G.H. Hardy, one of the greatest mathematicians of the 20th century wrote this:
A mathematician, like a painter or a poet, is a maker of patterns.
The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.
- H. Hardy, A Mathematician’s Apology, 1940
Hardy’s words apply not only to the math produced by professional mathematicians, they apply to the math produced by students as well. For students are makers of patterns and like painters and poets, their patterns must be beautiful; they must fit together harmoniously. The problems or projects we ask our students to do, must therefore, enable them to make beautiful patterns. For our job as teachers is to not only engage them in this process, but to encourage them to make more beautiful patterns.
This is what we mean by, learning math as a creative experience.