In my experience this is where the ability to learn from literature would really help. In this specific case you’d encounter Fourier analysis pretty damn quickly if you started to read around the subject. Likewise whilst I think my formal teaching gave me a grounding I actually value the self-learning aspect from my degree more. The hard problems are the ones you’ve not heard the solution too before. The main thing a formal education provides is a leg up and hopefully a solid set of skills to help find answers to hard problems.