Thomas Grimm, of Utrecht University and Harvard University, argues that ideas from tame geometry and o-minimality may explain why consistent physical theories produce finite, well-behaved descriptions rather than pathological ones. Delivered as part of the Institute for Advanced Study's Special Year Research Seminar, the talk traces how finiteness questions in quantum field theory and string theory connect to arithmetic geometry and Hodge theory. Grimm discusses spaces of effective theories, distinguished loci in moduli space, and structural constraints on scattering amplitudes, noting that perturbative amplitudes are naturally expressed through period integrals while non-perturbative examples push toward broader tame frameworks involving non-analytic, multisummable behavior. He emphasizes measures of complexity sharpened by recent work on sharp o-minimality, and closes with open questions on both the physics and mathematics sides of the program. The talk assumes graduate-level familiarity with string theory and algebraic geometry and runs just over an hour.