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I am a math student in the US preparing for an hour long defense of my thesis. I am assuming that the dissertation committee has already read my dissertation by the time of my defense.

  • Any advice for preparing and giving the dissertation defense talk?
  • What balance between presenting subtle parts of the proofs and a clear big picture of the results obtained should I aim for?
  • Would it be more interesting for the committee to hear me explaining more technical parts of the proofs rather then the statements of the main theorems obtained?
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    What did your advisor suggest? (You did ask your advisor, didn't you?)
    – JeffE
    Commented Jun 22, 2012 at 21:39

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I don't think there is a meaningful answer to this question that is helpful across all US math departments and advisors. There is too much variation in what is expected. You need to find out what your committee expects.

That said, if I had to answer without knowing your department or committee, I would recommend trying to focus on the big picture but making sure that you spend most of your time explaining your contribution to that big picture. That's certainly what you'll want to do for job talks, which you're presumably also giving around now.

If the committee is concerned about your understanding of the technical parts of the proofs, they can ask you in the closed exam following the public talk.

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Two general suggestions which can overrule anything else I'm going to say: Ask your advisor about the talk! Practice your presentation with your advisor, if that's alright with them.

In general, you should not give details of proofs unless pressed; even then, you should be careful. Proving real theorems in talks (even thesis defenses) is hard, time consuming, and generally of minimal benefit to the audience. You should instead try to give the general picture of what you've done.

Some other good resources for communicating math are:

http://www.ams.org/notices/200709/tx070901136p.pdf

http://www.ams.org/profession/leaders/workshops/gcoll.pdf

Neither are specifically about the thesis defense, but are general resources for math talks. I've found them both helpful at various points.

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