Is it advisable to drop out of a PhD and look for a new one? I am someone with an undergraduate degree in physics and am currently a over a year into a PhD in maths. However I am not feeling happy for several reasons:


I told my supervisor right from the beginning that my interests were
in physics (and very specific areas of physics), yet I have spent a 
year without doing any physics.
I have been studying a problem that     on the one hand seems
extremely difficult and on the other contains     no physics and
doesn't interest me, though I'm worried about souring our relationship if I tell him to his face that it doesn't interest me.
Part of what makes the problem so       difficult is that    my supervisor has
no clue how to solve the problem    and suggestions    he gives are
never useful. In my meetings my       supervisors often    says
things that are wrong and (combined with the lack of ideas on his end) it has somewhat       shaken my faith    in
him. On one occasion he got angry when I disagreed with him on something, even though I was right. I get a slight sense he resents me for this. Instead of being supervised by someone who seems knowledgeable I feel I am for all intents and purposes working on my own.
I am concerned that I have picked an area       that doesn't      interest me as much as I thought it did.


All of these things make me feel depressed and make me want to drop out and start again somewhere else, somewhere I can do research that interests me. I don't want to waste 4 years of my life simply out of a desire to "see it through." If I drop out and apply to another PhD program is the fact that you've already dropped out once damning?
[I] am currently a over a year into a PhD in maths. However...I told my supervisor right from the beginning that my interests were in physics (and very specific areas of physics), yet I have spent a year without doing any physics.


Seems like a rather obvious mismatch! Why are you in math if you want to do physics? 


  My supervisor has no clue how to solve the problem and suggestions he gives are never useful.


Another bad sign. Sometimes it's worth accepting a less-interesting area in exchange for an awesome advisor. But you don't seem to like your advisor either.


  All of these things make me...want to drop out and start again somewhere else...I don't want to waste 4 years of my life simply out of a desire to "see it through." 


Makes perfect sense. Also consider the quality of your work...once you have a PhD, people will care about your publications and letters -- slogging through a PhD you don't like is unlikely to produce nice publications or letters of recommendation.


  If I drop out and apply to another PhD program is the fact that you've already dropped out once damning?


Nope, changing departments is a reasonable reason to drop out. But, it would be nice if you could declare victory -- "I was a brilliant math student who got awesome grades and interesting results, but I realized I like physics better" sounds better than "I got my a** kicked at math and physics sounds easier." Consider what you can do over the next few months to salvage your year (publishing, securing letters of recommendation, getting good grades, etc.)