New hardware developments require -often completely new- methods to solving problems: the traditional approach of sequential-thinking is no longer useful in a highly parallel hardware world. We need approaches of parallel problem solving. This is a very challenging problem for the mathematical community:  re-think how each method developed for a particular problem can be solved in a parallel way (be careful here: not re-factor the method, like in traditional parallelisation of sequential solutions, but possibly create a totally new method to solve the problem). This would require collaboration crossing boundaries between Mathematics, Computer Science and even Electrical Engineering (plus possibly physics).