Why the Glove of Mathematics Fits the Hand of the Natural Sciences So Well :How Far Down the (Fibonacci) Rabbit Hole Goes

Abstract

Why does the glove of mathematics fit the hand of the natural sciences so well? Is there a good reason for the good fit? Does it have anything to do with the mystery number of physics or the Fibonacci sequence and the golden proportion? Is there a connection between this mystery (golden) number and Leibniz’s general question, why is there something (one) rather than nothing (zero)? The acclaimed mathematician G.H. Hardy (1877-1947) once observed: “In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy.” Is this also true of great physics? If so, is there a simple “preestablished harmony” or linchpin between their respective ultimate foundations? The philosopher-mathematician, Gottfried Leibniz, who coined this phrase, believed that he had found that common foundation in calculus, a methodology he independently discovered along with Isaac Newton. But what is the source of the harmonic series of the natural log that is the basis of calculus and also Bernhard Riemann’s harmonic zeta function for prime numbers? On the occasion of the three-hundredth anniversary of Leibniz’s death and the one hundredth-fiftieth anniversary of the death of Bernhard Riemann, this essay is a tribute to Leibniz’s quest and questions in view of subsequent discoveries in mathematics and physics. (In the Journal of Interdisciplinary Mathematics, Dec. 2008 and Oct. 2010, I have already sympathetically discussed in detail Riemann’s hypothesis and the zeta function in relation to primes and the zeta zeros. Both papers were republished online in 2013 by Taylor and Francis Scientific Publishers Group.)