most recent 30 from http://mathoverflow.net 2013-06-19T11:12:47Z http://mathoverflow.net/feeds/user/20299 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/37610/demonstrating-that-rigour-is-important/84680#84680 Imi Bokor 2012-01-01T11:17:21Z 2012-01-01T11:17:21Z

<p>In my experience, the two greatest difficulties in mathematics are:</p> <ol> <li><p>The obvious is not always true.</p></li> <li><p>The truth is not always obvious.</p></li> </ol> <p>Rigour is the essence of mathematics. A rigorous proof provides an explanation of why a particular mathematical statement is true, and, at the same time, takes care of all the "Yes, but what if"s.</p> <p>Rigour and proof provide the guarantee of correctness and reliability.</p> <p>Rigour and proof refine our mathematical insights and instincts so that the superficially "obvious" misleads us less frequently.</p> <p>When I pose the problem "1, 2, 3, x Find x." the initial response is usually a derisory laugh, of disbelief that I am serious, because "the answer is obviously 4". It is easy to demonstrate using practical examples that this statement is, as it stands, nonsense. A rigorous analysis is required.</p>