We present epistemological ruptures that have occurred in mathematical history and in the transformation of using technology in mathematics education in the twenty-first century. We describe how such changes establish a new form of digital semiotics that challenges learning paradigms and mathematical inquiry for learners today. We focus on drawing analogies between the emergence of non-Euclidean geometry with recent advances in technological environments that are dynamic and interactive both visually and haptically. This analysis yields a new digital semiotic theory.