Daniel Litt, Assistant Professor of Mathematics at University of Toronto, says AI achieving complete advantage over mathematicians in roughly 15 years would shift theorem-proving to machines while leaving fundamental questions open
Boaz Barak quoted and endorsed the view on human roles.
#133Boaz Barak@BOAZBARAKTCSTo be clear, while I believe human mathematicians will have role to play, it does not mean there won't be a dramatic shift, nor that there is not a sense of loss.
I will personally miss the days of being able to sit, with just pen and paper, and discover via pure thought a mathematical truth than no one knew before.
Boaz Barak@boazbaraktcsI think @littmath makes a good point. Erdos' quote aside, mathematicians are not machines to prove theorems, nor is human society or economy a machine to optimize anything else than what humans decide is valuable, and we need humans to do so.
#133Boaz Barak@BOAZBARAKTCSI think @littmath makes a good point. Erdos' quote aside, mathematicians are not machines to prove theorems, nor is human society or economy a machine to optimize anything else than what humans decide is valuable, and we need humans to do so.
Daniel Litt@littmathAssuming models have complete advantage over human mathematicians in all areas of math (IMO not guaranteed in 15 years, but likely enough), this seems to be a question about the shape of society. Arguably the answer is not at all special to math--presumably the answer is basically the same for all knowledge work (and maybe all professions?). I think in this world the most likely background situation is that humans are not really useful for proving theorems, but nonetheless lots of basic and understandable questions remain open, including many that are open today (since I think these have basically unbounded difficulty). And lots of other questions of basic interest have been resolved. So human activities might include (1) trying to understand solutions, (2) trying to understand progress and obstructions to resolving open questions, (3) (non-rigorously) understanding mathematical phenomena. In all these activities, the purpose of the human is to serve as a locus of understanding. There's an obvious question as to why we would pay someone to do this. One plausible answer is that maybe we want to avoid complete disempowerment--at a minimum we might want people to understand what they can about what the AIs are doing--which requires development of human capital.