The ideas of quantum physics have had a huge impact on the development of mathematics, all its fields have been influenced. Many notions have emerged, such as quantum groups and algebras, quantum calculus, many special functions. Numbers, the most elementary and ancient concept at the heart of mathematics since the Babylonians, should also have their place in the quantum landscape. This talk is an elementary and accessible overview of the emerging theory of quantum numbers, including motivations, first results, and the connection to other parts of mathematics.