Having just completed my masters degree in math, a not so passive thirst for continuing to review, refresh and explore mathematical ideas persists. I don’t think I will ever pursue further formal training in math, so books like this one will suffice.
I don’t remember my first encounter with the number e, but since having taught high school math over the past 10 years my fascination with the number compounded.
For those not familiar with the number and who have a modest recollection of high school math, this book traces a vivid and elementary history of this transcendent number. It begins with the development of logarithms by John Napier in the early 17th century. Logarithms were regarded primarily as a powerful computing tool. The development of the field led to some surprising coincidences when matched with infinitesimals and the financial interest equation:
The book then veers into the development of calculus and the mysterious connection between e and the solution to the quadrature of the hyperbole
I was impressed that my university paper on the fundamental theorem of calculus followed the same historical paths that this author did. The continuation of the development of calculus under the Bernoulli mathematicians and their further application of the natural logarithmic base are then expounded on – the account peppered with anecdotes of family squabbles.
Further discoveries of how e was instrumental in the equation of the catenary (hanging chain problem), the logarithmic spiral, various ways of generating e with sequences and an extensive dissertation of Euler’s masterful integration of complex numbers, polar coordinates, trigonometry and e to form the basis of what is called the most beautiful equation: Maor closes with a brief connection between number theory and the number e discovered by Gauss. He found that the number of prime numbers below a chose number x, as x increases to very large numbers grows closer and closer to the value of That is, the reciprocal function of the natural logarithm (base e) of the number chosen.
Overall, I enjoyed the brevity, simplicity and relative depth offered by this book on such a remarkable number.