From qed-owner Wed Aug 11 08:11:25 1993 Received: by antares.mcs.anl.gov id AA27154 (5.65c/IDA-1.4.4 for qed-outgoing); Wed, 11 Aug 1993 08:05:45 -0500 Received: from cli.com by antares.mcs.anl.gov with SMTP id AA27147 (5.65c/IDA-1.4.4 for ); Wed, 11 Aug 1993 08:05:42 -0500 Received: by CLI.COM (4.1/1); Wed, 11 Aug 93 07:59:45 CDT Date: Wed, 11 Aug 93 08:00:47 CDT From: Robert S. Boyer Message-Id: <9308111300.AA02955@dilbert.CLI.COM> Received: by dilbert.CLI.COM (4.1/CLI-1.2) id AA02955; Wed, 11 Aug 93 08:00:47 CDT To: qed@mcs.anl.gov Subject: Rigor in contemporary mathematics Reply-To: boyer@CLI.COM Sender: qed-owner There's an interesting article on proof in the Aug. 93 Scientific American, p. 26, by John Horgan. The article primarily comments an article by Jaffe and Quinn in the July issue of the Bulletin of the American Mathematical Society. The article by Jaffe and Quinn concerns the growing influence of superstring theory on mathematics, raises questions about rigor in proof in some recent mathematics, and recommends that conjectural work should be clearly distinguished from rigorous proof. Not a distinction that I, in my naivete, would have thought any contemporary mathematicians would have doubted. One interesting note in the article concerning dubious mathematics in this century: History has also shown the dangers of too speculative a style. Early in this century, Jaffe and Quinn recall, the so-called Italian school of algebraic geometry "collapsed after a decade of brilliant speculation" when it becaume apparent that its fundamental assumptions had never been properly proved. Later mathematicians, unsure of the field's foundations, avoided it. I mention this article to the qed mailing list mainly because of the following very anti-qed remark. Horgan quotes William Thurston of Berkeley as saying "The idea that mathematics reduces to a set of formal proofs is itself a shaky idea. In practice, mathematicians prove theorems in a social context. It think that mathematics that is highly formalized is more likely to be wrong" than mathematics that is intuitive. Bob