That is a deep philosophical quest and I find myself attached to it for my whole life. Now I would share some recent observations. A LISP program with one entr

That is a deep philosophical quest and I find myself attached to it for my whole life. Now I would share some recent observations. A LISP program with one entry function without side effects is the closest bridge between the conventional computation and conventional math. If such a program would consist from only a well known set of math functions (sin, cos etc) then it would be immediately ready for typical math instruments like differentiation, integration etc. Let's call such malleable functions as ones to be in _analytical_ form. Now add some Boolean logic. It's binary so you cannot apply the "analog" analytical math rules. But there is a trick. It is called Rvachev functions. They allow to represent Boolean functions in malleable analytical form. Having math and logic is very close to generic computation, but not enough. You also need a notion of conditional jump (sometimes called goto or branch) for it to be a Turing-complete. But functional languages like LISP provide a treasure trove here too. They often use jumps/gotos and functional recursion interchangeably. So, if a program is represented in malleable analytical form and uses recursion for control flow without side effects... it is not different from your typical math formula. So you can differentiate, integrate and do whatever a conventional math can do. Really intriguing. >To this day we have intuition about why deep networks work, but backing that intuition up with rigorous mathematical analysis has been very challenging and is quite incomplete. But when it works, it works far better than ideas rooted in automata. There were folks who translated trained networks to automata in order to squeeze them into smaller microcontrollers/FPGAs. Quite a result if you ask me. It shows that the trained AI and automata are interchangeable forms of the very same thing - computation.