Abstract
<jats:p>ˊNew Physics needs new mathsˊ s a long-standing demand for a mathematical approach to finally combine the Theory of Relativity and Quantum Physics. The reason for this failure so far is uncovered on the base of misunderstandings in vector and quaternion calculus. Their former discoverers Hermann Grassmann and William Rowan Hamilton described their ˊnew scienceˊ almost simultaneously around 1843. However, their mathematical systems differed fundamentally from each another, although they both dealt with the same domain of expansion. - Old mathematical models are reinterpreted and combined with new knowledge. - Connecting the infinitely small with the infinitely large by using imaginary units. - Proposal for solving the infinity problem by introducing imaginary calculus of wholeness. - Reference work of Unified - / Holistic Physics. In the end, mathematics, physics and philosophy are connected again. The mechanism of quantum entanglement gets its long-sought, missing mathematical element.</jats:p>