Prompted by the submission about neural nets approximating functions, I am posting another example of universality; this time, in the context of holomorphic (complex-differentiable) functions. The Riemann zeta function has this remarkable property that if you traverse the critical strip upwards, you will see snapshots of every non-zero holomorphic function to any accuracy you like. The precise statement can be found in the Wikipedia link, together with a high-level proof overview.