An anonymous review on a proposal on polynomiography submitted to the National Science Foundation (NSF - ITR):
Root finding is indeed a hard field to make a splash in. Since the Sumarians, ancient Greeks, Isaac Newton, through Hermann Weyl and Stephen Smale, the best minds have given it a shot. I have taught the material in the classroom and have avoided the glitz associated with a lot of fractal geometry for fear of giving students less than what they need.
Well, I am now turning my head!
The global nature of the author's root finding algorithms and their simple interpretation in terms of Voronoi diagrams, Toeplitz forms, and basic calculus will force me to both revise my lectures and rethink how to most effectively use computers.
The [Principal Investigator] called the proposal an intersection between math and art. I find this an understatement in the following sense: It is interdisciplinary in the best sense of the word. That is it does not merely lie in the intersection of two fields but has the potential to make serious contributions to both. That is global algorithms for root finding and computer generated art. Not only are the tools exciting, but they are accessible to all. (Now I know what I can do this summer with the kids if I want to interest them in wonderful mathematics while they think they're having fun!)
This proposal represents a serious contribution to global root finding algorithms, computer generated art, and "bringing it all to the masses". It would be a shame not to fund it.