Tobias Dantzig (1884–1956)

In Number : the language of science, Tobias Dantzig discusses numbers: real numbers, rational and irrational numbers, perfect numbers, primes, natural numbers, cardinal and ordinal numbers, finite numbers, imaginary numbers. Numbers, numbers, numbers. But there is much more. Dantzig discusses alphabet and its relationship to numbers, how we sense number when we don’t count, fractions and decimals, the theory of zero, infinity, and pi. The early mathematicians and their discoveries are recounted and in a section at the end, the author lists problems of math and their solutions.

My copy of Number is a 2007 edition edited by Joseph Mazur with the uncorrected text from Dantzig’s 4th edition. In addition to rearranging the text into two parts (number theory and mathematical problems), Mazur adds a forward by his brother Barry, endnotes to explain the text (although beware that the original text is not footnoted; Mazur only numbers the page to which he refers in his endnotes), a section on further reading which is up to date as of 2007, and an excellent index. Mazur also updates Dantzig’s work of 1954 to include solutions that had not been proven earlier.

The most interesting material for me was the early history of numbers, numbering and symbolism. I was also fascinated by the sections on geometry, especially referring to the Greeks. I learned of several mathematicians and their discoveries with which I was not familiar.

This is not a book for the faint of heart as Dantzig includes complex solutions. However, those that wish to skip these sections will still benefit from the rest of the text. Counting and arithmetic are second nature to us and learning that it wasn’t always so is a fascinating journey.… (plus d'informations)