<p>The decline of Moore’s law coupled with the rise of artificial intelligence has recently motivated research into photonic computing as a high-bandwidth, low-power strategy to accelerate digital electronics. However, many modern-day photonic computing strategies are analogue, making them susceptible to noise and intrinsically difficult to scale. Optical skyrmions offer a route to overcome these limitations through digitization in the form of a discrete topological number that can be assigned to the analogue optical field. Apart from an intrinsic robustness against perturbations, optical skyrmions represent a new medium that has yet to be fully exploited for photonic computing, namely, spatially varying polarization. Here we propose and experimentally demonstrate a method for performing perturbation-resilient integer arithmetic with optical skyrmions and passive optical components, achieving discrete mathematical operations directly using optical skyrmions without external energy input.</p>