This is a stub post, mostly existing so people can easily link to a post explaining what the Hamming question is. If you would like to write a real version of this post, ping me and I'll arrange to give you edit rights to this stub.
For now, I am stealing the words from Jacobian's event post:
Mathematician Richard Hamming used to ask scientists in other fields "What are the most important problems in your field?" partly so he could troll them by asking "Why aren't you working on them?" and partly because getting asked this question is really useful for focusing people's attention on what matters.
CFAR developed the technique of "Hamming Questions" as different prompts to get your brain to (actually) think about the biggest problems, bottlenecks, and unspoken desires in your life.
A transcript of Hamming's extensive 1986 talk "You and your research", touches upon a several elements of Hamming's philosophy, and includes this anecdote about the canonical "Hamming Question":
Over on the other side of the dining hall was a chemistry table. I had worked with one of the fellows, Dave McCall; furthermore he was courting our secretary at the time. I went over and said, "Do you mind if I join you?" They can't say no, so I started eating with them for a while. And I started asking, "What are the important problems of your field?" And after a week or so, "What important problems are you working on?" And after some more time I came in one day and said, "If what you are doing is not important, and if you don't think it is going to lead to something important, why are you at Bell Labs working on it?" I wasn't welcomed after that; I had to find somebody else to eat with! That was in the spring.
In the fall, Dave McCall stopped me in the hall and said, "Hamming, that remark of yours got underneath my skin. I thought about it all summer, i.e. what were the important problems in my field. I haven't changed my research," he says, "but I think it was well worthwhile." And I said, "Thank you Dave," and went on. I noticed a couple of months later he was made the head of the department. I noticed the other day he was a Member of the National Academy of Engineering. I noticed he has succeeded. I have never heard the names of any of the other fellows at that table mentioned in science and scientific circles. They were unable to ask themselves, "What are the important problems in my field?"
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. Let me warn you, "important problem" must be phrased carefully. The three outstanding problems in physics, in a certain sense, were never worked on while I was at Bell Labs. By important I mean guaranteed a Nobel Prize and any sum of money you want to mention. We didn't work on (1) time travel, (2) teleportation, and (3) antigravity. They are not important problems because we do not have an attack. It's not the consequence that makes a problem important, it is that you have a reasonable attack. That is what makes a problem important. When I say that most scientists don't work on important problems, I mean it in that sense. 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.
Vika Krakovna wrote up a report about how CFAR applies the technique in some of their workshops:
The CFAR alumni workshop on the first weekend of May was focused on the Hamming question. Mathematician Richard Hamming was known to approach experts from other fields and ask “what are the important problems in your field, and why aren’t you working on them?”. The same question can be applied to personal life: “what are the important problems in your life, and what is stopping you from working on them?”.
Over the course of the weekend, the twelve of us asked this question of ourselves and each other, in many forms and guises: “if Vika isn’t making a major impact on the world in 5 years, what would have stopped her?”, “what are your greatest bottlenecks?”, “how can we actually try?”, etc. The intense focus on mental pain points was interspersed with naps and silly games to let off steam. On the last day, we did a group brainstorm, where everyone who wanted to receive feedback took a turn in the center of the circle, and everyone else speculated on what they thought were the biggest bottlenecks of the person in the center. By this time, we had mostly gotten to know each other, and even the impressions from those who knew me less well were surprisingly accurate. I am very grateful to everyone at the workshop for being so insightful and supportive of each other (and actually caring).