Although machines have surpassed humans on visual recognition problems, they are still limited to providing closed-set answers. Unlike machines, humans can cognize novel categories at the first observation. Novel category discovery (NCD) techniques, transferring knowledge from seen categories to distinguish unseen categories, aim to bridge the gap. However, current NCD methods assume a transductive learning and offline inference paradigm, which restricts them to a pre-defined query set and renders them unable to deliver instant feedback. In this paper, we study on-the-fly category discovery (OCD) aimed at making the model instantaneously aware of novel category samples (i.e., enabling inductive learning and streaming inference). We first design a hash coding-based expandable recognition model as a practical baseline. Afterwards, noticing the sensitivity of hash codes to intra-category variance, we further propose a novel Sign-Magnitude dIsentangLEment (SMILE) architecture to alleviate the disturbance it brings. Our experimental results demonstrate the superiority of SMILE against our baseline model and prior art. Our code will be made publicly available. Our code is available at https://github.com/PRIS-CV/On-the-fly-Category-Discovery.