[nemo8551]

There I was all excited to show off some of my electrical chops on HN.

Not today.

[rzzzt]

Does mystified math lie beyond behind how the ratio of input and output voltages is equal to the ratio of the primary and secondary windings? Can it be derived from Maxwell's equations?

Off to a search...

[nihzm]

Not really mystified in any sense of the word but for more precise calculations of circuit diagrams with transformers you can formulate a system of coupled ODEs which can be written in matrix form leading to the very nice mathematics of matrix differential equations.

[amelius]

I bet that an LLM (which uses transformers) can explain those aspects of a transformer to you.