Perhaps nature does not use the square root of negative one

I've recently finished reading "Introduction to Smooth Manifolds" by John M. Lee, which I highly recommend if you want a solid and readable introduction to some aspects of differential geometry, Lie groups and Lie algebras, and a whole lot more. (I must be honest and admit that I think I would probably learn just as much as I did the first time if I read it a second time.)

Thoughts on quantum physics: The use of complex algebra in quantum physics is puzzling because sqrt(-1) does not make sense in our "classical" "real world".  However, it may be as simple as accepting that complex algebra is just isomorphic to whatever the algebra is of the quantities that quantum physics is modelling. In other words, nature doesn't take the square root of negative one, but whatever is going on works in the same way as if it did.