In 2012 the UK Government identified eight great technologies which would act as a focus for future scientific research and funding. Other governments have produced similar lists. These vary from Big Data, through Agri-Science to Energy and its Storage. Mathematics lies at the heart of all of these technologies and acts to unify them all. In this paper I will review all of these technologies and look at the math behind each of them. In particular I will look in some detail at the mathematical issues involved in Big Data and energy. Overall I will aim to show that whilst it is very important that abstract mathematics is supported for its own right, the eight great technologies really do offer excellent opportunities for exciting new mathematical research and applications.