I'm not too savvy with math, but I'm getting back into it (and, surprisingly [or maybe not] pd is helping a great amount), and I just can't help admiring the exquisite beauty of complex formulae/functions etc.

I was wondering if anyone had tried substituting some non-musical equations into their synthesis patches and got good results?

I've been toying around with simpler concepts for the moment, but once my skills are a bit better, I think I'll try my hand at inserting something like fluid dynamics equations and seeing what happens...

Depends on how you use it, of course. The classic way is to use waveshaping, which simply means you use an oscillator as the input into a function of whatever sort. You can do this using arrays; first write the function into an array with [tabwrite~], then put an [osc~] into a [tabread4~].

If it's really non-musical, can you expect musical results?

I know that's kind of a smart-ass answer, but what I'm really saying is it's more about how you use it. Just experiment and see what happens. I personally find it near impossible to see an equation on its own as being musical. You have to listen to it.

As an example, this is the basic equation for FM:

y[n] = Re{e^(jω_c + jz*cos(ω_m)} = cos(ω_c + z*cos(ω_m))

where ω_c = 2*pi*f_c*n/sr is the angular carrier frequency, ω_m = 2*pi*f_m*n/sr is the angular modulator frequency, sr is the sample rate, and z is the modulation depth.

That looks like gibberish to me, but it sounds great.

But I would also argue that the synthesis itself is not what make it musical. It's what you do with the resulting sound. Noise itself is pretty ugly, but musicians have made some pretty good music with noise.