The study of precision measurements, or metrology, is a recurring theme in all scientific research. Recent applications of ideas originated by Aharonov have pierced some of these limitations, leading to advances beyond the current state-of-the-art (including breaking the diffraction limit). The mathematical underpinnings for these advances lie in a concept called superoscillations and its study from a mathematical point of view, includes their optimization, longevity in time, their ubiquitous occurence in a broad spectrum of different settings such as group theory.