In the end I use almost nothing that I learnt in my EE degree to do software development, and certainly none of the really hard math/sig pro stuff
Maybe you've simply demonstrated your ability to handle advanced mathematical thinking in general, and therefore do have a grasp for less specific mathematical properties of programs? Which, after all, are just complicated representations of mappings, so being able to intuitively handle situations like "if I write is like this, condition X never occurs" or "if I write it like this, cases A, B and C handle possible inputs exhaustively" and such are helpful.
In the realm of scientific observation, luck is granted only to those who are prepared. - Louis Pasteur