MATH.23:4.6 - Choose a next problem and begin its mathematical work

Compare the few continuations whose answers would change further work. A useful result can supply a missing lemma, a reusable combining operation, an explanation of failure, or a method that makes another class of questions approachable. Immediate engineering application is one possible use; developing a new mathematical operation can also enable later inquiry whose destination is not yet known.

Choose a first attempt that the available contributors can perform. For a broad characterization, this might be one direction of the theorem. For an extremal problem, it might be one explicit improved construction or a bound. For a limit question, it might be the estimate needed to justify one passage to the limit.

Return the conjecture, the mathematical basis that suggested it, the most revealing success or obstruction, and the next operation. An expression and a short argument can carry this result.

Use B.5.QD and C.40.CD when several questions and ways must develop together. E.10.INT helps distinguish the interest of further possible work from surprise, fame or a search score. C.36.RP supplies retention of the reconstructible method when continuing capability is at stake. Obtain further observations or checking only when their possible outcomes can change the next move enough to justify the effort.