The flatness conjecture and the question of an infinite or a finite space reappear in the history of understanding the structure of our world. Riemann's geometry and Einstein's theory of gravitation have proposed solutions in terms of the possibility of curved finite space-forms without boundary. Still, contemporary cosmology rests on the assumption of an infinite space without curvature. This article explains a recently opened research field aiming to explain the Dark Energy and Dark Matter problems by generalizing the cosmological model in the spirit of this old question and its proposed answers.