Fibonacci Sunflowers, Mathematical Objects & Cubic Electrons

Abstract

We examine the uncanny involvement and influence of mathematical truths on the minutest and largest properties and phenomena of the physical world and the remarkable effectiveness of mathematics in describing and predicting natural phenomena. Indeed, mathematics - a vast and ingenious conceptual structure without empirical content - is an indispensable and powerful theoretical instrument for the scientific understanding of virtually every aspect of the physical world. Selected examples show the remarkable associations among specific mathematical objects and macroscopic and quantum matter and phenomena.