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.

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> ##### 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!


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