User sunil nanda - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T15:49:21Z http://mathoverflow.net/feeds/user/6566 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/27126/interpreting-the-famous-five-equation Interpreting the Famous Five equation Sunil Nanda 2010-06-05T02:54:38Z 2010-06-29T09:12:37Z <p>$$e^{\pi i} + 1 = 0$$</p> <p>I have been searching for a convincing interpretation of this. I understand how it comes about but what is it that it is telling us? </p> <p>Best that I can figure out is that it just emphasizes that the various definitions mathematicians have provided for non-intuitive operations (complex exponentiation, concept of radians etc.) have been particularly inspired. Is that all that is behind the slickness of the Famous Five equation?</p> <p>Any pointers?</p> http://mathoverflow.net/questions/28788/nontrivial-theorems-with-trivial-proofs/28795#28795 Answer by Sunil Nanda for nontrivial theorems with trivial proofs Sunil Nanda 2010-06-20T02:16:09Z 2010-06-20T02:16:09Z <p>Euclid's proof for the infinitude of prime numbers seems to satisfy your criteria for a trivial proof for a non-trivial theorem.</p> <p>Theorem. There are more primes than found in any finite list of primes. Proof. Call the primes in our finite list p1, p2, ..., pr. Let P be any common multiple of these primes plus one (for example, P = p1p2...pr+1). Now P is either prime or it is not. If it is prime, then P is a prime that was not in our list. If P is not prime, then it is divisible by some prime, call it p. Notice p can not be any of p1, p2, ..., pr, because all of them leave a remainder of 1 when dividing P. So this prime p is some prime that was not in our original list. Either way, the original list was incomplete. </p> http://mathoverflow.net/questions/27126/interpreting-the-famous-five-equation/27127#27127 Comment by Sunil Nanda Sunil Nanda 2010-06-06T04:15:20Z 2010-06-06T04:15:20Z A couple of quotes on this equation from people who seem to have given it serious thought. Benjamin Pierce &quot;Gentlemen, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it must be the truth.&quot; Lukoff &amp; Nunez &quot;The expression makes sense if, but only if, we understand that mathematics consists of the metaphorical extension of familiar notions into unfamiliar areas.&quot;