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] > ##### Problem 18: Limits of Intelligence > > _What are the limits of intelligence, both artificial and human?_ > > Penrose (1991) attempts to show some limitations of artificial > intelligence. His argumentation brings in the interesting question of > whether the Mandelbrot set is decidable (dealt with in [Blum and > Smale, 1993]) and implications of the Gödel incompleteness theorem. > > However, a broader study is called for, one which involves deeper > models of the brain and of the computer, in a search of what > artificial and human intelligence have in common, and how they differ. > I would look in a direction where learning, problem-solving, and game > theory play a substantial role, together with the mathematics of real > numbers, approximations, probability, and geometry. > > --- > I hope to expand on these thoughts on another occasion. > > --- 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