<story><title>Terry Tao on how to compute non-converging infinite sums (2010)</title><url>http://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/</url></story><parent_chain></parent_chain><comment><author>drakaal</author><text>String theory likes this math because it assumes that there is a curve to the sum, it will get smaller eventually. This helps make the &amp;quot;vibration&amp;quot; part of sting theory work.&lt;p&gt;But just because you can prove something with math doesn&amp;#x27;t mean it is &amp;quot;real&amp;quot;.&lt;p&gt;We all know that if you add any number of positive integers you get a positive integer. This is very &amp;quot;provable&amp;quot;.&lt;p&gt;The two are in contradiction. The sum of all natural numbers can&amp;#x27;t be 1&amp;#x2F;12th if the sum of any two positive integers is another positive integer.</text></comment>
<story><title>Terry Tao on how to compute non-converging infinite sums (2010)</title><url>http://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/</url></story><parent_chain></parent_chain><comment><author>mpyne</author><text>Wonderful article, though I got slightly distraught once he got through all that hard math only to state essentially that it would get more interesting below the fold.&lt;p&gt;I used to understand some of that (Taylor and Maclaurin series). I think the &amp;quot;Integral Test&amp;quot; had been my high-water mark, it&amp;#x27;s amazing to see how much further the mathematical concepts can be carried.</text></comment>