Today's previous entry quoted a review by Edward Rothstein of Jung's The Red Book. The entry you are now reading quotes a review by Jim Holt of a notable book by Rothstein:
The Golden Book—
Cover illustration— Arithmetic and Music,
Borgia Apartments, The Vatican
Jim Holt reviewing Edward Rothstein's Emblems of Mind: The Inner Life of Music and Mathematics in The New Yorker of June 5, 1995:
Advent
"The fugues of Bach, the symphonies of Haydn, the sonatas of Mozart: these were explorations of ideal form, unprofaned by extramusical associations. Such 'absolute music,' as it came to be called, had sloughed off its motley cultural trappings. It had got in touch with its essence. Which is why, as Walter Pater famously put it, 'all art constantly aspires towards the condition of music.'
The only art that can rival music for sheer etheriality is mathematics. A century or so after the advent of absolute music, mathematics also succeeded in detaching itself from the world. The decisive event was the invention of strange, non-Euclidean geometries, which put paid to the notion that the mathematician was exclusively, or even primarily, concerned with the scientific universe. 'Pure' mathematics came to be seen by those who practiced it as a free invention of the imagination, gloriously indifferent to practical affairs– a quest for beauty as well as truth."
Related material: Hardy's Apology, Non-Euclidean Blocks, and The Story Theory of Truth.
See also Holt on music and emotion:
"Music does model… our emotional life… although
the methods by which it does so are 'puzzling.'"
Also puzzling: 2010 AMS Notices.