Number Theory and Its History

Pros: 1. The book could teach basic number theory to a wide range of readers, from mathematically inclined high-school students to much more advanced lovers of mathematics. 2. It is enlivened by nice historical allusions. 3.The author shows and shares his fascination with the subject in the writing. 4. On a less lofty side, the font is large enough to avoid eye strain. Cons: 1. First published 59 years ago, the book has to be dated. For example, many beautiful applications of number theory had been unknown at the time of writing. 2. Not all exercises require creativity, many of them are routine drills. Bottom line: If number theory is not your fortress, the book could strike a balance between enjoyable reading and learning.

Ore's book is an excellent introduction to the fascinating topic of number theory. He takes his time explaining the history of numbers and goes into Euclid's algorithm so smoothly you hardly realize what you've learned. He discusses prime numbers and I was particularly delighted to see diophantine equations explained with lots of examples and an easy to follow method. The book is filled with interesting concepts, lots of examples, and good problems to do on your own.At the end, for example, Ore talks of how number theory relates to geometry and I wish there were more of that in it. I took this book on a very long trip, worked through many of the problems and simply found it a wonderful companion. If you get it, enjoy. One caution: if you already know some number theory you may find this book too simplistic. Still, it's worth having.

A noted conjecture of the author's on the harmonic mean of the divisors is tucked unobtrusively in this pleasant reader: "Every harmonic number is even." See problem B2 in Richard K. Guy's Unsolved Problem's in Number Theory. A good book (but not a great book). Very basic. For the more advanced historical approach, Andre Weil's Number Theory: An approach through history" is to be recommended. Or even Guy's book mentioned above.

This book goes into detail on number theory, but it is often hard to follow with the history mingled with the theory. More advanced material is referenced without proofs. Two readers will especially like this book: those who want an introduction to number theory and those who want a good introduction to the history of number theory.