Learning how to do research

 

There is no recipe for good research. Some students expect or hope to be provided with step-by-step instructions or guidelines on how to find or tackle problems. That's not how it works. Here are a few indications of what is involved.

Learning by thinking

The first rule of research is to think, think and think again. Never hesitate to throw your mind at anything. That should be the first thing you try. Before looking up a book or paper, before asking anyone, think. For example, suppose you are reading a paper and there is a lemma, with the proof referred to another paper. Should you go get the other paper to look it up? No. First, try to prove the lemma yourself. If you don't succeed after a reasonable time, go look it up. But if you solve it yourself, you will have understood it better. What you solve by thinking is your baby from then on; what you look up you will forget and have to look up again and again.

Never be lazy about thinking. That's how you build up understanding and develop a bag of techniques that you can use.

Thinking is fun. If you don't find it so, it's an indication you are in the wrong business.

Learning by example

You pick up how research is done by seeing examples and extrapolating. Papers, and discussions with your advisor or peer, are a source of materiel. You learn how to write a paper by looking at other papers. Make anologies. When you see a new primitive or problem, ask yourself what kinds of questions were asked about previous ones and use that to ask questions about the new one.

As you go on, you should be able to extrapolate more and more, and farther and farther.

Natural learning

Perhaps the best indicator I have seen of a student's research proclivity is the extent to which they find the ``right'' things ``natural''. There are some students who, when shown some technical item, react, somehow naturally having good reactions and viewpoints, about the import of the item and what to do next. These are simply people who learn extremely well by example.

Understanding versus knowledge

It is more important to understand well what you know than to know a lot. Successful research comes from having a good understanding, especially of the basics.

When you read a paper, ask yourself questions. What if I changed the scheme in the following way: would it be secure or not? How does this compare to the following other scheme? Why is this novel? Can I come up with a different proof? Understanding means the ability to go beyond the immediate. It means knowing not just what is the item in question, but how it fits into a larger context, what are its variants, and what happens if you ``perturbe'' it one way or another.

Questions

When do you think about research problems? (Mark all that apply)

1. I sometimes think about research problems at odd times, like in the shower or while driving
2. I think about research problems only when I am at the lab
3. I think about research problems at home
4. I think about research problems as little as possible

With regard to how you fit into this research game

1. I think I'm a natural
2. I think I can pick it up fairly easily and like it
3. I think I can with effort learn the ways of this world and function in it
4. It's like being on Mars, but I can stand it for a few years
5. I feel totally out of place with all these nerds; what am I doing here?