What is mathematical maturity?
An ability to …
make and use connections with other problems and other disciplines,
fill in missing details,
spot, correct and learn from mistakes,
winnow the chaff from the wheat, get to the crux, identify intent,
recognize and appreciate elegance,
read, write and critique formal proofs,
draw a line between what you know and what you don’t know,
recognize patterns, themes, currents and eddies,
apply what you know in creative ways,
remain focused, and
bring instinct and intuition to bear when needed.
To gain mathematical maturity, a student must be prepared to reflect deeply on mathematics for an extended length of time, to muse mathematics. To gain mathematical maturity, a student must develop a guiding mathematical spirit, their own mathematical muse.
mathematical maturity » inner muse of mathematics » musemathematics.
“Numbers it is. All music when you come to think. Two multiplied by two divided by half is twice one. Vibrations: chords those are. One plus two plus six is seven. Do anything you like with figures juggling. Always find out this equal to that. Symmetry under a cemetery wall. He doesn't see my mourning. Callous: all for his own gut. Musemathematics. And you think you're listening to the etherial. But suppose you said it like: Martha, seven times nine minus x is thirtyfive thousand. Fall quite flat. It's on account of the sounds it is.”
James Joyce’s Ulysses, Chapter Eleven: The Sirens
Bloom, the character speaking here, is claiming that music is nothing but mathematics, the mathematics of the Muses. He labels their mathematics “musemathematics”. By reducing music to calculations and mathematics, Bloom is not allowing himself to be overpowered by the emotions of music. Bloom laments that his friend is so intoxicated by the music that he does not even notice that Bloom is in mourning.
This famous scene from Joyce’s Ulysses is an allusion to the mythical Ulysses, as portrayed in Homer’s Odyssey. Ulysses does not allow himself to fall prey to the call of the Sirens song by having his crew strap him to a mast pole and having his crew plug their ears with wax until their ship had sailed safely past the Sirens.
For some more fun take a look at:
All music is mathematics …
All mathematics is music …