The mathematician Richard Hamming worked with some extraordinary people. At Los Alamos, he saw Feynman, Fermi, Teller, Oppenheimer, and Bethe up close. And at Bell Labs, he shared an office with Claude Shannon. In his talk “You and Your Research,” the Turing Award winner observes the differences between those who did significant things and those who didn’t.

One difference Hamming found was the ability to ask oneself, “What are the important problems in my field?” Hamming believes many people have greatness within their grasp but fail because they don’t work on important problems.

The great scientists thought carefully about what the most important problems in their field were and were always looking for an attack. Meanwhile, average scientists spent almost all of their time working without carefully considering the relative importance of problems.

It’s not just Hamming who noticed the importance of “problem selection.” Nobel Prize winner P. B. Medawar wrote in Advice to a Young Scientist, “any scientist of any age who wants to make important discoveries must study important problems.” It's also a major theme of the book Apprentice to Genius, which studies the chain-link of apprenticeships between famous scientists that created a string of incredible discoveries in biology.

If you want to do great work, you must work on important problems.

To ensure he worked on important problems, Hamming adopted something he called “Great Thoughts Time.” From Friday lunch through the weekend, he would only discuss great thoughts. By great thoughts, he meant things like “How will computers change science?”

Hamming suggests this practice helped him earn the Turing Award in 1968:

“I saw that computers were transforming science because I spent a lot of time asking, ‘What will be the impact of computers on science and how can I change it?’… I thought hard about where was my field going, where were the opportunities, and what were the important things to do. Let me go there so there is a chance I can do important things.”

However, he didn’t just brainstorm in a room by himself. He talked with people. Specifically, he talked with people who could push back on and stimulate his ideas:

“You want to pick capable people... When you get too many sound absorbers, you give out an idea and they merely say, ‘Yes, yes, yes'... [What you want to hear is] ‘Yes, that reminds me of so and so,' or, ‘Have you thought about that or this?'... I picked my people carefully with whom I did or whom I didn't brainstorm because the sound absorbers are a curse. They are just nice guys; they fill the whole space and they contribute nothing except they absorb ideas and the new ideas just die away instead of echoing on. Yes, I find it necessary to talk to people. I think people with closed doors fail to do this so they fail to get their ideas sharpened... On my visit here, I have already found several books that I must read when I get home. I talk to people and ask questions when I think they can answer me and give me clues that I do not know about. I go out and look!"

While Hamming’s advice is directed at people who want to be first-class scientists, I think this topic of problem selection applies to many areas of life. Each of us has one life to live, and what we choose to spend our time on is important. If you want to do great work, you have to make sure you’re working on important problems. And if you want to live a great life, you need to know that the little things are little, and the big things big, before it’s too late.

Carving out some time every week for “great thoughts” to make sure you’re spending time on the right stuff seems like a worthwhile investment. This could be talking with capable people, as Hamming suggests. But it could also be writing. I find that writing forces a precision and clarity of thought that is difficult to achieve in conversation.