# The Mathematical Perspective

### Greeting a Problem

• Learn to welcome a problem. Give it room to roam in your head.
• Make a careful formulation of the problem. It may have arrived improperly attired.
• Identify the assumptions: the ones it brought, the ones you add.
• Decide what type of answer it has requested:
• A number - how accurate?
• A function, vector, matrix, or other mathematical object?
• An algorithm - how efficient?
• A proof - in math, arguments must be conclusive, not merely persuasive.

### Solving a Problem

• Learn to recognize common problem types. Does your problem have relatives?
• Reformulate it in a different setting. Everyone likes a change of scenery.
• Ask more questions. Make conversation.
• Get up close. Narrow your perspective or simplify the problem.
• Step back. Widen your perspective or generalize the problem.
• Divide the problem into several shorter ones.
• Experiment - don't be afraid to be wrong. Most problems are playful.
• Take a break. Most problems are patient.
• Come back. It won't solve itself.