William Tutte apparently introduced the concept of the thickness of a graph. I have a memory of reading or being told that the concept of the coarseness of a graph arose because Paul Erdos misunderstood the definition of thickness.
There was indeed a great deal of pushback to the New Math. You can find a brief summary of this on pp. 12-16 of my textbook, from which I will quote liberally:
To say that these curricula were ambitious would be a dramatic
understatement. Inspired by the mathematicians of the Bourbaki
movement, New Math curricula stressed mathematical structures as a