This is a rather cryptic post, so bare with me. I just want to remember where I am and maybe get some feedback. Let's get started:
Artificial Intelligence and mathematics are about solving problems that have been framed by a programmer or a mathematician. Can an automatic system frame problems, or do we always need a human in the loop?
Computer programs have inputs and outputs. At the very basic level these are just symbols to which the programmer gives meaning. How can the manipulation of symbols produce Intelligence?
The world around us is inherently stochastic. Our computing devices based on bits are designed to avoid stochasticity. How could we build artifacts that benefit from the inherent physical properties, instead of constraining them? It seems to me that 70 years of Turing theory are counterproductive here and new approaches have to be imagined.