Is Beauty Truth and Truth Beauty? How Keats’s famous line applies to math and science

From Scientific American:

WHY BEAUTY IS TRUTH: A HISTORY OF SYMMETRY by Ian Stewart.Tiger The title of Ian Stewart’s book (he has written more than 60 others) is, of course, taken from the enigmatic last two lines of John Keats’s “Ode on a Grecian Urn”: “Beauty is truth, truth beauty,”–that is all Ye know on earth, and all ye need to know. But what on earth did Keats mean? Stewart’s first 10 chapters, written in his usual easygoing style, constitute a veritable history of mathematics, with an emphasis on the concept of symmetry. When you perform an operation on a mathematical object, such that after the operation it looks the same, you have uncovered a symmetry.

Stewart concludes his book with two maxims. The first: “In physics, beauty does not automatically ensure truth, but it helps.” The second: “In mathematics beauty must be true–because anything false is ugly.” I agree with the first statement, but not the second. We have seen how lovely proofs by Kempe and Dudeney were flawed. Moreover, there are simply stated theorems for which ugly proofs may be the only ones possible.

Because symmetry is the glue and tape that binds the pages of Stewart’s admirable history, a stanza from Lewis Carroll’s immortal nonsense ballad The Hunting of the Snark could serve as an epigraph for the book:

You boil it in sawdust: you salt it in glue:
You condense it with locusts and tape:
Still keeping one principal object in view–
To preserve its symmetrical shape.

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