Cutting edge technology - mechanical, civil, or computer engineering?

I have received offers from Imperial to do these subjects. Concerning the actual chance with working on cutting edge stuff (or more like solutions that haven't been thought of before) - which one - mechanical engineering, civil engineering or computing (that's what Imperial call it) has a higher chance to work on those stuff?

I kind of like mechanical and civil engineering (well, i like all of them), but my career teacher informed me that I'd have very little chance to work on cutting edge/new things/new solutions for mechanical engineering, and an even smaller chance for civil engineering. He told me to go to computing which I have a higher chance. Is this true? Any suggestions?

Thank you both. I am not sure what I would excel in - I am pretty good in both physics and maths - just consider my ability to excel in both or any one of them not a problem. I kind of like all of them - logic stuff. I am kind of thrilled to work with big structures - I am not sure if that's a thing to take note of - so maybe mechanical and civil would suit me for this; but I also want to work on some gadgets (and for this, it will be computing) or maybe just some transport - new cars, maybe? I may also note that I like space technology but I kind of also like more pure physics/maths. I like robotics, too. I want to work in a big company like Ford (for mechanical engineering), Shell or bp (for civil engineering) or Google (for computing) - and for all these 3 companies Imperial graduates are able to enter them for their respective fields, so I suppose that is not a concern.

My best area in physics is mechanics (as of motion and force), favorite is mechanics and atomic physics, and my most hated physics related discipline is optics and maybe gases.
My best/favorite area in advanced maths is matrices and mathematical induction, and I do not particularly like vectors, differentiation, integration, and I resent binomial theorem and maybe trigonometry.

I once interned in a company that specializes in internal system design (connecting all electrical stuff) - I looked at one of their mechanical engineering booklet - not particularly liking the thing or the system connections. (I liked mechanics, however, or so I believe). I'm not sure after this.

Maybe you should do a degree that's general to begin with, for the first few years, before specialising? That way you'll get to experience a multitude of different disciplines before making up your mind.

I do not exactly hate resolving - those are easy (at least for now) for physics, eg. resolving forces - those are actually fun - what I hate is the 'prove tan 3a/csc a + cot 2a = xxx' stuff that I find in advanced maths. I think now the choice could be narrowed to mechanical/computing, but then after that I don't know.