tag:blogger.com,1999:blog-3722233.post9122075582706163619..comments2024-07-08T08:20:09.315-05:00Comments on Computational Complexity: Personal Reflections on Dick Lipton in honor of his 1000th blog/75th bday.Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-3722233.post-74860162869861238342022-01-26T12:44:16.140-06:002022-01-26T12:44:16.140-06:00Dudley checked all his proofs, and (when he was my...Dudley checked all his proofs, and (when he was my advisor) all my proofs. But, even Dudley sometimes made a mistake. Dudley already knew that his proof of that theorem was wrong, but didn't have a proof that the theorem (as stated) was false.David Marcushttps://www.blogger.com/profile/07084520656051241766noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-90759608223642337242022-01-26T09:55:00.159-06:002022-01-26T09:55:00.159-06:00@DM: Very relevant topic! If my recollections serv...@DM: Very relevant topic! If my recollections serve me well, Dudley made you disprove one of his published theorems via counterexample! <br />So, you witnessed the phenomenon of flawed published proofs first hand. EGnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-60883525719501411332022-01-26T00:51:13.134-06:002022-01-26T00:51:13.134-06:00@TC: Good points! Voevodsky is indeed a very inter...@TC: Good points! Voevodsky is indeed a very interesting story,<br />and figure in this space. <br />The DLP paper that Bill refers to in (2) highlights some other<br />stories that have equally surprised me. Well-written gem!<br /><br />The Easter Egg in the DLP paper is the spelling of Norbert Wiener as "Norbert Weiner"; I wonder what feedback this oversight generated. <br />Then again CACM has not surprised me, my eyes have come across<br />quite a few hiccups that the editors/reviewers should have spotted. (Who was the editor/reviewer for this piece back then ...).<br />EGnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-13778798982857848662022-01-25T14:57:57.293-06:002022-01-25T14:57:57.293-06:00There are definitely lots of errors in the math li...There are definitely lots of errors in the math literature. There are many MathOverflow questions on this topic; e.g.,<br /><br />https://mathoverflow.net/q/35468<br />https://mathoverflow.net/q/96510<br />https://mathoverflow.net/q/291158<br />https://mathoverflow.net/q/352249<br /><br />Voevodsky got interested in formal proofs in part because of wrong proofs that he himself had published. https://www.ias.edu/ideas/2014/voevodsky-origins<br /><br />In other cases, a theorem is announced as proved, but the proof has yet to appear, even after many years. In some cases, later researchers have built on those theorems, despite the lack of proofs. https://mathoverflow.net/q/357317Timothy Chowhttp://alum.mit.edu/www/tchownoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-22788215112224555022022-01-25T09:53:26.877-06:002022-01-25T09:53:26.877-06:00I confess to sometimes using a theorem without che...I confess to sometimes using a theorem without checking the proof.David Marcushttps://www.blogger.com/profile/07084520656051241766noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-58705362920053731602022-01-23T19:43:15.685-06:002022-01-23T19:43:15.685-06:00In an ideal world one would check the proofs of al...In an ideal world one would check the proofs of all theorems one uses in a proof. In the real world this could be difficult. Hence I do wonder if some big result will end up not having a correct proof. Or even incorrect! gasarchhttps://www.blogger.com/profile/03004932739846901628noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-45691616156244721912022-01-23T16:06:36.017-06:002022-01-23T16:06:36.017-06:00> A scary thought: most results in math, once p...> A scary thought: most results in math, once published,<br />> are never looked at again. So there could be errors in<br />> the math literature.<br /><br />If you don't use the result, then not much harm. If you use the result, maybe you should check the proof!David Marcushttps://www.blogger.com/profile/07084520656051241766noreply@blogger.com