| Generalising a question of Hirzebruch, Kotschick asked the following: which Chern numbers are determined up to finite ambiguity by the underlying smooth manifold? Together with S. Schreieder, I treated this question in dimension higher than 3, showing that most Chern number are unbouded. After explaining such results, I will talk about the 3 dimensional case, where it is believed that Chern numbers are bounded. Results in this direction have been obtained in a preprint with P. Cascini. |