Many discrete optimization challenges in Computer Science, such as the travelling salesman problem or train scheduling, can often be solved optimally in practice, with performance guarantees for large-scale instances. This is a great achievement; these problems are usually NP-complete, which is a strong theoretical certificate for intractability. Continuous computational challenges are intractable in practice even on moderately sized scales. We want to show that many algorithmic challenges are complete for the complexity class ER. This captures the aforementioned intractability phenomenon from a theoretical perspective, in the process, unveils deep relations to real algebraic geometry and implies that discretizing the problem is unlikely to be possible. One such continuous intractable problem is motion planning (MP). A practical example of MP is the control of a robot arm to perform a given mechanical task without collisions. The continuous nature of movement in MP is the intuitive reason why methods, which have been applied to problems in NP, fail for MP. Showing ER-completeness makes this intuition a tangible fact. Awareness of this relation is crucial for algorithm designers as it is used to identify tractable cases. In a recent paper, Mikkel Abrahamsen, Anna Adamaszek and I could show that the Art Gallery Problem is ER-complete, settling the complexity of this long-standing open problem and implying that all current practical approaches are non-optimal. In a subsequent paper, in preparation, I designed a provably correct algorithm avoiding the lower bound in a careful way. A student is currently implementing and testing the algorithm.