Following Evelyn’s last post\u00a0about the new Breakthrough Prize in Mathematics, I will now discuss the opposite of wild mathematical success.<\/p>\n
Depending on how excited you are about public speaking, the moments before giving a talk at a math conference may\u00a0be full of anticipation or anxiety. \u00a0So what happens when the speaker says something incorrect? At best, it’s embarrassing \u2013 like messing up in the middle of a recital in front of other musicians who know that music. What if the speaker presents an argument that is somehow fundamentally flawed? We talk a lot about how to handle students’ mistakes and how valuable they are – see Evelyn’s February blog post<\/a>. But what about\u00a0colleagues’ mistakes? How can we take it ins stride when we<\/em> make mistakes in front of peers?<\/p>\n That\u2019s one topic of the entertaining short story \u201cThe Penultimate Conjecture<\/em>\u201d by the late celebrated writer Leonard Michaels. One of a series of seven stories featuring fictional mathematician named Nachman, this story is\u00a0read by Rebecca Curtis at the New Yorker\u2019s monthly podcast<\/a>\u00a0posted on the first of this month. In just 45 minutes listeners can soak up some literature\u00a0with a mathematical flavor and a dark sense of humor. According to Alex Kasman, who maintains the site Mathematical Fiction<\/a>, this is the most mathematical of all of Michaels\u2019 stories about Nachman, who, after attending fellow mathematician Lindquist\u2019s much-anticipated presentation of the proof of the long-outstanding Penultimate Conjecture, realizes that the presenter\u2019s proof is flawed. Should he say something to Lindquist? It\u2019s not clear what he will do, and we share his uneasiness at being the messenger of bad news. Kasman files all the Nachman stories under the \u201canti-social mathematician\u201d banner, but unlike the clich\u00e9s in other stories about mathematicians, this one seems more true-to-life to me. Like the New Yorker\u2019s fiction editor who chats with Ms. Curtis at the end of the reading, I am interested to know what the Ultimate Conjecture might be, and I tend to agree with this blogger<\/a> that it is probably meant to be that of Nachman. However, one thing that isn’t discussed during the New Yorker podcast\u00a0is the remaining possibility that Lindquist\u2019s work will be fruitful in other ways besides what he aimed. My thoughts turn to the Math Overflow post concerning the Most Interesting Mistakes in Mathematics <\/a>, in which many fascinating examples of mistakes made by preeminent mathematicians led to innovations. The most recent example mentioned concerns the Perko Pair, a pair of knots once thought to be non-isomorphic (due to a theorem that was later disproven), and later shown to be isomorphic (by a lawyer named Perko).<\/p>\n Most of us lack preeminence, and for the pessimists among us, the quality of famous mathematicians\u2019 mistakes might just be a reason to save the contents of every Field\u2019s medalist\u2019s wastebasket. But for the optimists among us, it\u2019s also encouraging to think that exercising ones intellect is bound to be fruitful even if it\u2019s not in the manner intended. An interesting side note \u2013 in an effort to find a discussion about how mistakes during talks should be handled, I found pretty much nothing, which reinforces my belief that mathematicians are a very polite (or perhaps just confrontation-averse) bunch. I did, however, find a post on Math Overflow about how to correct mistakes in published work<\/a>. Of course, step one is always to email the author. I also ran into this recent nice post by Orr Shalit<\/span>\u00a0at his blog Noncommutative Analysis<\/a>, in which Shalit\u00a0discusses how he handled the discovery of a mistake in a 16-year-old paper. \u00a0What are your thoughts on mistakes in our field? On mathematical literature?<\/p>\n