O'Reilly logo

The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

VIII.1 The Art of Problem Solving

A. Gardiner

Where there are problems, there is life.

Zinoviev (1980)

In English the word “problem” has negative connotations, suggesting some unwanted and unresolved tension. Zinoviev’s reminder is therefore important: problems are the stuff of life—and of mathematics. Good problems focus the mind: they challenge and frustrate; they cultivate ambition and humility; they show up the limitations of what we know, and highlight potential sources of more powerful ideas. By contrast, the word “solving” suggests a release of tension. The juxtaposition of these two words in the expression “problem solving” may encourage the naive to think that this unwelcome tension can be massaged away by means of some “magic formula” ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required