Friday, October 30, 2015

The Beauty of Mathematics and the Mathematics of Beauty

The purpose of Online Renaissance, for which this blog is just a sort of bulletin board, is to foster a renewed Humanism. This I hope to see achieved through a broader understanding of mathematics and art as twin windows onto a higher reality. 

Mathematics concerns itself with the compulsory features of the imagination (in Michael Shapiro's elegant formulation.). For example, if I tell you to picture "green," you are unlikely to see what I have in mind. But if I tell you to visualize a circle, we both see a shape identical in every important particular. Mathematics deals with the agreeing features of mind, found in all people. And these are, I assert an intellectual patent of nobility.
Then let us consider mathematical proofs. If you are not familiar with any of these, then picture a basic geometric form, like an equilateral triangle or a square — for these essential shapes are so composed of law and proportion they may fairly be called proofs incarnate. 

Mathematical proofs, whatever they say in particular, all of them demonstrate that truth, order, fullness and perfection, validity and meaning, are intrinsic to the human mind, and to the world.

Mathematics, thus understood, are a proper pursuit for a poet; Greek philosophy and computer coding are both essential attainments for a renaissance woman or man.