SEL4: Mathematically Verified Software Kernels (2014) [pdf]
I would bet pretty good money that automated theorem proving is better than the best humans within 10 years.<p>There&#x27;s still not a lot of good research in combining machine learning and theorem proving, and intuitively it seems feasible. It&#x27;s clearly somewhere between beating Go and general AI, and probably closer to Go since it&#x27;s basically just a tree search with heuristics.<p>If this happens, it would radically change the software industry. High level application development might not change that much since the problems are usually poorly specified. But it might dramatically reduce the cost of writing system software. We&#x27;d see innovation in that space we haven&#x27;t seen since the 70s. Unix and its abstractions that dominate the whole market might look as antiquated as punch cards.<p>Additionally, professional mathematicians might become more like philosophers, guiding the procession of mathematics and deciding what is interesting to prove.