Mathematical Ways of Thinking

In the textbook The Heart of Mathematics, its authors Edward Burger and Michael Starbird offer their favorite top ten mathematical ways of thinking:

1. Just do it.
2. Make mistakes and fail but never give up.
3. Keep an open mind.
4. Explore the consequences of new ideas.
5. Seek the essential.
6. Understand the issue.
7. Understand simple things deeply.
8. Break a difficult problem into easier ones.
9. Examine issues from several points of view.
10. Look for patterns and similarities.