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When somebody presents the paper, the attendees ask questions about the paper. But what if they raise a legitimate objection when they ask about our work and we know that they are right? Should we accept that or should we defend ourselves?
I ask this, because recently I attended a conference, and in one presentation I saw an important mistake on one of the presentations' algorithms. But he denied my reasons, and both of us knew that my reasons were legitimate.
Should we accept that
If somebody points out a flaw in your work, be thankful. They are giving you free advice. Don't try to be right at all costs. Of course it's awkward when people point out major flaws in your work when there is an audience, but it's part of the game.
If you believe you are right, defend your point using objective arguments. If you know the critique is founded, accept it and try to make the best of it.
I've been on both sides of the podium for this sort of situation, and there are a number of issues that make it not straight-forward to deal with. Most importantly:
If you are the speaker, then you need to be open to the fact that you are wrong: don't get defensive about your work. At the end of the day, it's not about you: the world is what the world is, and no amount of defending your position will change the facts. If you agree with the questioner about the flaw, then you need to admit it. This has most frequently happened to me when I am giving a class lecture and a student notices a potential mistake on a slide: rather than look at it as a problem, I thank the student and turn sanity checking the equation or algorithm into part of the lesson, where we exercise other knowledge and intuition to check the material. That's generally less possible in a conference talk, of course.
If you disagree or aren't sure that you agree with the questioner, though, don't get into a fight. If you can show they are wrong simply, do so simply and gently, with the assumption that it is a misunderstanding (per first bullet above). If it's complicated or you aren't sure, just say so and offer to talk with them about it more outside of the talk.
Conversely, if you are the questioner, you don't need to make the other person admit defeat. Even if you are right and the other person is confident enough that they would be willing to admit it, they may not be in a position to do so because they've only had 30 seconds to consider it and aren't certain enough whether they agree with your critique. And if the speaker is not self-confident, they may be too afraid of losing face to admit an error directly. That doesn't matter: if you raise an issue publicly, such that the rest of the audience is not blindly accepting a dubious element of the work, that is enough.
So a third person could nail the problem of your algorithm just from your presentation, without looking at the code for hours!? You'd better not deny it completely, because there'd be others who thought the same, but were not really sure. You would look really dumb to all of them if you plainly denied it or brushed it away.
"We will look into it." and "We should discuss this over buffet." could be two possible answers, a good answer would combine the two.
