title: Elements of Mathematics: From Euclid to G&ouml;del
author:  John Stillwell 
description: <b>&quot;One of Forbes.coms 10 Best Astronomy, Physics and Mathematics Books of 2017, chosen by GrrlScientist&quot;</b><br /><br />"[Stillwell] writes clearly and engagingly. . . . [<i>Elements of Mathematics</i>] can appeal to various constituencies at different levels of mathematical sophistication."<b>---Mark Hunacek, <i>MAA Reviews</i></b><br /><br />"A great exploration of elementary mathematics, its limitations, how infinity complicates things, and how various branches of mathematics fit together."<b>---Antonio Cangiano, <i>Math-Blog</i></b><br /><br />"Stillwell is . . . One of the better current mathematical authors: he writes clearly and engagingly, and makes more of an effort than most to provide historical detail and a sense of how various mathematical ideas tie in with one another. . . . The features we have learned to expect from Stillwell (including, but not limited to, excellent writing) are present in [<i>Elements of Mathematics</i>] as well." (<i>MAA Reviews</i>)<br /><br />"An accessible read. . . . Stillwell breaks down the basics, providing both historical and practical perspectives from arithmetic to infinity."<b>---Gemma Tarlach, <i>Discover</i></b><br /><br />"[<i>Elements of Mathematics</i>] is quite a tour de force, organized by areas of mathematics--arithmetic, computation, algebra, geometry, calculus, and so on--and in each area Stillwell manages to distill down the big ideas and the connections with other areas. He is a master expositor, and the text manages to be engaging and accessible without watering down the mathematics. I definitely learned new things from the book!"<b>---Brent Yorgey, <i>Math Less Traveled</i></b><br /><br />"From a lifetime of teaching, Stillwell has distilled some nice examples from the entire gamut of elementary mathematics." (<i>Mathematical Reviews Clippings</i>)<br /><br />"[A] wonderful book. . . . I think that [<i>Elements of Mathematics</i>] will itself become a modern classic and a reference work for anyone trying to learn basic topics in any of the major fields of mathematics."<b>---Victor Katz, <i>Bulletin of the American Mathematical Society</i></b><br /><br />"<i>Elements of Mathematics</i>is a fine . . . overview of the field of mathematics. . . . The writing is clear, succinct, organized, and the diagrams [and] illustrations excellent. . . . While some of the discussion is introductory or elementary, it always leads to deeper, more challenging ideas. . . . [T]his will make a fine basic addition to most mathematicians' bookshelves." (<i>Math Tango</i>)<br /><br />"Stillwell uses his broad and impressive command of mathematics to transport a reader through each topic and to a higher level of understanding and questioning." (<i>Convergence</i>)
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  ![](images/00021.jpg)
  
  Elements of Mathematics
  
  
  Elements of
  
  Mathematics
  
  FROM EUCLID
  
  TO GÖDEL
  
  John Stillwell
  
  P R I N C E T O N
  
  U N I V E R S I T Y
  
  P R E S S
  
  P R I N C E T O N
  
  A N D
  
  O X F O R D
  
  Copyright c
  
  2016 by John Stillwell
  
  Requests for permission to reproduce material from this work
  
  should be sent to Permissions, Princeton University Press
  
  Published by Princeton University Press, 41 William Street,
  
  Princeton, New Jersey 08540
  
  In the United Kingdom: Princeton University Press, 6 Oxford Street,
  
  Woodstock, Oxfordshire OX20 1TR
  
  [press.princeton.edu](http://press.princeton.edu)
  
  Jacket art: The Ideal City  by Fra Carnevale (c. 1420–1484).
  
  Donated by the Walters Art Museum, Baltimore, MD
  
  Excerpt from “Mr. Harrington’s Washing” (taken from Ashenden)
  
  by W. Somerset Maugham reproduced by permission
  
  of United Agents LLP on behalf of The Royal Literary Fund
  
  Excerpt from The Adventures of Don Quixote  by Miguel de Cervantes Saavedra,
  translated by J. 