The aesthetics of mathematics
Mathematicians often appreciate the beauty and elegance of particular theorems, proofs, and definitions, attaching importance not only to the truth but also to the aesthetic merit of their work.
Yet the tendency to judge mathematical work according to aesthetic standards raises a number of difficult questions. What is mathematical beauty? Can abstract mathematical objects be literally beautiful? Is it reasonable to classify some mathematics as art?
Examples like the image above of the newton fractal of a 7th order complex polynomial, rendered from z = -16/9 + i to z = 16/9 – I, produces beautiful fractal patterns.
A number of authors in aesthetics and the philosophy of mathematics have tried to shed light on mathematical beauty by highlighting its relation to factors such as order, harmony, unity, symmetry, and simplicity.
Image credit: Colored Newton Fractal 2 by Recursiterative. CC-BY-SA-3.0 via Wikimedia Commons.
Was there a Scientific Revolution?
Was there a “Scientific Revolution”? The answer depends on who’s writing about it. The French philosopher Alexandre Koyré surmised that it began with Copernicus in the 1500s and ended with Newton over a period of 150 years, whereas A. Rupert Hall (a British historian) included other sciences beyond cosmology and motion, determining the revolution was double that length. H. Floris Cohen, a historian of science, focuses on “transformations in methods,” which confines the Scientific Revolution to the seventeenth century.
Whichever the definition, the scientists, philosophers, and mathematicians of the 1600s were key to the growth of scientific knowledge in Europe. In particular, the experiments and writings of René Descartes, Galileo Galilei, and Isaac Newton changed the course of Western thought forever.
Image: Galileo pushes away the Bible before the Inquisition in 1633, CC BY 4.0 via Wikimedia Commons.
Happy Birthday, Isaac Newton
“The truth is my notions about things of this kind are so indigested that I am not well satisfied my self in them, […] especially in natural Philosophy where there is no end of fancying.”
Merry Christmas, as well as a happy birthday to Isaac Newton – born on this day in 1642! Here, he writes a wonderfully exemplified note to Robert Boyle on “æthereal substances” and “physical qualities.”
Image Credit: ‘Portrait of Isaac Newton’ by Sir Godfrey Kneller (1689), Public Domain via Wikimedia Commons.