All great achievements involve some measure of collaboration.

There is the case of Emily Dickinson. But looking closer, it becomes clear that she was immensely interested in people and wrote hundreds of poems for particular people, and sending them to them.

Some competition is important. Rivalry can push people to great heights. When one does excellent work, the other feels the need to do even better.

The power of collaboration shows up everywhere: between professor and student, where the student learns from the professor, and the professor discovers new things from the questions of the student.