Not quite! How do we produce such fake solutions? I will review work of several authors (Coppersmith, Elkies, Bombieri-Pila, Heath-Brown) about this, and the related question of bounding the number of integral solutions to a polynomial equation P(x1, ..., xn) = 0. I will then explain a recent result with Lawrence and Ellenberg (https://arxiv.org/abs/2109.01043) showing that integral points are "rare" on many natural moduli spaces. Speaker(s): Akshay Venkatesh (Institute for Advanced Study)