The development of Mathematics was marked by far-reaching new ideas, known as "Programs", and associated to top Mathematicians, e.g. Galois, Klein, Lie, Noether, Hilbert, Grothendieck, Langland and much more. They become "Principles" that changed the landscape of Mathematics and led to breakthroughs in Sciences, notably in Physics, but also in Chemistry and Biology. This presentation highlights the relation between such general principles, ensuing from the actual historical connections between their proponents, with excerpts from stories one needs to know, e.g. Einstein’s talk and Hilbert’s "homework" to his assistant Emmy Noether, or the productive collaboration and friendship between Felix Klein and Sophus Lie. New developments are mentioned: how Theory of Algebraic Periods, in the context of the recent quantization of system of units leads to explain the "unreasonable effectiveness of Mathematics": Natural Laws are Period laws.