We’ll start with Richard Hamming’s original question: what are the most important problems in your field?
(At this point, you should grab pencil and paper, or open a text file, or whatever. Set a timer for at least two minutes - or five to ten if you want to do a longer version of this exercise - and write down the most important problems in your field. The rest of the questions will be variations on this first one, all intended to come at it from different directions; I recommend setting the timer for each of them.)
Imagine that your field achieved perfection - the ultimate theory, perfect understanding, building The Thing.
What has been achieved in the idealized version of the field, which has not yet been achieved today? What are the main barriers between here and there?
Often, in hindsight, a field turns out to have been bottlenecked on the development of some new measurement method, ranging from physical devices like the thermometer to abstract ideas like Shannon’s entropy and information channel capacity.
In what places does it look like your field is bottlenecked on the ability to usefully measure something? What are the main barriers to usefully measuring those things?
The difficult thing, in most pre-paradigmatic and confused problems at the beginning of some Science, is not coming up with the right complicated long sentence in a language you already know. It's breaking out of the language in which every hypothesis you can write is false. [...] The warning sign that you need to 'jump-out-of-the-system' is the feeling [of] frustration, flailing around in the dark, trying desperate wild ideas and getting unhelpful results one after another. When you feel like that, you're probably thinking in the wrong language, or missing something fundamental, or trying to do something that is in fact impossible. Or impossible using the tools you have. - Mad Investor Chaos
What are the places where your field is flailing around in the dark, trying desperate ideas and getting unhelpful results one after another? What are the places where it feels like the problem is formulated in the wrong language, and a shift to another frame might be required to ask the right question or state the right hypothesis?
Sometimes, we have a few different models, each of which works really well in different places. Maybe it feels like there should be some model which unifies them all, which could neatly account for all these phenomena at once - like the unification of electricity, magnetism and optics in the 19th century.
Are there different models in your field which feel like they point to a not-yet-known unified model?
One of the main ways we notice (usually implicit) false assumptions in our models is when they come into conflict with some other results, patterns or constraints. This may look like multiple models which cannot all be true simultaneously, or it may look like one model which looks like it cannot be true at all yet nonetheless keeps matching reality quite well. This is a hint to reexamine the assumptions under which the models are supposedly incompatible/impossible, and especially look for any hidden assumptions in that impossibility argument.
Are there places in your field where a few models look incompatible, or one model looks impossible, yet nonetheless the models match reality quite well?
Giant Search Space
The space of possible physical laws or theorems or principles is exponentially vast. Sometimes, the hard part is to figure out what the relevant factors are at all. For instance, to figure out how to reproducibly culture a certain type of cell, a biologist might need to provide a few specific signal molecules, a physical medium with the right elasticity or density, a particular temperature range, and/or some other factors which nobody even thought to test yet.
Are there places in your field where nobody even knows what key factors must be controlled for some important outcome to robustly occur?
Finding The True Name
Sometimes, most people in the field have an intuition that some concept is important, but it’s not clear how to formulate the concept in a way that makes it robustly and generalizably useful. “Causality” was a good example of this, prior to Judea Pearl & co. Once we can pin down the right formulation of the idea, we can see arguments/theorems which follow the idea, and apply them in the wild. But before we have the right formulation, we have to make do with ad-hoc proxies, “leaky abstractions” which don’t quite consistently generalize in the ways we intuitively want/expect.
Are there places in your field where some concept seems very central to understanding, but nobody knows its True Name yet?
Sometimes social problems in a field prevent the most important problems from being addressed - e.g. bad incentives, key ideas reaching too few people, people with complementary skillsets not running into each other, different groups using different language and tools, etc.
At the social level, what are the barriers to solving the main problems in the previous two questions? Why aren’t they already solved? Why isn’t progress being made, or made faster?
There’s a condition called pica, where someone has a nutrient deficiency (e.g. too little iron), and they feel strong cravings for some food which does not contain that nutrient (e.g. ice). The brain just doesn’t always manage to crave things which will actually address the real problem; for some reason things like ice will “look like” they address the problem, to the relevant part of the brain.
Are there places where your field as a whole, or you personally, pursue things which won’t really help with the main problems (but might kind of “look like” they address the problems)?
Other Peoples’ Answers
Pick someone you know, or a few people, who are smart and have good judgment. What would their answers to these questions be?
Hamming’s original question was not just “What are the most important problems in your field?”. He had two follow-up questions:
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?"
To further quote Hamming: if you do not work on important problems, it's unlikely you'll do important work.