achines cannot discover theorems using algorithms, yet

Consequences achines cannot discover theorems using algorithms, yet AY Eee do it all the time. Do the rest of us break the logic limit? It seems we do. People appear creative — painting, composing, sculpting and so forth. But, are these endeavors creative in the mathematical sense. To prove this, ironically we need to find something outside mathematics that is definitely non-computable. This is tricky. Most artistic things are fuzzily defined and there are no written rules we can apply. How can we prove a work of art could not have been generated by a computer? Trivial proofs exist but they are rather contrived. For example, it would not be possible to make a film with a solution to the still unproven Riemann Hypothesis on the blackboard in the background of a movie scene. All the mathematics Good Will Hunting had been already discovered before the movie was made. New mathematics cannot be accidentally generated by a set designer — unless, of course, they also happened to be a world class mathematician. These trivial proofs might lead a mathematician to argue the theory is proven. There are some artworks which cannot be computed. QED. But these are not very satisfactory proofs. I could create almost any movie I wanted without tripping over this rule. What I really wanted to know is whether Good Will Hunting as a whole could have been generated by a computer. Not that some weird version with a particular mathematical proof on the blackboard is forbidden. Movies are a difficult subject for HOUSE_OVERSIGHT_015947