We compute the Galois group of a polynomial whose roots are determined by the critical points of a scalar potential in type IIB compactifications. We focus our study on certain perturbative models where it is feasible to construct a de Sitter vacuum within the effective theory by introducing non-geometric fluxes, D-branes or non-BPS states. Our findings clearly show that all de Sitter vacua derived from lifting AdS stable vacua are associated with an unsolvable Galois group. This suggests a deeper connection between the fundamental principles of Galois theory and its applications in the construction of dS vacua. •In the present manuscript it is demonstrated that all de Sitter vacua from uplifting Anti-de Sitter stable vacua have associated a unsolvable Galois groups.•Due to their association with unsolvable Galois groups, all dS vacua lack analytic solutions.•The findings significantly impact the string theory landscape, offering a new perspective on the complexity of scalar potentials and its critical points as well as the stability of dS spaces.•Utilizing Galois theory to explore scalar potentials introduces a novel methodology, bridging advanced mathematical theories with string phenomenology and opening new research avenues for dS spaces in string theory.