Sometimes I catch glimpses from an alternate multiverse. I have a classroom of students, and I give them open ended assignments, assignments where they read a passage that their professor has strategically selected. They come back (the next day?) to the class and give a summary report and provide some answers to additional questions that I pose independently to each of them.
“Read pages 1-11. Give an overview to the class. Pay particular attention to the passage on Kepler. Do some additional research. Give the class a summary of his equal area law and how it is related to angular momentum.”
“Read pages 12-18. Give an overview of the class. Pay particular attention to the passage on Newton and Leibniz. Do some additional research. Give the class a brief summary of their two notations for derivatives.”
“Read pages 19-25. Give an overview of the class. Pay particular attention to the passage on Copernicus. Do some additional research. Give the class a brief summary of how and why he used epicycles in his model of the solar system.”
The thoughts pop into my head from time to time — usually when I am reading a book that would be an ideal assignment for the students to read from. And of course, I have no such students, none who could handle such an assignment. I never will. Mine struggle with simpler things. My contributions to their lives will very likely not involve mathematics. But there will be contributions. That is certainly something, and it’s something important.
Still… there are those glimpses and the echoes of alternatives.