<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; ">Chronologically between Kitcher and Fauvel & Gray, is <FONT class="Apple-style-span" face="Palatino">De Millo, Richard A., Lipton, Richard J., & Perlis, Alan J. (1986). Social processes and</FONT><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Palatino">proofs of theorems and programs. In Thomas Tymoczko (Ed.), </FONT><FONT class="Apple-style-span" face="Palatino"><I>New directions in the</I></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Palatino"><I>philosophy of mathematics </I></FONT><FONT class="Apple-style-span" face="Palatino">(pp. 267-285). Boston: Birkhauser. (The Tymoczko book is generally interesting and has a discussion of the philosophical significance of the 4-color theorem.)</FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Palatino"><BR class="khtml-block-placeholder"></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Palatino">There was also the "death of proof" controversy: <FONT class="Apple-style-span" face="Times" size="4"><SPAN class="Apple-style-span" style="font-size: 16px;">Horgan, J. (1993). </SPAN></FONT><FONT class="Apple-style-span" face="Times" size="4"><SPAN class="Apple-style-span" style="font-size: 16px;"><I>The Death of Proof.<BR></I></SPAN></FONT><FONT class="Apple-style-span" face="Times" size="4"><SPAN class="Apple-style-span" style="font-size: 16px;"> Scientific American, 269(4), 93-103</SPAN></FONT></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Palatino"><BR class="khtml-block-placeholder"></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Palatino">--Cathy</FONT></DIV><DIV><BR class="khtml-block-placeholder"></DIV><BR><DIV><DIV>On Feb 20, 2006, at 7:48 PM, Jered Wasburn-Moses wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Jennifer:</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I don't think that this is a new claim. Gila Hanna is perhaps the most</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">consistent, but by no means the only, writer making a similar claim for some</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">time. (The first sentence you quote is quite problematic, incidentally, as</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Hanna and others would argue!)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Frequently cited mathematical events include the proof (?) of the 4-color</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">theorem and the classification of finite groups.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">You also might look at something like Kitcher's The Nature of Mathematical</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Knowledge (1983), which is somewhat outdated in this regard but still</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">informative, or the slightly more recent History of Mathematics: A Reader</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(1987) by Fauvel and Gray.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Hope this helps,</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">--Jered</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">--- Jennifer Smith <<A href="mailto:jenn.smith@mail.utexas.edu">jenn.smith@mail.utexas.edu</A>> wrote:</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV> <BR><BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">A colleague sent this URL to me, and I am really curious to hear what others</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">think!</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Title: Mathematical Proofs Getting Harder to Verify</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Excerpt:</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">A mathematical proof is irrefutably true, a manifestation of pure logic. But</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">an increasing number of mathematical proofs are now impossible to verify</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">with absolute certainty, according to experts in the field.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">"I think that we're now inescapably in an age where the large statements of</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">mathematics are so complex that we may never know for sure whether they're</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">true or false," says Keith Devlin of Stanford University in California, US.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">"That puts us in the same boat as all the other scientists."</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Link to story: <A href="http://www.newscientist.com/channel/fundamentals/dn8743.html">http://www.newscientist.com/channel/fundamentals/dn8743.html</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">--</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Jennifer Christian Smith</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Assistant Professor</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Center for Science and Mathematics Education</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">The University of Texas at Austin</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Office: (512) 232-9682</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Fax: (512) 471-8460</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Home page: <A href="http://teachnet.edb.utexas.edu/~jenn_smith">http://teachnet.edb.utexas.edu/~jenn_smith</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><<A href="http://teachnet.edb.utexas.edu/%7Ejenn_smith">http://teachnet.edb.utexas.edu/%7Ejenn_smith</A>></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">AIM: drjennsmith</DIV> <BR><BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">_______________________________________________</DIV> <BR></BLOCKQUOTE><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Rume mailing list</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><A href="mailto:Rume@betterfilecabinet.com">Rume@betterfilecabinet.com</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><A href="http://betterfilecabinet.com/mailman/listinfo/rume_betterfilecabinet.com">http://betterfilecabinet.com/mailman/listinfo/rume_betterfilecabinet.com</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV> <BR></BLOCKQUOTE><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">__________________________________________________</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Do You Yahoo!?</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Tired of spam?<SPAN class="Apple-converted-space"> </SPAN>Yahoo! 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