**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,

think abstractly,

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,

approximate appropriately,

teach yourself,

generalize,

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*.

So,

**mathematical
maturity ****»****
inner muse of mathematics ****»****
musemathematics**.

**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**

http://www.gutenberg.org/etext/4300

http://en.wikipedia.org/wiki/Ulysses_(novel)

Interpretation (?)

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 …**

http://plus.maths.org/issue35/features/rosenthal/index.html

http://en.wikipedia.org/wiki/Mathematics_of_musical_scales

http://en.wikipedia.org/wiki/Music_and_mathematics

**All
mathematics is music**
**…**

http://us.metamath.org/mpegif/mmmusic.html