A supplementary question: would "mathematics" refer to the use of the constants that scientists recognize as being invented by man (pi, or Euler's number), or natural constants ([theoretical] E=mc^2)? Or would it refer to the current acceptance of numbers as being of human invention, not being "real" at all?
There are other natural constants, less defined than Einstein's, but which cry out for further understanding; eg.:
absolute zero: -273.2 degrees celcius
expansion of gas as heated by one (celcius) degree: 1/273.2
one sidereal month (orbit of moon to same position in relation to the background sky): 27.32 days
Moon acceleration around the Earth: 273cm/sec^2
Human conception to birth: 273 days
Female oestral cycle: sidereal month
Please for give the profanity of trampling on the hallowed ground of the various scholastic branches in one breath (this did not exhaust the correlations), but lest's look at the current state of the Academia. A magnanimous scientific spirit would apear the only option in the current state of affairs.
A recent trend (initiated by the Chemist-turned interscholastic, "Peter Plichta") approaches a unification of the two mathematical categories, based on a view of the universe as "harmonious;" changes in process in space occurring at points correlating to prime numbers (disharmonious points), beginning with the various powers of electron shells, and expanding into space ad infinitum.
In brief, we can assume that both the natural and man-made mathematical contstants, as well as the proposed new mathematics (and all sciences, for that matter) converge, at the equation 1=1. In the larger processes, only by leaping to infinity can we hope affirm a claim of the self-evidence of mathematics (N.B. granted, individually we may leap to infinity at some point).
Would a new variety of mathematics necessarily cancel the old one? "Classical" mathematics as yet remains beyond our understanding, and yet it is harmonious in it's relation to real-world physics.
A postulation: we will only ever be able to observe things that are material, and countable, therefore, mathematic ["old"].
To which one may say, "merely to the limits of observation" -which is why there are various physical "theories." But one should not say "mathematical theory," unless semantics itself is theoretical, which begs the question of any purpose for theories -it is a semantic item, after all.
On a comletely un-scientific note, consider the enjoyment one has of a harmonious Vivaldi concerto, or some Bach (I'll put Tchaikovsky up there in the celestial realms) and the differential but non-exclusive operation of sound waves, according to current mathematical theory (arithmentic!) Is this out the window?
