Cybernetics is fairly formalized, but a lot of research into it was dropped. Cybernetics is based on information theory and approaches systems in a probabilistic way which is in direct contrast to the AI approach of the 50s and 60s which were really about processing discrete pieces of data.

If you read cybernetics texts today, they paint a picture very similar to neural networks and the statistical methods for processing data. "Introduction to Cybernetics" by W. Ross Ashby is a decent text with a lot of good exercises. I still think there's a lot to learn here.

>It does. It unifies all of mathematics at the lowest level

This was attempted before by Russel & Whitehead before Godel proved that any sufficiently complicated system can produce non-truths and false statements that cannot be verified by that same system.