[FOM] Mathematics ***is*** formalising of our thought and intuition

[Vaughan Pratt]

Regarding what mathematicians and physicists are up to, a more neutral 
and simpler situation is tac -tac-toe or noughts and crosses, vs. the 
game of forming a set of three numbers that sum to 15 by taking turns 
naming a previously unnamed nonzero decimal digit.  These are the "same" 
game via the obvious translation using the square

816
357
492

Now one could imagine visually challenged but highly numerate children 
playing the second game for so long that they'd developed reliable 
strategies not only for avoiding ever losing but even beating beginners 
quite reliably.  Yet an expert player of this game might well be 
reliably beaten at tic tac toe by a tic tac toe expert, for want of the 
isomorphism.

Yet one might argue, via the isomorphism, that the numbers expert is 
nonetheless a tic tac toe expert, her abysmal performance at the game 
notwithstanding.

To what extent does the culture gap between mathematics and physics 
contain elements of this situation?

Vaughan Pratt