Mention of open problems in statement of purpose 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 the 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?
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.