the recent amazing successes of "model free" neural net algorithms (alpha go, outstanding language translation, ultra-realistic sounding voice synthesis, etc) makes me wonder whether somehow these techniques eventually could be, or perhaps already have been, applied to the creation of new and interesting mathematics. if things were to proceed along the lines of the progress to date on other problems, someone might possibly start modestly from a large training set of data (say 10,000 first year calculus exams, together with their grades), and somehow train a neural network to recognize the difference between incorrect and correct calculus question-answering. (i am just making this up). or, perhaps take textbooks and their answer keys. or polya's problems and someone's answers. it seems to still be far away from something likely to succeed, somehow, in generating a proof of a hard theorem or even creating say a simple paper i might want to read, but i had a similar reaction to what I was reading about alpha go in its early days. at the very least, a useful virtual mathematical interlocutor seems possibly feasible from a suitably large corpus of training data of "actual" mathematical back and forth interactions between teachers and students, or between researchers, maybe?