As a student, Andreessen set up one of Francis' courses in an early computer graphics laboratory and Levchin started Francis' graphics lab in the math department. Francis said his former students are sprinkled throughout academia and industry.
"Many of them are still here in town, working at NCSA or working here at Beckman and other places," he said.
Francis utilizes what he calls associated mentors - former students, collaborators, and colleagues both in the United States and abroad - who work with his students on projects.
"That means that what students do is very often determined by what the mentor is interested in," Francis said. "For example, the mentor might provide data and students work on visualization of that data. I see to it that everybody learns a lot of mathematics in doing it."
In the summer he has a Research Experience for Undergraduates program that gives his students real-world experience.
"I like to teach," Francis said. "I feel it's very important to involve undergraduates if they are bright enough and also graduate students if they are interested in what I do."
Francis plans to take a sabbatical next year, though it's hard to imagine he will be taking any time off. His sabbatical proposal states that he plans to work on four grant proposal projects, continue his work with ISL and other IVEs, and continue working on a scholarly piece on real-time interactive computer animation (RTICA) in mathematical visualization.
In his proposal Francis writes that his "research over the past two decades has been intimately connected with his interest in mentoring undergraduates to create RTICAs that visualize mathematics in cutting-edge IVEs" and that this complements his "long-time interest in creating mathematical and computational tools for artists engaged in realizing deep mathematical ideas."
Sharing those ideas either through art will continue to be a driving motivation for Francis.
"I think these exhibits invariably speak to some people as finally somebody is showing me something that I think I understand about a subject that people are rarely willing to talk about," he said.