For most problems found in mathematics textbooks, mathematical reasoning is quite useful. But how often do people find textbook problems in real life? At work or in daily life, factors other than strict reasoning are often more important. Sometimes intuition and instinct provide better guides; sometimes computer simulations are more convenient or more reliable; sometimes rules of thumb or back-of-the-envelope estimates are all that is needed.

Philosophically, mathematics is not a part of science. Mathematics studies patterns, science studies nature

For most problems found in mathematics textbooks, mathematical reasoning is quite useful. But how often do people find textbook problems in real life? At work or in daily life, factors other than strict reasoning are often more important. Sometimes intuition and instinct provide better guides; sometimes computer simulations are more convenient or more reliable; sometimes rules of thumb or back-of-the-envelope estimates are all that is needed.

Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and mathematics that a more apt definition became fully evident: mathematics is the science of patterns.

Mathematics is the science of patterns.

What humans do with the language of mathematics is to describe patterns... To grow mathematically children must be exposed to a rich variety of patterns appropriate to their own lives through which they can see variety, regularity, and interconnections.

What humans do with the language of mathematics is to describe patterns.