Table of Contents

Context
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Learned in this study
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Analogy
Auxiliary elements: An element that we introduce in the hope that it will further the solution
Bright idea
Can you check the result?
Can you derive the result differently?
Can you use the result?
Carrying out
Condition
Contradictory
Corollary
Could you derive something useful from the data?
Could you restate the problem?
Decomposition and recombining
Definition
Determination, hope, success
Diagnosis
Did you use all the data?
Do you know a related problem?
Draw a figure
Examine your guess
Figures
Generalization
Have you seen it before?
Here is a problem to yours and solved before
Heuristic
Heuristic reasoning
If you cannot solve the proposed problem
Induction and mathematical induction
Inventor’s paradox
Is it possible to satisfy the condition?
Lemma
Look at the unknown
Modern heuristic
Notation
Pedantry and mastery
Practical problems
Problems to find, problems to prove
Progress and achievement
Puzzles
Reductio ad absurdum and indirect proof
Redundant
Routine problem
Rule of discovery
Rule of style
Rule of teaching
Separate the various parts of the condition
Setting up equations
Signs of progress
Specialization
Subconscious work
Symmetry
Terms, old and new
Test by dimension
Variation of the problem
What is the unknown?
Working backwards