{"id":24080,"date":"2013-09-28T12:00:59","date_gmt":"2013-09-28T16:00:59","guid":{"rendered":"http:\/\/blogs.ams.org\/mathgradblog\/?p=24080"},"modified":"2013-10-12T15:54:49","modified_gmt":"2013-10-12T19:54:49","slug":"proofs-book","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/mathgradblog\/2013\/09\/28\/proofs-book\/","title":{"rendered":"Proofs from The Book"},"content":{"rendered":"

\"book_2006_ProofsFromTHEBOOK\"I recently came across an article on Stack Exchange<\/a>\u00a0that\u00a0asks readers what proofs they think other mathematicians should\u00a0know and why. There are 23 answers on the post (it is a closed\u00a0question now unfortunately) with many different proof suggestions.\u00a0This reminded me of Paul Erd\u00f6s’ common reference to The Book.<\/p>\n

Although an\u00a0atheist,\u00a0he spoke of “The
\nBook”, an imaginary book in which\u00a0God\u00a0had written down
\nthe best and most elegant proofs for mathematical
\ntheorems.\u00a0Lecturing in 1985 he said, “You don’t have to
\nbelieve in God, but you should believe in\u00a0The
\nBook<\/i>.” He himself doubted the existence of God, whom he
\ncalled the “Supreme\u00a0Fascist” (SF).\u00a0He accused the SF of
\nhiding his socks and Hungarian\u00a0passports, and of keeping the
\nmost elegant mathematical proofs to himself. When he saw a
\nparticularly\u00a0beautiful mathematical proof\u00a0he would
\nexclaim, “This one’s from\u00a0The Book<\/i>!”. This
\nlater inspired a book entitled\u00a0Proofs from THE
\nBOOK<\/i>.\u00a0[1]<\/a><\/p><\/blockquote>\n

<\/p>\n

The book entitled Proofs from THE BOOK<\/a> by Martin Aigner<\/a> and G\u00fcnter M. Ziegler<\/a>\u00a0is a draft of\u00a0the book mentioned by Erd\u00f6s. The book is sectioned into five\u00a0different categories: Number Theory, Geometry, Analysis,\u00a0Combinatorics, and Graph Theory. Each proof (or set of proofs when\u00a0multiple proofs are given for the same statement) is its own\u00a0chapter with 40 chapters total. The authors give references at the\u00a0end of each chapter, which is a neat and useful addition to the\u00a0book. What do you say? Do you believe in The Book, as Erd\u00f6s insists\u00a0you must? What are some of your favorite proofs?<\/p>\n

<\/div>","protected":false},"excerpt":{"rendered":"

I recently came across an article on Stack Exchange\u00a0that\u00a0asks readers what proofs they think other mathematicians should\u00a0know and why. There are 23 answers on the post (it is a closed\u00a0question now unfortunately) with many different proof suggestions.\u00a0This reminded me of … Continue reading →<\/span><\/a><\/p>\n

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