[Alamo-Girl]

Thank you so very much for all your insightful comments!

Or if not God, where did all the intricate mathematical structure come from and why does it relate so directly to reality?

Indeed, why is pi what it is and not something else?

Beyond what we know of our reality and acknowledging their role in our reality, do imaginary numbers play some intimate, direct role in some strange, undiscovered reality?

That appears to be where Hawking is headed with his No Boundary theory - within his metaphysical naturalist view of "reality."

[Phaedrus]

And "out of left field", the brightest of the bright among the mathematicians and physicists, Dirac for example, also had "feel". Those of us not afraid of the word would call it intuition.

[Doctor Stochastic]

Indeed, why is pi what it is and not something else?

Because Pi is a defined constant, not a contingent quantity.