Mathematics

   1) The World of Mathematics Is Really a Beautiful World

   The world of mathematics, which you contemn, is really a beautiful world; it has nothing to do with life and death and human sordidness, but is eternal, cold and passionless. To me pure mathematics is one of the highest forms of art; it has a sublimity quite special to itself, and an immense dignity derived from the fact that its world is exempt from change and time. I am quite serious in this. . . .

athematics is the only thing we know of that is capable of perfection; in thinking about it we become Gods. (Russell [to Helen Thomas, 30 December 1901], 1992, Letter No. 98, p. 224)

   2) Why Mathematics Works

   One of the deepest problems of nature is the success of mathematics as a language for describing and discovering features of physical reality. In short, why does mathematics work? . . .

   We humans have stripped back the clouds that cloak our understanding of our cosmic beginning and our current persistence to the stage that exposes the mathematical structure of the world more clearly than it has ever been observed before. . . . Furthermore, the attention of seriously equipped thinkers, those thinkers we call scientists, is at last beginning to turn to that other great conundrum of being: consciousness. . . . If we can understand why that supreme construct of the human intellect, that archdisembodiment of intellect, mathematics, works as a description of the world, then maybe we shall have an insight into cognition. . . .

   The name deep structuralism is intended to convey the idea that the physical world has the same logical structure as mathematics. By implication, the reason why mathematics works as a description of physical reality is that they share the same logical structure.

   . . . By weak deep structuralism I shall mean that mathematics and physical reality merely share the same logical structure and mathematics is a mirror that can be held up to nature. By strong deep structuralism I shall mean that mathematics and physical reality do not merely share the same logical structure but are actually the same. In other words, according to the hypothesis of strong deep structuralism, physical reality is mathematics and mathematics is physical reality. . . . The reason why we may be conscious of the world, including the inner, introspective world of emotion and intellect, may be that our brains are material portrayals of the same deep structure. That may also be the reason why brains can generate the mathematics that we need to comprehend the world. (Atkins, 1992, pp. 99-101, 109-111)