you can check your understanding; monographs don't have exercises so you're on your own.

Review articles fall somewhere between the two extremes.

There are badly written examples of all types of work, as there are well-written examples. But even a well-written non-review article will likely be inaccessible to someone who is not familiar with the basic results of the field.