"The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful." J.H.Poincare (1854-1912)
I've always enjoyed math as far back as I can remember. I was good in math in school. I remember other students wanting my help ... wanting my homework! I also remember in 8th grade wanting to take Algebra 1 and my first year of a foreign language. I requested to take both but I was told that I could not ... I was allowed to take the foreign language but not the algebra. (I remember that incident as gender bias.)
Even though I enjoyed math as a student, I didn't see the beauty of math until much later. As I began to attend math conferences as a teacher, I heard people talk about patterns, connections, references in math that to the best of my knowledge I wasn't taught in school. It was in learning about the patterns and connections that I determined to share the beauty of math with my students.
One of my favorite exercises is exploring the patterns in Pascal's Triangle. With elementary students we explore even and odd numbers - coloring them in - discovering the pattern of Sierpinski triangles. In middle school we look at the patterns of polygonal numbers - square numbers, triangular numbers - and look for others in Pascal's Triangle. In high school, the connection between the binomial theorem and Pascal's Triangle are noted. At various levels we explore the connection between Fibonacci's Sequence and the Triangle ... with the challenge to discover other hidden beauty!
A favorite author I use as a resource to learn more about the beauty of mathematics is Theoni Pappas. She has written numerous books, some of which I own, and I find her books accessible at all levels of learning. One book I like to keep near my desk is her compendium of mathematical quotations. I know that you can find hundreds online in the blink of an eye ... but there is something special about having a small volume of pertinent quotes on your desk!
I love to share quotes about the beauty of math with students because for so many students, math is painful and sometimes while learning the language and processes of math they miss out on the beauty!
"The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics. " G. H. Hardy (1877 - 1947)