IMHO TCS is a branch of mathematics and I would put it a bit broader. We live in the algorithmic age, almost everybody, in all human activities, invents/reinvents algorithms, mainly heuristics. But some of those algorithms are 1. good; 2. contain (burried) answers to deep mathematical questions; 3. Wait for a professional mathematical analysis/improvement/attention. My personal experience: a stunning power of one physics/machine learning heuristic, namely the Bethe Approximation, as a proof technique. The main problem is that possible encounters of this kind mainly happen in the industry, where nobody cares about those non-product related insights/revelations.