[FabHK]

> As the mathematician V.I.Arnold famously said, "mathematics is a branch of physics where experiments are cheap".

I think that is not so much subsuming mathematics under physics as a cheeky way of avowing mathematical Platonism, where eternal mathematical truths reside in some Platonic realm of ideas and wait to be discovered (not invented or proven) by mathematicians.

[enriquto]

You can read the whole text that starts with that quote here:

https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html

As you say, it is written in a playful and cheeky manner, but it is just a rhetorical device; the meaning is certainly very deep. Even deeper and longer, but in a similar spirit, you have this text:

http://math.ucr.edu/home/baez/Polymath.pdf

It starts with a famous quote, replicating Caesar's gallic war:

All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA).