This snippet is from Smale's paper Smale, Steve (1999). "Mathematical problems for the next century". In Arnold, V. I.; Atiyah, M.; Lax, P.; Mazur, B. (eds.). *Mathematics: frontiers and perspectives*. American Mathematical Society. pp. 271–294. ISBN 978-0821820704. [![enter image description here][1]][1] Did he follow up on these thoughts (hopefully) in a mathematical way? Since his list of $18$ problems is intended to be in mathematics, I was hoping this last question on his list has a mathematical exposition! [1]: https://i.sstatic.net/2rcwS.png