Twelve Favorite Problems

intermediate3 min readeducation · science · psychology · creativity · business

A heuristic for maintaining a constant set of important unsolved problems, allowing the mind to make unexpected connections and synthesize ideas over time, as exemplified by Richard Feynman and Stephen King.

THE IDEA

Twelve Favorite Problems

Have you ever noticed how little children are constantly asking why?

Warren Berger, author of A More Beautiful Question, claims that children ask an average of forty thousand different questions between the ages of two and five. That’s more than thirty-six novel questions a day, every day, for three years! How many questions have you asked so far today?

Familiarity can make it easy to stop asking questions, even when much remains unexplained.

Richard Feynman was a philomath: someone who loves to learn. His habit was to retain interesting unsolved problems and return to them as he encountered new ideas. A question could remain useful long before he knew how to answer it.

During a talk at MIT, mathematician Gian-Carlo Rota mentioned that Richard Feynman liked to say: “My approach to problem-solving is to carry around a dozen interesting problems, and a dozen interesting solutions to unrelated problems, and eventually, I’ll be able to make connections. You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state.”

According to Feynman, “Every time you hear a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, ‘How did he do it? He must be a genius!’”

Look for connections. Just because you don’t know the answer yet doesn’t mean the question isn’t worth asking again later, when you may know more. Many people have discovered novel and complex solutions to problems precisely because they were able to synthesize a collection of ideas that nobody had thought to link together until then.

In his much-loved book On Writing, Stephen King talks about new ideas he would have for novels, explaining, “These were all situations which occurred to me while showering, while driving, while taking my daily walk and which I eventually turned into books. It’s that sudden flash of insight when you see how everything connects.”

Keep a collection of questions and revisit it when you learn a technique, read an unfamiliar argument, or notice a useful analogy. An idea encountered elsewhere may provide a way forward.

When to use it

A scientist reading across disciplines to discover novel applications of a technique to their own research.
An entrepreneur brainstorming business models by checking each new idea against persistent market problems.
A writer developing plots by keeping a list of character dilemmas and combining them with unexpected events.
A student studying multiple subjects, looking for cross-domain principles that explain diverse phenomena.
Record partial attempts alongside each research question so that revisiting it builds on earlier work.
Share an unresolved design question with a colleague from another field and compare possible approaches.
Set aside time to revisit a household problem after learning a relevant skill or tool.
Remove resolved or obsolete questions from a learning notebook to keep the remaining problems useful.

FROM THEORY TO EVERYDAY LIFE

In practice

Richard Feynman's Dozen Problems

In Rota’s account, Feynman kept a dozen interesting unsolved problems in mind and tested new techniques against them. The habit gave him repeated opportunities to connect a new result with an older question.

Stephen King's Novel Ideas

King describes ideas for novels arriving while showering, driving, or walking. His account illustrates how a story can take shape away from the desk when previously encountered situations connect.

A scientist's dozen research questions

A physicist keeps a dozen unsolved problems in quantum mechanics in mind. While reading a paper on a different topic, she notices a mathematical technique that applies to one of her problems, leading to a breakthrough.

An entrepreneur's business challenges

An entrepreneur maintains a list of a dozen key business challenges. During a conversation with a friend about an unrelated industry, a new business model emerges that solves one of the challenges.

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A MOMENT TO REFLECT

Put it to work.

What are the dozen most important problems or questions that you want to keep in mind right now?
How can you routinely expose yourself to new ideas and test them against your favorite problems?
What recent insight or connection did you make by linking a new piece of information to an old problem?
Which problem on your list has become less important, and what would you replace it with?
How can you keep these problems in mind daily, even when not actively working on them?
How would you test whether an appealing connection actually helps solve the problem?