How to Choose a Subproblem
A researcher at the Alignment Research Center (ARC) diagnoses the biggest weakness they see in junior researchers: problem-solving strategy. Olympiad medalists and straight-A MIT grads who have never touched a problem that took more than ten hours flounder when handed a 400-hour research problem, because nobody can write down a 400-step plan. The skill to learn is decomposition — peeling a 20-hour subproblem off a 400-hour problem, then 1-hour problems off that, in a fractal structure.
Three natural moves generate a subproblem:
- Ask a simpler question — "start small": take the simplest case you don't already understand (means before cumulants, tree-level before loop amplitudes, polynomial-time before O(N²)).
- Ask about a simpler system — toy problems and limits. The goal is "the very simplest system which has the thing you actually care about."
- Ask what the f is even going on — fact-finding (read the papers; learn the asymptotics), plus its key variant fact-processing*: reshape information so your brain can use it, above all by putting it in a picture.
A good subproblem pays off in three currencies: scientific information (especially actionable information that changes your strategy), human capital (getting better at the problems you want to solve), and strategic information (learning early whether an approach is doomed). The author pushes back on Jacob Steinhardt's "sort tasks by expected failure probability per unit time" — the underlying assumption that one failed subtask kills the whole approach and all intermediate work is worthless is, in their words, "a quitter attitude." Steinhardt's model fits ARC's unusually all-or-nothing payoff structure better than most research.
Red flags for a bad subproblem: too vague (you can't tell if you're making progress), too hard, too easy, too useless. The best gauge of difficulty is how complete your plan of attack is — number of plans, completeness of the best one, length of each. And when it's time to quit, turn to "the ultimate destroyer of hope: other people" — tell someone what you've tried and get their frank read, because the cost of giving up too late vastly exceeds giving up too early.