Mathematics, in the common lay view, is a static discipline based on formulas taught in the school subjects of arithmetic, geometry, algebra, and calculus.
But outside public view, mathematics continues to grow at a rapid rate, spreading into new fields and spawning new applications.
The guide to this growth is not calculation and formulas but an open-ended search for pattern.
Mathematics has traditionally been described as the science of number and shape.
Number and shape—arithmetic and geometry—are but two of many media in which mathematicians work.