astro picture for the day

Credit & Copyright: T. A. Rector (U. Alaska), T. Abbott, NOAO, AURA, NSF

One of my non-Hubble favorites; not sure If I've posted this before; can't believe I hadn't!

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I was rereading some Jacob Bronowski articles from "The Visionary Eye" a week or two ago.  He mentioned something that came up when talking to someone just an hour or so ago; so, I've decided it's important enough to mention.

People are forever trying to size down mathematical science by telling those who do mathematics about great art and artists.  But, what never gets mentioned is the mathematicians know, appreciate lots of great art.  But, the artists never know the great mathematics.  Sure, they've heard of maybe even gotten through a first semester of calculus; but, do they know about pythagorean triples?  The Greek initial efforts at a pellian equation to approximate the square root of two?  How about Archimedes logical proof and calculation of Pi?  Have they even heard of Euclid's "Elements"?  Appolonius's "conics"? The three delian problems; Pappas's theorem about projective geometry? Galois theory; do they know that groups and fields are more associated with algebra and Galois theory while rings have to do with number theory? How about David Hilbert's recasting of Euclidean geometry in terms of of his number fields, and the relation of projective geometry to algebras? Lie theory and it's relation to the classification of finite simple groups? Do they know how the effort to prove the Poincare conjecture led to much of the topology(and fields medals) of the 20th century?  How about abel's theorem and it's relations to algebraic geometry, and then Alain connes non-commutative geometry?  Have they heard of Cardano?  Ferrari?(cardano's student and colleague), How many mathematicians have the artists ever heard of?  Fermat by now!  How about Vieta?  Leonardo Euler, Lagrange, Gauss, Dirichlet, Riemann, Poincare, Hilbert, Emmy Noether, Emil Artin, Serre, William Thurston, Atiya, Alain Connes and plenty more!  No, they know nothing about mathematics! Once again, the non-mathematicians have everything backwards!