Cole definitely wrote this book for people with minimal mathematical abilities. The only equation is Fermat's Last Theorem. The Universe and the Teacup explores various themes, foremost being truth.
Cole discusses various forms of truths. There are scientific truths, mathematical truths, and social truths. Mathematical truth is the most reliable because it is based on logic. However, twentieth century mathematicians have uncovered limitations of logic-based mathematics. With the development of Chaos Theory and Fuzzy Logic, mathematics have taken into account the ambiguity and uncertainty that is inherent in the world.
Besides mathematical truth, there is social truth. This form of truth is prejudiced. Drawing on the work of Kenneth Arrow, Cole provides an account of how voting results can be legally manipulated.
Cole's book also explores symmetry in nature. Particle physicists, for example, have discovered that subatomic particles are paired. However, symmetry in nature isn't universal. DNA, unlike other biological molecules, does not have right-handed and left-handed components. Instead, DNA is right-handed.
To sum, Cole's book explores the aesthetics of nature, and one role of mathematics is to enable humans to express nature's simplicity and complexity.