> I would be surprised to meet a mathematician who enjoyed learning theorems/proofs more than finding theorems and proving things on their own.
One must crawl before one can walk. Reading the work of others is quite enjoyable. And not everyone yearns to reinvent the wheel -- for many problems, understanding the prior work gives one more than enough satisfaction.
> That's why I said the interesting part is the process of manipulating expressions rather than the expressions themselves.
A finished equation can stand alongside the finest art, and garner the same kind of appreciation. People still read Einstein's relativity equations, and Maxwell's electromagnetic equations, with a deepening appreciation of their beauty, quite apart from the degree to which they describe reality.
Also, there is the interesting task of applying equations to real-world problems. I don't need to rewrite the gravitational and tidal equations to discover new things while applying them.
> Based on your gravity/tides example, I think you would take the same stance (Do you?).
Not really. It would be like asking someone whether they prefer reading, or writing. Obviously the full experience of literacy involves both.
Here's a comparison -- a common problem for student writers, usually pointed out by someone with more experience, is that they haven't read enough to be able to write effectively. There's a parallel in mathematics -- those who take the trouble to read enough mathematics, by so doing learn how to express themselves more efficiently.
For me, the two equations I posted earlier, one that describes the gravitational force, and the other the tidal force, the mathematically interesting thing is the relationship between them, not so much the equations themselves -- the fact that a simple derivative operation produces the second equation (in physical terms it's because the tidal force is felt by any two adjacent masses placed arbitrarily close together).
For physical equations, working with them means either imagining their consequences, or modeling them, usually with a computer. In that case, you don't manipulate the equations, you use them to model reality. So having an equation that's known to represent some aspect of reality is just the beginning of a research program that models the consequences of the equation and compares the model to reality.
Here's an example. Observations of Jupiter's moon Io revealed the possibility of a large, static tidal force on its mass. You may be aware that a static force doesn't require any energy expenditure (imagine a book lying on a table). Then someone pointed out that Io has an elliptical orbit, which means Io is constantly moving toward, and away from, Jupiter. This would have the effect of changing the tidal force, and a changing tidal force would perpetually change the moon's shape -- and changing the moon's shape would require energy. This would generate a lot of heat. Shortly thereafter, volcanoes were observed on Io, a moon too small to have the kinds of volcanoes we have here, and the explanation was the elliptical orbit and tidal force.
That's mathematics.