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	<title>Ars Mathematica &#187; 2008 &#187; January &#187; 20</title>
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		<title>Why the Riemann Hypothesis?</title>
		<link>http://www.arsmathematica.net/archives/2008/01/20/why-the-riemann-hypothesis/</link>
		<comments>http://www.arsmathematica.net/archives/2008/01/20/why-the-riemann-hypothesis/#comments</comments>
		<pubDate>Sun, 20 Jan 2008 18:36:19 +0000</pubDate>
		<dc:creator>Walt</dc:creator>
				<category><![CDATA[Mathematics]]></category>

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		<description><![CDATA[Way back when, I had a post about explaining the Riemann hypothesis in elementary terms. I thought I&#8217;d go into some more detail. The Riemann hypothesis is regarded as one of the outstanding open problems in mathematics. Part of the &#8230; <a href="http://www.arsmathematica.net/archives/2008/01/20/why-the-riemann-hypothesis/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>Way back when, I had a <a href="http://www.arsmathematica.net/archives/2005/07/03/elementary-version-of-riemann-hypothesis/">post</a> about explaining the Riemann hypothesis in elementary terms.  I thought I&#8217;d go into some more detail.</p>
<p>The <a href="http://en.wikipedia.org/wiki/Riemann_hypothesis">Riemann hypothesis</a> is regarded as one of the outstanding open problems in mathematics.  Part of the reason is that it has a certain mystique, since Riemann conjectured it back in 1859, and it has withstood many attempts to prove it since then.  A bigger reason is that it solution (either positive or negative) is the main obstacle to answering the question &ldquo;How many primes are there?&rdquo;</p>
<p>The fact that there are infinitely many primes goes back to Euclid.  The next most logical question is to ask how many primes there are less than a given number.  Thanks to the <a href="http://en.wikipedia.org/wiki/Prime_number_theorem">Prime Number Theorem</a>, we know that there are approximately <i>n / ln n</i> primes less than a given number.  But this is only an approximation.  How good or bad of an approximation is it?  We don&#8217;t know.  <i>That</i> is the question the Riemann hypothesis is trying to answer.</p>
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		<title>Comments</title>
		<link>http://www.arsmathematica.net/archives/2008/01/20/comments/</link>
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		<pubDate>Sun, 20 Jan 2008 18:31:15 +0000</pubDate>
		<dc:creator>Walt</dc:creator>
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		<description><![CDATA[We&#8217;ve just had our first really serious flame war. While I respond to flame wars the way most people do &#8212; taking sides and flinging insults, I decided to resist my natural inclinations. As an experiment, I have hidden the &#8230; <a href="http://www.arsmathematica.net/archives/2008/01/20/comments/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>We&#8217;ve just had our first really serious flame war.  While I respond to flame wars the way most people do &mdash; taking sides and flinging insults, I decided to resist my natural inclinations.  As an experiment, I have hidden the inflammatory comments to let things cool off.</p>
<p>And remember.  People are not stupid.  It&#8217;s only math that&#8217;s stupid.  Okay, that doesn&#8217;t sound quite right&#8230;</p>
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