Is a beautiful poem still beautiful if it is written in a language that you don't understand?
I conjecture that the inherent beauty of mathematics is overstated. The beauty of Euler’s identity is like the sublime beauty of a Himalayan peak shrouded in thick fog. A lot of the pleasure and reward stems as much from the effort to climb above the fog to view the peak in all its majesty as from any structural formal beauty. There are only so many ways formal structures can relate to each other aesthetically.
> There are only so many ways formal structures can relate to each other aesthetically.
I think that a lot of the inherent beauty of mathematics (there is also the beauty of the climb, as you very nicely described it) comes precisely from the realisation that, sensible as this claim is, it doesn't seem to be true: there seem always to be more relationships out there to discover, and their hidden and surprising natures can make them all the more beautiful once uncovered.
There is even a mathematical case to be made that there are always "more relationships out there to discover." One of the more plausible, sober interpretations of the various limitative phenomena in the foundations of mathematics discovered throughout the 20th century is that mathematics is not reducible to fintary symbol manipulation. Perhaps this is a bit loose and controversial, but the point is just that we don't necessarily need to solely lean on the observed fact that there have always been "more relationships out there to discover."
I conjecture that the inherent beauty of mathematics is overstated. The beauty of Euler’s identity is like the sublime beauty of a Himalayan peak shrouded in thick fog. A lot of the pleasure and reward stems as much from the effort to climb above the fog to view the peak in all its majesty as from any structural formal beauty. There are only so many ways formal structures can relate to each other aesthetically.
At least that's what I think today.