phukraut

Are we depriving ourselves? Who knows? I would guess though there is sufficient influence from academic subcultures to make up for it: mathematicians talking amongst themselves, scientists requesting math models, etc.

Here is something I missed before. Mathematicians, particularly amateurs or number theorists, will look at things produced by culture for inspiration of research. Examples include describing the mathematical implications of Chess moves, or mathematical patterns in music or visual arts (see Escher and group theory).

Here we have the fruits of culture influencing mathematical discourse just for the hell of it---it's a curiosity or it's for Beauty's sake, or whatever the reason. Sometimes these cultural explorations can lead to deeper results.

You also implied something worth talking about. What is considered mathematics? When one sees a paper in a journal, how can one tell it is a mathematics paper? If something counts as mathematics only when it's discussing proofs, or logical progressions, then there is exactly zero cultural influence, yeah.

On the other hand, if we view mathematics like a jelly donut, where gooey center is the logical discourse, and the outer pastry includes everything else---like speculation and conjecturing, exploration of real world examples, and empirical analysis to guide proofs (very common in number theory)---then culture may indeed have definite influence, such as we both just talked about.

Here's a question for you: who is missing out more from the lack of interaction between culture and mathematics---the general public, or mathematicians? Is that even a fair question?