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--></style></head><body lang=EN-US link=blue vlink="#954F72" style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal>No one can know if the Riemann conjecture is true until, or if ever, it is proved. It seems to be true, but we can’t know for sure. Gödel's incompleteness theorem demonstrates with certainty that there are mathematical statements that are true, but cannot be proved to be true. More precisely, for any system that can evaluate whether a mathematical statement is true or not, there will always be true statements that the system cannot prove to be true. We are “systems” so this applies to us too.</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Experimentation really is the backbone of knowledge. When our proving methods fail to give an answer, we must rely on experimentation. If a statement holds for a billion random numbers, then we can be reasonable certain that it holds for all numbers. For some claims, this is probably the best we will ever get.<span style='font-size:12.0pt;font-family:"Arial",sans-serif;background:white'><o:p></o:p></span></p><div style='mso-element:para-border-div;border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal style='border:none;padding:0in'><b>From: </b><a href="mailto:extropy-chat@lists.extropy.org">William Flynn Wallace via extropy-chat</a><br><b>Sent: </b>Wednesday, March 24, 2021 2:09 PM<br><b>To: </b><a href="mailto:extropy-chat@lists.extropy.org">ExI chat list</a><br><b>Cc: </b><a href="mailto:foozler83@gmail.com">William Flynn Wallace</a><br><b>Subject: </b>Re: [ExI] favor for a friend</p></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'>Thanks. Now - what is an odd perfect number? For that matter - never mind -looked it up. No practical applications in mind, just play, right?<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'>This part of math is not a science. You know the Riemann conjecture to be true but cannot prove it - just backwards from science. bill w<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>On Wed, Mar 24, 2021 at 12:32 PM spike jones via extropy-chat <<a href="mailto:extropy-chat@lists.extropy.org">extropy-chat@lists.extropy.org</a>> wrote:</p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> </p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> </p><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b>…</b>> <b>On Behalf Of </b>William Flynn Wallace via extropy-chat<br><b>Subject:</b> [ExI] favor for a friend</p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> </p><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'>He wanted to know the meaning of this statement:</span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'> </span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-family:"Arial",sans-serif;color:black'>Mathematics is true, but it doesn't exist.</span><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>"</span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-family:"Comic Sans MS";color:black'> </span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>bill </span><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>w</span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:10.0pt;font-family:"Arial",sans-serif'> </span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:10.0pt;font-family:"Arial",sans-serif'> </span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:10.0pt;font-family:"Arial",sans-serif'> </span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'>Bill it is a mathematician’s joke, a little self-referencing humor. Pure mathematics is all about proving theorems. There are many mathematical ideas called conjectures until they are proven. An example is the conjecture that an odd perfect number exists. Plenty of people agree that one is true, but we have no known way of finding it, nor is there a proof that it exists (or doesn’t exist.)</span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'> </span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'>I chose that example because I worked on it for a while, but found myself not smart enough by a coupla orders of magnitude. A better example is the Riemann hypothesis:</span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:28.0pt'> </span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:18.0pt;color:black;background:white'>In mathematics, the <b>Riemann hypothesis</b> is a </span><span style='font-size:20.0pt'><a href="https://en.wikipedia.org/wiki/Conjecture" target="_blank" title=Conjecture><span style='font-size:18.0pt;color:black;background:white'>conjecture</span></a></span><span style='font-size:18.0pt;color:black;background:white'> that the </span><span style='font-size:20.0pt'><a href="https://en.wikipedia.org/wiki/Riemann_zeta_function" target="_blank" title="Riemann zeta function"><span style='font-size:18.0pt;color:black;background:white'>Riemann zeta function</span></a></span><span style='font-size:18.0pt;color:black;background:white'> has its </span><span style='font-size:20.0pt'><a href="https://en.wikipedia.org/wiki/Root_of_a_function" target="_blank" title="Root of a function"><span style='font-size:18.0pt;color:black;background:white'>zeros</span></a></span><span style='font-size:18.0pt;color:black;background:white'> only at the negative even integers and </span><span style='font-size:20.0pt'><a href="https://en.wikipedia.org/wiki/Complex_number" target="_blank" title="Complex number"><span style='font-size:18.0pt;color:black;background:white'>complex numbers</span></a></span><span style='font-size:18.0pt;color:black;background:white'> with </span><span style='font-size:20.0pt'><a href="https://en.wikipedia.org/wiki/Real_part" target="_blank" title="Real part"><span style='font-size:18.0pt;color:black;background:white'>real part</span></a></span><span style='font-size:18.0pt;color:black;background:white'> </span><span class=gmail-m-4483004925243221952num><span style='font-size:16.0pt;color:black;background:white'>1</span></span><span class=gmail-m-4483004925243221952slash><span style='font-size:16.0pt;color:black;border:none windowtext 1.0pt;padding:0in;background:white'>/</span></span><span class=gmail-m-4483004925243221952den><span style='font-size:16.0pt;color:black;border:solid windowtext 1.0pt;padding:0in;background:white'>2</span></span><span style='font-size:18.0pt;color:black;background:white'>.</span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'> </span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'><a href="https://en.wikipedia.org/wiki/Riemann_hypothesis" target="_blank">https://en.wikipedia.org/wiki/Riemann_hypothesis</a></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'> </span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'>That one is true, but no one has ever been able to prove it. That a proof doesn’t exist is more remarkable than my example with odd perfect numbers because math graduate students are given instruction on the Riemann zeta function and plenty of them take a shot it. But the zeta shoots back, hard. The fusillade of return fire is awesome on that one.</span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'> </span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'>Do feel free to forward what I have written to your friend.</span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'> </span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:18.0pt;font-family:"Comic Sans MS";color:black'>spike</span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-family:"Comic Sans MS";color:black'> </span></p></div></div></div></div></blockquote></div><p class=MsoNormal style='margin-left:4.8pt'>_______________________________________________<br>extropy-chat mailing list<br><a href="mailto:extropy-chat@lists.extropy.org" target="_blank">extropy-chat@lists.extropy.org</a><br><a href="http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat" target="_blank">http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat</a></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>