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The real unsolved problems of mathematics

By Jason Rosenhouse

With the arrival of the new year, you can be certain that the annual extravaganza known as the Joint Mathematics Meetings cannot be far behind. This year’s conference is taking place in Baltimore, Maryland. It is perhaps more accurate to say that it is a conference of conferences, since much of the business to be transacted will take place in smaller sessions devoted to this or that branch of mathematics. In these sessions, researchers at the cutting edge of the discipline will discuss the most recent developments on the biggest open problems in the business. It will all be terribly clever and largely impenetrable. You can be certain, however, that the real open questions of mathematics will barely be addressed.

It is hardly a secret that large conferences like this are as much about socialization as they are about research. This presents some problems, since the Joint Meetings can be a minefield of social awkwardness and ambiguous etiquette.

For example, imagine that you are walking across the lobby and you notice someone you know slightly coming the other way. Should you stop and chat? Or is a nod of acknowledgement sufficient? If you do stop, what sort of greeting is appropriate? A handshake? A hug? And how do you exit the conversation once the idle chit chat runs out? Sometimes you stop and chat, and then someone friendlier with the other person arrives to interrupt. One minute you’re making small talk about your recent job histories, and the next you’re just standing there watching your conversation partner make dinner plans with someone who just appeared. Now what do you do? Usually your only course is to mutter something about being late for a talk and then slink off with whatever dignity you can muster.

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The exhibition center presents its own problems. How long can you stand in one place perusing a book before it becomes rude? Quite a while, apparently, if we are to judge from some of the stingier characters we inevitably meet. If the book is that interesting just buy it and be done with it. Come to think of it, when you are standing there looking through books, what is the maximum allowable angle to which you can separate the covers? Cracking the spine is definitely frowned upon. How many Hershey’s miniatures can you reasonably pilfer from the MAA booth? Which book should you buy to burn up your AMS points? Let me suggest that the answer to that one depends on which book will look best on your shelf, since you know full-well you are never going to read it.

Actually presenting a talk brings with it some challenges of its own. Perhaps you are giving a contributed talk, and you get the first slot after lunch. So it’s just you, the person speaking after you, and whoever drew the short straw for moderation duty. Do you acknowledge the lack of an audience? Or do you go through the motions like you’re keynoting? After giving your talk, is it acceptable simply to leave? Or are you ethically obligated to stay for the talk right after yours? What do you do if you notice an error in someone else’s talk? Should you expose it to the world during the question period, or just discuss it privately with the speaker afterward?

Perhaps we need a special session to discuss these questions. That, at least would be a session where everyone could understand what was being said. On the other hand, given the occasionally strained relationship between mathematicians and social graces, perhaps I should not be so cavalier about that.

Jason Rosenhouse is Associate Professor of Mathematics at James Madison University. He is the author of Taking Sudoku Seriously: The Math Behind the World’s Most Popular Pencil Puzzle with Laura Taalman; The Monty Hall Problem: The Remarkable Story of Math’s Most Contentious Brain Teaser; and Among The Creationists: Dispatches from the Anti-Evolutionist Front Lines. Read Jason Rosenhouse’s previous blog articles.

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Image credit: Complex formulae on a blackboard. © JordiDelgado via iStockphoto.

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