I recently read the transcript of a talk given by Richard Hamming and realised many of us may have been missing a trick. He makes the point that we should aim to work on the important problems in our field. This is one of those ideas that seems obvious once you read it, but is somehow easy to overlook during the bustle of day-to-day research.

Why is it important to work on important problems?

Imagine you have a miracle year of work. You're in the zone 100% of the time, every hunch you have turns out to be right and every project you touch turns to gold. Now consider the difference in the impact of your work depending on whether you had been working on important problems or unimportant ones. In the first case, you might have done truly great, maybe Nobel-worthy work. In the second case, you've still done good work but it's not going to change the world. Which would you rather have happen?

What if you work on unimportant problems?

I'm not suggesting that you should exclusively identify important problems and only work on them. After all, you can't be 100% sure your list of "important" is complete and/or completely accurate. However, if all you work on are problems that are unimportant, by definition you limit the impact and value that your work will ever have. Unimportant problems are just that. By all means spend a bit of time tinkering with such problems if they really interest you, but don't waste your career on them.

What are the important problems in your field?

This really boils down to being able to identify what the important problems are in your field/s. This is more difficult than one might imagine, but with some time and thought you can make some headway. Take time to think about what you consider the important problems to be. Read some articles for inspiration. See if any other academics in your area have posted on this topic on the Web. And ask people! A great question over coffee or at a conference dinner is, "What do you think the important problems are in our field?".

Some of these problems will be intractable. Finding an exact O(n) solution to the travelling salesman problem would be awesome, but seems unlikely. And formulating a Grand Unified Theory of physics would be nice, but many people have tried and no-one has just succeeded. It can be tricky to distinguish between problems that are difficult and ones that are (or are likely to be) impossible to solve. There are judgement calls to be made here as to how much time to spend on each problem.

And then there are the problems about which we're uncertain. Is it important or not? Again, this is a judgement call. If the problem is interesting to you, plus you think you can make good progress on it quite quickly, then it's probably worth working on just in case it's important.

Nowhere so far have I mentioned a couple of other considerations that I think are also important. You should probably work on problems that inspire/enthuse you. And you should work on problems to which you're suited, in terms of abilities, skills andtemperament. If you're no mathematician, you shouldn't be trying to work on the Reimann hypothesis. And if you thrive on a sense of rapid progress and individuality, perhaps it's not such a great idea to work on that huge physics project that won't begin generating data for 5 more years.

In conclusion...

It's not the only consideration, but deciding on the important problems in your field and working on them is a pretty good starting point for scientific research.

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