There are very few disciplines which mathematics has not penetrated. As a pupil finds such gem in the calculus problem of theory of rumors, he wonders if such field has application in vaudevillian arts such as tarot reading or theory of juggling. As one digs further one may finds terms as oracle, Napier's bone, Polya urn model, Witch of Agnesi, Faddeev-Popov ghost and Soul theorem which of course has nothing to do with occult in general. Although the field has been applied to understanding phenomenon which at first seemed improbable to understand gambling or betting on race horses, one is equally vexed to find there is no mathematics of vexillology. One fondly remembers the scene in A Beautiful Mind where a young John Nash was studying flight of pigeons for game theory.
Since a mathematician is prone to see patterns between seemingly disconnected fields it brings me to question what further areas can be bridged by cross-pollination?
Some fuel for thought of fields where the subject can be applied:
Mathematics of Vexillology and Heraldry
How can a formal theory be constructed that will aid to generate random, new geometrical patterns (designs) from the constraint of 63 representing symbols?
Mathematics of Choreography
Can one apply braid theory to choreograph puppetry, fencing, kali or dancing patterns from software?
Mathematics of Locksmithing
Although theory of locksmithing exist, can one apply algebraic topology to generalize the concept of locks using knot theory?
Mathematics of Smuggling or "Hustling"
In youtube one can find videos of the show Hustle which conceives elaborate means of schemes and hustle. How can the process of transporting a concealed object from an agent to agent around obstacles be modeled or formalized using graph theory?
"Theory of Plots and Sub-Plots"
Aristotle's Three Act structure is still used in screenwriting. However, can one create templates for story? Do patterns exist between story plots or heist? Can it be modeled mathematically? or even plots based on data-mining of musical scores.
In pursuit of Loebner prize now bots are eavesdropping on twitters; computers can even detect sarcasm. Similarly is it possible to create a program generating witty, one-liner advertising slogans from data-mining from twitters, proverbs, foreign expressions, existing ad slogans, etcetera?
Mathematics of Culinary Theory & Recipes
Can swarm intelligence be used to model NFL or NHL offense patterns?
Of course, a general question would be to ask: Can creativity be automated? But, one can, break down the notion of creativity to further sub-divisions.
What fields would you like to see applications of mathematics?
I sincerely believe this endeavor will encourage non-mathematicians chancing upon this site shed their inputs for a collaboration in a marriage of disparate fields.