Abstract: Mysterious duality was discovered by Iqbal, Neitzke, and Vafa in 2002 as a convincing, yet mysterious correspondence between certain symmetry patterns in toroidal compactifications of M-theory and del Pezzo surfaces, both governed by the root system series E_k. It turns out that the sequence of del Pezzo surfaces is not the only sequence of objects in mathematics which gives rise to the same E_k symmetry pattern. I will present a sequence of topological spaces, starting with the four-sphere S^4, and then forming its iterated cyclic loop spaces L_c^k S^4, within which we will see the E_k symmetry pattern via rational homotopy theory. For this sequence of spaces, the correspondence between its E_k symmetry pattern and that of toroidal compactifications of M-theory is no longer a mystery, as each space L_c^k S^4 is naturally related to the compactification of M-theory on the k-torus via identification of the equations of motion of (11-k)-dimensional supergravity as the defining equations of the Sullivan minimal model of L_c^k S^4. This gives an explicit duality between rational homotopy theory and physics. Thereby,  Iqbal, Neitzke, and Vafa’s mysterious duality between algebraic geometry and physics is extended to a triality involving algebraic topology, with the duality between topology and physics made explicit, i.e., demystified. The mystery is now transferred to the mathematical realm as duality between algebraic geometry and algebraic topology. This is a report on the recent work arXiv:2111.14810 [hep-th] with Hisham Sati.