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I'm an undergraduate working on a small project with an esteemed scientist, whom I met through a connection. I'm communicating via email due to distance. The problem is that I'm having a lot of troubles with this project, and the last time I asked him a question he just told me to re-read the information he sent me.

I want to tell him that it doesn't make sense (I think he made an error), but to do so without appearing arrogant or ignorant. He's intimidating and it always seems like he's two seconds away from declaring me incompetent. Yet, I am very interested in his field and this project could yield a publication.

I don't know what to do; should I just keep asking questions (if so, how do I word them in a way that shows that I'm not just being lazy), or find a way to drop the project? I don't want to close doors on future collaborations when I'm more knowledgeable.

Thank you.

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If you think your advisor made an error, then I would suggest you figure out how to prove he made an error. This is the first step to showing someone they've made an error without being ignorant or arrogant (the rest follows from general customs about politeness, but you absolutely must do this first bit. He supposes, presumably in good faith, that he proved something to you; the "burden of proof" that he's wrong now lies in your hands). Besides, this is a good exercise. Lots of things don't seem like they make sense until you yourself figure out how to make them make sense to you. This can be a lot of work. This act of "hacking" someone else's grand idea until it makes sense to me is how I spend most of my time. Thankfully this often leads to totally new ideas and directions that the first guy didn't see (or thought too trivial or obviously wrong to mention, yes that happens too...)

The problem is that, in very many fields, undergraduates are actually extremely frustrating to work with. They don't yet speak the language, or have the baseline knowledge that all of your colleagues share. But nonetheless, this person is not the ideal advisor if he lacks the patience to put up with a lot of questions -- this is absolutely normal behavior for an undergraduate advisee, totally to be expected and many advisors find the interactions quite rewarding!

On the other hand though, you have some hard questions to ask yourself. Basically, you say that you want to ask questions without sounding lazy, but you must be honest with yourself about whether or not you are in fact asking lazy questions. The research process (again, at least in fields I'm familiar with) is most emphatically not "do exactly what some famous guy told you to do." It generally involves painfully slogging through material that no one really understands and proving everything you think you know to yourself repeatedly, and then to others, and then occasionally having it pointed out that you made a really silly assumption, or that some obscure paper already solved everything you had set out for. Again, the point is to create new knowledge, and so you have to know your tools inside and out. In fact, if your advisor is explaining anything at all clearly and to your satisfaction, what he is explaining is, by definition, old knowledge.

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I want to tell him that it doesn't make sense (I think he made an error),

I would suggest you to write an e-mail to him to explain the error you found.

Do re-read the information he sent you earlier before you write the e-mail. Verify the error is indeed an error. Then write the e-mail in concise manner. Explain the error in details, step by step. Don't just say there is an error. Use evidence, theory to support your claim.

Of course, etiquette is important. However, this has nothing to do with arrogance or ignorance. It has everything to do with finding the truth. Every scientist I have met would like to know any error found before the research project is finished, the earlier the better.

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