For instance, classical mathematicians by definition rely on Plato's theory of forms as the underlying basis of their mathematical worldview. The Platonist assumes the existence of true, immutable, and universal forms and structures that the mathematician approaches through the language of numbers and equations. For instance, the classical mathematician holds to the Platonic belief in the expansion of pi; to approach the expansion of pi from any other perspective "would require a restructuring of all of mathematical analysis," (p. 414). The paradigm would have to change; a most likely candidate for the restructured mathematical analysis would be constructivism, which relies more exclusively on the number system. The very existence of varied paradigms in mathematics points to the essentially "soft" core underlying all mathematical pursuits.

Finally, the growth of mathematics depends partly on the evolution of technology as well as the evolution of thinking. Paper and pencil has largely given way...
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