>some problems in mathematics will remain beyond the limits of quantum computing<p>I don't think it's surprising that quantum computers, by themselves, will not be able to solve mathematical problems. Problem solving is not a feature of hardware per se, it is done by humans. Perhaps one day by AIs, too, if we can discover how to program them.<p>Two tantalising potential benefits of Quantum Computers:<p>(1) the ability to model all kinds of matter efficiently at the molecular level which will spur the development of nanotech<p>(2) people will ask 'Where are these humongous computations being performed?' and then embrace the 'many worlds interpretation' of quantum mechanics, which will in turn create further scientific and philosophical progress