From owner-qed Mon Nov 21 07:48:27 1994 Received: from localhost (listserv@localhost) by antares.mcs.anl.gov (8.6.4/8.6.4) id HAA17695 for qed-out; Mon, 21 Nov 1994 07:46:44 -0600 Received: from emu.pmms.cam.ac.uk (root@emu.pmms.cam.ac.uk [131.111.24.1]) by antares.mcs.anl.gov (8.6.4/8.6.4) with SMTP id HAA17690 for ; Mon, 21 Nov 1994 07:46:39 -0600 Received: by emu.pmms.cam.ac.uk (UK-Smail 3.1.25.1/1); Mon, 21 Nov 94 13:46 GMT Message-Id: Date: Mon, 21 Nov 94 13:46 GMT From: Thomas Forster To: LYBRHED@delphi.com, qed@mcs.anl.gov Subject: Re: Errors in Mathematics Sender: owner-qed@mcs.anl.gov Precedence: bulk Lyle says: About false theorems: we still don't have any. The examples given were all correct results with incorrect or incomplete proofs. The Four Color Theorem, the Hard Lefschetz Theorem, and Dehn's Lemma all turned out to be true. Not only that, the erroneous proofs were noticed by human mathematicians, not by automated reasoning systems. I have never encountered a false theorem that was used as the foundation for other theorems, with disastrous results. And I don't think anybody else has, either. There are many imperfections in the mathematical literature, and some incomplete proofs, but I don't think there are any substantive errors that affect the integrity of mathematics. Isn't this what people call a selection effect? We don't remember false proofs of falsehoods! Thomas