most recent 30 from http://mathoverflow.net 2013-05-24T00:44:38Z http://mathoverflow.net/feeds/question/11408 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/11408/looking-for-book-with-good-general-overview-of-math-and-its-various-branches Robert Houben 2010-01-11T04:57:25Z 2011-03-16T19:41:51Z

<p>Is there something in the order of a Goedel Escher Bach type book? If you've read it you know what I mean. Something compelling that you have to read a couple of times in order to start to get it, but it's so interesting you can't put it down!</p>

http://mathoverflow.net/questions/11408/looking-for-book-with-good-general-overview-of-math-and-its-various-branches/11409#11409 Qiaochu Yuan 2010-01-11T05:00:32Z 2010-01-11T05:00:32Z

<p>I'm going to answer your title question instead of your body question (which to my mind is completely different): what you're looking for in the title is <a href="http://www.amazon.com/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809" rel="nofollow">the Princeton Companion to Mathematics</a>.</p>

http://mathoverflow.net/questions/11408/looking-for-book-with-good-general-overview-of-math-and-its-various-branches/11413#11413 Steve Huntsman 2010-01-11T06:18:23Z 2010-01-11T06:18:23Z

<p><a href="http://www.amazon.com/Modern-Mathematics-Light-Fields-Medal/dp/1568810830" rel="nofollow">Modern Mathematics in the Light of the Fields Medal</a>, which is pretty darn good for all its flaws</p> <p><a href="http://books.google.com/books?id=1V4-kdN6aGkC" rel="nofollow">A Panorama of Pure Mathematics</a>, which looks good but I haven't read</p>

http://mathoverflow.net/questions/11408/looking-for-book-with-good-general-overview-of-math-and-its-various-branches/11423#11423 David Speyer 2010-01-11T12:31:29Z 2010-01-11T12:31:29Z

<p>Penrose's <em>The Road to Reality</em> covers large portions of mathematical physics. This isn't a textbook, and omits many details, but it is as meaty as <em>GEB</em>.</p>

http://mathoverflow.net/questions/11408/looking-for-book-with-good-general-overview-of-math-and-its-various-branches/11424#11424 David Speyer 2010-01-11T12:33:55Z 2010-01-11T12:33:55Z

<p>The classic answer to this is Courant and Robbins, <em>What is Mathematics?</em> A bit dated, but certainly worth looking at if you haven't yet.</p>

http://mathoverflow.net/questions/11408/looking-for-book-with-good-general-overview-of-math-and-its-various-branches/11426#11426 Marko Amnell 2010-01-11T12:45:46Z 2011-03-16T19:41:51Z

<p>Saunders MacLane, <a href="http://en.wikipedia.org/wiki/Mathematics,_Form_and_Function" rel="nofollow"><em>Mathematics: Form and Function</em>.</a> Very good overview of undergraduate mathematics, showing interconnections between different areas. As might be expected from one of the inventors of category theory, MacLane defends categories as a foundation for mathematics.</p>

http://mathoverflow.net/questions/11408/looking-for-book-with-good-general-overview-of-math-and-its-various-branches/11429#11429 Jaikrishnan 2010-01-11T13:35:47Z 2010-01-12T01:28:07Z

<p><a href="http://www.amazon.com/Mathematics-its-History-John-Stillwell/dp/0387953361/ref=sr%5F1%5F3?ie=UTF8&amp;s=books&amp;qid=1263216510&amp;sr=8-3%20%22Mathematics%20and%20it%27s%20History%22" rel="nofollow">Mathematics and its History by John Stillwell</a></p> <p>This book aims to give a unified picture of Mathematics through it's history. The good things about this book are the extremely beautiful figures, interesting exercises and emphasis on the interplay of Algebra and Geometry.</p>

http://mathoverflow.net/questions/11408/looking-for-book-with-good-general-overview-of-math-and-its-various-branches/12398#12398 AKE 2010-01-20T08:22:30Z 2010-01-20T08:22:30Z

<p><a href="http://www.amazon.co.uk/Mathematics-Its-Content-Methods-Meaning/dp/0486409163" rel="nofollow">Mathematics: Its Content, Methods and Meaning</a> is an excellent overview of the full body of mathematics. It is large (3 volumes), but comes in a paperback edition that includes all three.</p> <p>The draw is that it is edited by three well-known Russian mathematicians (Aleksandrov, Kolmogorov, Lavrentev) who wrote some of the articles and solicited the rest from many other Russian luminaries. It was developed as a compendium able to communicate both the vibrancy as well as the importance of each of the areas of the mathematics so that science ministers in Russia could better understand mathematics as mathematicians do. </p> <p>The translation into English is excellent.</p> <p>The first article, a General View of Mathematics, is highly recommended from a philosophical, historical, and phenomenological point of view.</p>