{"id":28,"date":"2009-02-27T15:37:55","date_gmt":"2009-02-27T20:37:55","guid":{"rendered":"http:\/\/mathgradblog.williams.edu\/?p=28"},"modified":"2009-02-27T15:37:55","modified_gmt":"2009-02-27T20:37:55","slug":"stick-to-the-content","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/mathgradblog\/2009\/02\/27\/stick-to-the-content\/","title":{"rendered":"Stick to the Content"},"content":{"rendered":"

By Daniel Erman<\/a><\/p>\n

There is a wealth of information on the internet about how to give a\u00a0good Mathematics talk, including:<\/p>\n

(*) \u00a0 Gian-Carlo Rota’s essay “Ten lessons I wish I had been taught”<\/a><\/p>\n

(*) \u00a0 John Baez’s “Advice for the young scientist”<\/a><\/p>\n

(*) \u00a0 Terence Tao’s “Talks are not the same as papers”<\/a><\/p>\n

In this post, I’d like to consider an aspect of lecturing which is not\u00a0emphasized in the above sources, but which I think is extremely\u00a0important. \u00a0Lecturing necessarily involves choosing to emphasize some\u00a0aspects of the material over others. A common pitfall I’ve seen among\u00a0speakers\u2014especially student speakers\u2014is to apologize during the\u00a0talk for such choices, or to make self-deprecating jokes. \u00a0This is\u00a0nearly always a bad idea, as it distracts from the point of your talk. <\/p>\n

Let’s take an example. \u00a0Imagine you are giving an expository talk on a\u00a0topic which involves a theorem with a complicated proof, and you don’t\u00a0understand the proof very well. \u00a0However, you have a clear view of why\u00a0this theorem is important, and you know how to apply the theorem. \u00a0So\u00a0you decide that, in your talk, you will avoid the proof of the theorem\u00a0and focus instead on an application which illustrates the big picture.\u00a0You prepare your talk along these lines.<\/p>\n

As the date for the talk approaches, you start getting nervous about\u00a0the fact that you don’t understand some of the details of the proof.\u00a0A common reaction to such nervousness is, when skipping the proof, to\u00a0apologize for this choice; e.g. “Now I’m going to skip the proof,\u00a0since I don’t understand it.” \u00a0Offering up this personal detail\u00a0doesn’t help the audience understand your talk any better, and it\u00a0generally makes the speaker look uncomfortable. \u00a0After presenting the\u00a0statement of theorem, it would be better to state: \u00a0“We will focus on\u00a0applications of the theorem rather than the proof.”<\/p>\n

This is not to say that you should try to fool the audience into\u00a0thinking you know more than you do. \u00a0However, you should only include\u00a0such details when relevant. \u00a0For instance, if an audience member asks,\u00a0“Could you tell us about the proof?”, then this is the time to say,\u00a0“Honestly, I didn’t understand the proof well enough to give a\u00a0sketch.” \u00a0However, preempting such questions by discussing your own\u00a0struggles tends to distract from the message of your lecture.<\/p>\n

Your lecture should focus on the material you have\u00a0chosen to present. \u00a0Though you may feel the desire to apologize\u00a0for\/joke about some aspect you are omitting, such apologies\/jokes are\u00a0usually distracting.<\/p>\n

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By Daniel Erman There is a wealth of information on the internet about how to give a\u00a0good Mathematics talk, including: (*) \u00a0 Gian-Carlo Rota’s essay “Ten lessons I wish I had been taught” (*) \u00a0 John Baez’s “Advice for the … Continue reading →<\/span><\/a><\/p>\n

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