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I graduated with a first class honors in dual degrees (bachelor of electrical engineering and mathematics) from Australia and would like to study for a phd in USA.

One of my dreams is to work on a specific open problem in control theory for my phd. I got a WAM (weighted average mark) of 95 (out of 100) for my dual degree.

Is it unrealistic to state in my statement of purpose that I like to work on a specific open problem in control theory? and would it have any negative effect on my admission?

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    In math departments, if you put in your statement of purpose that you are interested in working on a specific open problem, it might help you. But if that problem is the Riemann hypothesis or P ≠ NP, you may have killed any chance you had of getting in. I don't know what the control theory equivalent of these problems are, but you should figure this out before writing your statement. – Peter Shor May 21 '16 at 15:10
  • @PeterShor: Thanks for your comment. You said that "if that problem is the Riemann hypothesis or P ≠ NP, you may have killed any chance you had of getting in". Can I ask why? Is it because they are too hard and it would take someone more than 20 years to solve them? – user104690 May 22 '16 at 1:10
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    Countless excellent mathematicians have been working very hard on proving the Riemann hypothesis over the last 150 years. Thinking you are going to waltz into graduate school and solve it for your PhD thesis reveals—something—naivety? insanity? egotism? – Peter Shor May 22 '16 at 13:07
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It is a GREAT idea to list some specific problem. I got a national scholarship and one reason was I wrote about a specific problem I wanted to work on (even with a couple citations to literature).

A little real meat on the bone content helps differentiate from hordes of people who just say how great they are.

I would maybe just give yourself a little flexibility to say that you will look at other topics of interest when accepted into school and choosing a lab group.

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    Definitely give yourself some flexibility in graduate school applications (probably more than "a little"). If you're applying to a EE department, and from your statement it looks like you are only interested in working on problem X, if nobody on the faculty is interested in problem X, you have just made it much harder for them to accept you. For national scholarships, on the other hand, you don't need as much flexibility. – Peter Shor Jan 6 at 22:07
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    You should have at least one dude working on something in the region of that problem or not have it on your list of schools to apply to. Write that you are interested in that one problem and then leave an opening so you can look at other faculty (don't name the 1-3 who are in your immediate problem interest, they'll recognize it well enough). – guest Jan 6 at 23:35

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