Book Review - The Mathematical Universe

Some books never grow old. This is so true of William Dunham's The Mathematical Universe. Dunham's book is a vintage tour through the history of mathematics highlighting some of the most interesting personalities and problems that have shaped the mathematical landscape across the ages. Dunham begins the journey by taking the reader on a brief, but fascinating tour of number theory including remarkable properties and tales of Mersenne numbers and culminating with the classic proof of the infinitude of primes. He continues this very lucid exposition of the primes in Chapter P by guiding the reader through a mathematical journey leading up to the famous Prime Number Theorem, discovered and proved in the nineteenth century, which integrates Calculus into number theory to estimate the numbers of primes less than a given number N.
Chapter O presents a concise overview of the remarkable contributions of several ancient civilizations such as the Egyptians, Babylonians, Hindus, and Chinese in the development of fundamental mathematical concepts. There is a wealth of geometry spanning several chapters of the book dating back to the classical geometry of Euclid and other ancient Greek mathematicians followed by Descartes' unification of algebra and geometry through the use of coordinate systems. There are two magnificent chapters devoted to the topics of spherical surfaces and the Isoperimetric Problem.
Of course, this mathematical tour would not be complete without a brief glimpse of Calculus. This introductory chapter on Differential Calculus has excellent follow-up chapters on the contributions of Leibniz and Newton in the evolution of Calculus. The table of contents below gives an indication of the scope and breadth of the topics discussed in this book. The book is written in a manner which addresses a variety of topics intended for a wide range of readers from high school students to college professors. It is certainly "an Oldie, but a Goodie" !!!
Contents:
Arithmetic
Bernoulli Trials
Circle
Differential Calculus
Euler
Fermat
Greek Geometry
Hypotenuse I
soperimetric Problem
Justification
Knighted Newton
Lost Leibniz
Mathematical Personality
Natural Logarithm
Origins
Prime Number Theorem
Quotient
Russell's Paradox
Spherical Surfaces
Trisection Utility
Venn Diagrams
Where Are the Women?
X-Y Plane
Z