Taking the solveit.answer.ai course which is somewhat based on the book “How to Solve It” by George Polya, written in 1945.

My favorite quote from “How to Solve It”: “Teaching to solve problems is education of the will.”

“How to Solve It” might be read as a specification for an AI agent called ‘teacher’, who is trying to solve problems by “educating the will” of the students, guiding them to the “mental operations” that keep them engaged, encouraged, and making progress.

The words in italics below refer to entries in Part 3, the Dictionary of Heuristic.

The main prompt for the teacher AI Agent is in Modern Heuristic.

The teacher knows what phase the student currently is in the ‘How to Solve It’ framework (Part 1), and the student’s progress (Diagnosis, Progress and Achievement, Signs of Progress).

The “mental operations” that students use to solve the problem are triggered by questions and suggestions from the teacher – some of the main mental ops are Variation of the problem, Analogy, Generalization, Specialization.

If you squint your eyes, the math is like coding. Notation and Setting Up Equations are like variable naming and functions. Writing and testing the two lines of code at a time are described in Carrying out the plan: “Carrying out your plan of the solution check each step. Can you see clearly that the step is correct?”

I like the parts about two ways of approaching problem – starting from nothing, or starting as if the problem is solved. Then ‘plausibly coding’ (guessing and checking) working either forward or backwards (Pappus, Heuristic Reasoning, Working Backwards).