Are you familiar with the work that Fresco mentioned above? In case you are not, let me quote a few passages summarizing 'Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being'. Lakoff is a psycholinguist who has developed a cognitive-psychology based explanation of the origin of mathematics that in many respects in comparable to the position I have been arguing.
"In the course of our research, we ran up against a mythology that stood in the way of developing an adequate cognitive science of mathematics. It is a kind of “romance” of mathematics, a mythology that goes something like this:
.•Mathematics is abstract and disembodied—yet it is real.
•Mathematics has an objective existence, providing structure to this universe and any possible universe, independent of and transcending the existence of human beings or any beings at all.
•Human mathematics is just a part of abstract, transcendent mathematics.•Hence, mathematical proof allows us to discover transcendent truths of the universe
.•Mathematics is part of the physical universe and provides rational structure to it. There are Fibonacci series in flowers, logarithmic spirals in snails, fractals in mountain ranges, parabolas in home runs, and pin the spherical shape of stars and planets and bubbles.
•Mathematics even characterizes logic, and hence structures reason it-self—any form of reason by any possible being.
•To learn mathematics is therefore to learn the language of nature, a mode of thought that would have to be shared by any highly intelligent beings anywhere in the universe.
•Because mathematics is disembodied and reason is a form of mathematical logic, reason itself is disembodied. Hence, machines can, in principle, think.It is a beautiful romance—the stuff of movies like 2001, Contact, and Sphere.It initially attracted us to mathematics.
But the more we have applied what we know about cognitive science to understand the cognitive structure of mathematics, the more it has become clear that this romance cannot be true. Human mathematics, the only kind of mathematics that human beings know, cannot be a subspecies of an abstract, transcendent mathematics. Instead, it appears that mathematics as we know it arises from the nature of our brains and our embodied experience. As a consequence, every part of the romance appears to be false, for reasons that we will be discussing. Perhaps most surprising of all, we have discovered that a great many of the most fundamental mathematical ideas are inherently metaphorical in nature:
•The number line, where numbers are conceptualized metaphorically as points on a line.
•Boole’s algebra of classes, where the formation of classes of objects is conceptualized metaphorically in terms of algebraic operations and elements: plus, times, zero, one, and so on
.•Symbolic logic, where reasoning is conceptualized metaphorically as mathematical calculation using symbols.
•Trigonometric functions, where angles are conceptualized metaphorically as numbers.
•The complex plane, where multiplication is conceptualized metaphorically in terms of rotation."
"Metaphor is not a mere embellishment; it is the basic means by which abstract thought is made possible. One of the principal results in cognitive science is that abstract concepts are typically understood, via metaphor, in terms of more concrete concepts."
Do you agree with any of this?