I am revisiting essays I've read to assure I've rated them. Yours is one that states views clearly and vividly. I too see math as a tool of the mind and a construction in our sandbox, something that can and does change to meet changing needs. Utilizing the connections of mind, math, and physics, I cite quantum biology, DNA and LHC as examples.
I find that I did not rate yours, so I will rectify. I hope you get a chance to look at mine, as I believe we have similar ideas: http://fqxi.org/community/forum/topic/2345.