I've heard a lot of people talk about Richard Hamming's advice on how to do valuable research, but I only just got around to properly reading the transcript of his talk "You and Your Research." Here's a few things he talks about I found particularly interesting.
Have the courage to pursue independent thoughts, and to believe you can do important work:
“One of the characteristics you see, and many people have it including great scientists, is that usually when they were young they had independent thoughts and the courage to pursue them. For example, Einstein somewhere around 12 or 14, asked himself the question, “What would a light wave look like if I went with the velocity of light to look at it?”... He could see a contradiction at the age of 12, 14, or somewhere around there, that everything was not right and that the velocity of light had something peculiar.
One of the characteristics of successful scientists is having courage. Once you get your courage up and believe that you can do important problems, then you can. If you think you can’t, almost surely you are not going to. ”
“When you are famous it is hard to work on small problems. This is what did Shannon in. After information theory, what do you do for an encore? The great scientists often make this error. They fail to continue to plant the little acorns from which the mighty oak trees grow. They try to get the big thing right off. And that isn’t the way things go.”
If you can’t solve a problem, turn it around:
“I think that if you look carefully you will see that often the great scientists, by turning the problem around a bit, changed a defect to an asset. For example, many scientists when they found they couldn’t do a problem finally began to study why not. They then turned it around around the other way and said, “But of course, this is what it is” and got an important result.”
Don’t underestimate the importance of drive and commitment...:
“You observe that most great scientists have tremendous drive. I worked for ten years with John Turkey at Bell Labs. He had tremendous drive... I went storming into Bode’s office and said, “How can anybody my age know as much as John Turkey does?” He leaned back in his chair, put his hands behind his head, grinned slightly, and said, “You would be surprised Hamming, how much you would know if you worked as hard as he did that many years.”... What Bode was saying was this: “Knowledge and productivity are like compound interest.”... The more you know, the more you learn; the more you learn, the more you can do; the more you can do, the more the opportunity.
If you are deeply immersed and committed to a topic, day after day after day, your subconscious has nothing to do but to work on your problem. And so you wake up one morning, or on some afternoon, and there’s the answer. For those who don’t get committed to their current problem, the subconscious goofs off on other things and doesn’t produce the big result. So the way to manage yourself is that when you have a real important problem you don’t let anything else get the center of your attention - you keep your thoughts on the problem. Keep your subconscious starved so it has to work on your problem, so you can sleep peacefully and get the answer in the morning, free.”
...but maybe don’t overestimate it either:
“The misapplication of effort is a very serious matter. Just hard work is not enough - it must be applied sensibly.”
Learn to be comfortable with ambiguity:
“Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you’ll never notice the flaws; if you doubt too much you won’t get started.”
And of course, work on problems you really believe are important:
“If you do not work on an important problem, it’s unlikely you’ll do important work. It’s perfectly obvious. Great scientists have thought through, in a careful way, a number of important problems in their field, and they keep an eye on wondering how to attack them.... The average scientist, so far as I can make out, spends almost all his time working on problems which he believes will not be important and he also doesn’t believe that they will lead to important problems.”