Computability and Decidability
http://www.maa.org/taxonomy/term/41907/0
enHow Mathematicians Know What Computers Can't Do
http://www.maa.org/programs/maa-awards/writing-awards/how-mathematicians-know-what-computers-cant-do
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><b>Award:</b> George Pólya</p>
<p><b>Year of Award:</b> 1997</p>
<p><b>Publication Information:</b> <i>The</i> <i>College Mathematics Journal</i>, Vol. 27, No. 1, (1996), pp. 37-42</p>
<p><b>Summary:</b> A discussion of mathematical proofs of non-computability.</p>
<p><a title="Read the Article" href="/sites/default/files/pdf/upload_library/22/Polya/07468342.di020770.02p0197w.pdf">Read the Article</a></p>
<p class="MsoNormal"><b>About the Author:</b> (from<i> The</i> <i>College Mathematics Journal</i>, Vol. 27, No. 1, (1996))</p></div></div></div>Thu, 17 Jul 2008 17:22:48 +0000saratt113700 at http://www.maa.orgWhat Is a Random Sequence
http://www.maa.org/programs/maa-awards/writing-awards/what-is-a-random-sequence
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="MsoNormal"><b>Year of Award</b>: 2003</p>
<p class="MsoNormal"><b>Publication Information:</b> <i>The American Mathematical Monthly</i>, vol. 109, 2002, pp. 46-63</p>
<p class="MsoNormal"><strong>Summary:</strong> This paper examines the question of whether it is possible at least to obtain a mathematically rigorous and reasonable definition of randomness.</p>
<p class="MsoNormal"><a href="/sites/default/files/pdf/upload_library/22/Ford/Volchan46-63.pdf" title="Read the Article:">Read the Article:</a></p></div></div></div>Fri, 19 Sep 2008 10:41:47 +0000saratt113730 at http://www.maa.orgLarge Numbers and Unprovable Theorems
http://www.maa.org/programs/maa-awards/writing-awards/large-numbers-and-unprovable-theorems
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="MsoNormal"><b>Year of Award</b>: 1984</p>
<p class="MsoNormal"><strong>Award:</strong> Lester R. Ford</p>
<p class="MsoNormal"><b>Publication Information:</b> <i>The American Mathematical Monthly</i>, vol. 90, 1983, pp. 669-675</p>
<p class="MsoNormal"><strong>Summary:</strong> This article looks at some fast-growing recursively-defined sequences, and examines the sense in which these can be beyond the scope of Peano Arithmetic. A connection to Paris and Harrington's combinatorial statement that is "true but unprovable in PA" is also discussed.</p></div></div></div>Mon, 22 Sep 2008 11:38:09 +0000saratt113783 at http://www.maa.orgAlan Turing in America
http://www.maa.org/publications/periodicals/convergence/alan-turing-in-america
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Alan Turing visited the United States during 1936-38 and 1942-43. This article describes how two of Turing's greatest accomplishments, in logic and computer design, were influenced by the first of his two visits to the U.S.</p>
</div></div></div>Mon, 12 Jan 2015 19:40:18 +0000drkclark606725 at http://www.maa.orgAlan Turing in America – Introduction
http://www.maa.org/publications/periodicals/convergence/alan-turing-in-america-introduction
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="rteindent1"><img alt="" src="/sites/default/files/images/upload_library/46/Zitarelli_Turing/Turing.jpeg" style="width: 283px; height: 326px;" /></p>
<p><strong>Figure 1</strong>. Alan Turing (1912-1954) (<em>Source:</em> <a href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Turing.html">MacTutor History of Mathematics Archive</a>)</p></div></div></div>Mon, 12 Jan 2015 20:06:50 +0000drkclark606728 at http://www.maa.orgAlan Turing in America – Logic
http://www.maa.org/publications/periodicals/convergence/alan-turing-in-america-logic
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>It does not seem to be well-known that <strong>Alan Mathison Turing</strong> (1912-1954) spent two academic years at Princeton University, from the summer of 1936 to the summer of 1938. Before then Turing had entered Cambridge University in 1931 and while there in the spring of 1935 took a course given by the topologist M.H.A.</p></div></div></div>Mon, 12 Jan 2015 20:13:25 +0000drkclark606753 at http://www.maa.orgAlan Turing in America – Computers
http://www.maa.org/publications/periodicals/convergence/alan-turing-in-america-computers
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="rteindent1"><img alt="" src="/sites/default/files/images/upload_library/46/Zitarelli_Turing/Turing_2.jpeg" style="width: 251px; height: 326px;" /></p>
<p><strong>Figure 4.</strong> Alan Turing on a 2000 "millennium" stamp commemorating his 1937 theory of digital computing. Turing was based at Princeton University throughout 1937. (Source: <a href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Turing.html">MacTutor History of Mathematics Archive</a>)</p></div></div></div>Mon, 12 Jan 2015 20:19:07 +0000drkclark606756 at http://www.maa.orgAlan Turing in America – Cryptography
http://www.maa.org/publications/periodicals/convergence/alan-turing-in-america-cryptography
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>The play <em>Breaking the Code</em> and the movie <em>The Imitation Game</em> popularized Alan Turing’s decisive role in deciphering codes produced by the German encrypting/decrypting machines. In fact, his interest in cryptography may have been sparked in Princeton when he set out to build the binary-multiplier machine. In any event, Turing spent the war years at Bletchley Park, a country mansion housing Britain’s leading cryptanalysts. He was assigned to work with naval communications and, using information supplied by Polish mathematicians, was intimately in</p></div></div></div>Mon, 12 Jan 2015 20:25:03 +0000drkclark606757 at http://www.maa.orgAlan Turing in America – 1942–1943
http://www.maa.org/publications/periodicals/convergence/alan-turing-in-america-1942-1943
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Alan Turing returned to the U.S. during WWII as a liaison between the two communities of cryptanalysts for about four months, from November 1942 to March 1943. He arrived in New York City on November 12, 1942, before heading to the headquarters of the U.S. Secret Service (now the CIA) in Washington, D.C. By that time, officers in the U.S.</p></div></div></div>Mon, 12 Jan 2015 20:29:40 +0000drkclark606758 at http://www.maa.orgAlan Turing in America – Conclusion
http://www.maa.org/publications/periodicals/convergence/alan-turing-in-america-conclusion
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>At the end of the war Alan Turing resumed work on computers, this time for the National Laboratory in London. By March 1946 he completed a report proposing the design and implementation of an Automated Computing Engine (ACE) but it was regarded as impractical and hence not approved. He was way ahead of his time!</p></div></div></div>Mon, 12 Jan 2015 20:34:47 +0000drkclark606763 at http://www.maa.orgAlan Turing in America – References and About the Author
http://www.maa.org/publications/periodicals/convergence/alan-turing-in-america-references-and-about-the-author
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h3>References</h3>
<p><strong>[1</strong>] Booker, Andrew R., Turing and the Riemann Hypothesis, <em>Notices Amer. Math. Soc</em>. <strong>53</strong> (2006), 1208-1211.</p>
<p>[<strong>2</strong>] Church, Alonzo, An unsolvable problem of elementary number theory, <em>Amer. J. Math</em>. <strong>58</strong> (1936), 345-363.</p>
<p>[<strong>3</strong>] Copeland, B. Jack (ed.), <em>The Essential Turing</em>, New York: Oxford Univ. Press, 2004.</p></div></div></div>Mon, 12 Jan 2015 20:42:05 +0000drkclark606764 at http://www.maa.org