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Biscuits of Number Theory

Arthur T. Benjamin and Ezra Brown, editors
Mathematical Association of America
Publication Date: 
Number of Pages: 
Dolciani Mathematical Expositions 34
[Reviewed by
Charles Ashbacher
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The term biscuit can be used to refer to everything from a tiny little morsel to a meal consisting of bread stuffed with meat and veggies. That description can also be used to describe the material in this book. Some of the articles are short, literally one-sentence proofs of results in number theory or diagrams of a proof without words. Others are much more substantial, requiring in-depth thought and reflection.

As so many have commented, number theory is the one area of mathematics where the problems are often easy to state. People possessing only a rudimentary knowledge of mathematics can understand many of the major ones. Yet many of the problems take centuries to be resolved and some of those continuing unknowns are mentioned in this book.

The titles of the seven parts are:

  • Arithmetic
  • Primes
  • Irrationality and Continued Fractions
  • Sums of Squares and Polygonal Numbers
  • Fibonacci Numbers
  • Number-theoretic Functions
  • Elliptic Curves, Cubes and Fermat’s Last Theorem

Each part includes several articles. A few of the articles come with “second helpings,” in which the authors update the results and/or point to further reading.

Number theory seems to be the one area of mathematics in which all mathematicians are interested. And for good reason: it is a delight to work in. If you have any doubts, read this book and intellectually salivate over some of the best mathematical articles ever written.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.

The table of contents is not available.