> Tesla and Steinmetz figured out the theory of AC machines in the early 20th century. This was the first industrial technology where you needed advanced math to get anything to work right. Complex numbers. Calculus. Laplace transforms. That bothered some people, such as Edison. By the 1930s it was figured out, and generations of EEs struggled through rotating machine theory in college.

It's always interesting to observe differences in history from different vantage points.

In Europe the story told goes like this: Some time in the early 19th century people noticed that a thing called induction exists. Then in the later 19th century a chap called Ferraris (also known for his AC energy meter) developed multi-phase AC and the general idea of an induction motor. Some bit later, a Russian guy named Dolivo Dobrowolsky, invented a two-phase induction motor. Meanwhile, some other folks started to build transformers. Not even a handful decades later and virtually everyone in Europe used AC and both synchronous and asynchronous generators and motors were used everywhere for everything in industry.

The reason for these differences is of course that in these few years key advancements were made by different people at the same time.