Number: The Language of Science"Number is an open doorway into the world of math. Tobias Dantzig explains the foundations of mathematics with ease, and eloquently explores deeper philosophical questions that arise along the way. He describes the properties of all kinds of numbers  integers, primes, irrationals, transcendentals, and more. He explains the significance of zero, and shows that its invention has revolutionary consequences for arithmetic. He shows how the invention of symbols for use in algebra  a radical departure from tradition at the time  ushered in a new era of math; how arithmetic and geometry reflect each other; and how calculus uses infinity to model the continuity of space and time." "With a new afterword, notes section, and bibliography written by math professor and author Joseph Mazur, and a new foreword by mathematician Barry Mazur, the Masterpiece Science edition of Number  which was first published in 1930  is the first update of Dantzig's classic work in over fifty years. It is a story that ranges from the dawn of man to the genius of history's greatest mathematicians, vividly revealing how the pursuit of knowledge transcends the rise and fall of civilizations." Book Jacket. 
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Review: Number: The Language of Science
User Review  David  GoodreadsExcellent insights into how some of the greatest mathematicians understand irrational and imaginary numbers. Imaginary numbers, in particular, are very strange to me, and it was reassuring and illuminating to learn more about how the understanding of numbers evolved. Read full review
Review: Number: The Language of Science
User Review  Steve Gathje  GoodreadsWho could have thought a history of numbers could be so interesting. Okay, I could have thought that. And it was very interesting! Read full review
Contents
Fingerprints  1 
The Empty Column  19 
Numberlore  37 
The Last Number  59 
Symbols  79 
The Unutterable  103 
This Flowing World  125 
The Art of Becoming  145 
The Domain of Number  187 
The Anatomy of the Infinite  215 
The Two Realities  239 
Appendix A On the Recording of Numbers  261 
Appendix B Topics in Integers  277 
On Roots and Radicals  303 
On Principles and Arguments  327 
Filling the Gaps  171 
Common terms and phrases
aggregate algorithm analysis analytic geometry Archimedes argument arithmetic calculating called Cantor cardinal number century Chapter coefficients complex numbers continued fraction continuum convergent correspondence counting cubic cubic equation Dantzig Dedekind Descartes digits Diophantus divisible divisors equal equation Euclid Euler existence expressed fact Fermat Fermat prime finite formula Gauss Gematria geometrical sequence Georg Cantor Greek idea induction infinite number infinite processes infinity integers intuition irrational Leibnitz limit logic magnitudes mathe mathematical induction mathematician mathematics matter means method metic modern natural numbers notation number concept number sense number theory number words objects operations polynomial positive prime numbers principle problem proof properties proposition proved Pythagoreans quadratic quadratic equation rational domain rational numbers real numbers reality represented roots sequence solution square symbols theorem theory of numbers tion transcendental true twin prime conjecture twin primes whole numbers Wilson's theorem Zeno zero