Comment by fmap

I'm personally very excited about the progress in interactive theorem proving. Before the current crop of deep learning heuristics there was no generally useful higher-order automated theorem proving system. Automated theorem proving could prove individual statements based on existing lemmas, but that only works in extremely restricted settings (propositional or first-order logic). The problem is that in order to apply a statement of the form "for all functions with this list of properties, ..." you need to come up with a function that's related to what you're trying to prove. This is equivalent to coming up with new lemmas and definitions, which is the actually challenging part of doing mathematics or verification.

There has finally been progress here, which is why you see high-profile publications from, e.g., Deepmind about solving IMO problems in Lean. This is exciting, because if you're working in a system like Coq or Lean your progress is monotone. Everything you prove actually follows from the definitions you put in. This is in stark contrast to, e.g., using LLMs for programming, where you end up with a tower of bugs and half-working code if you don't constantly supervise the output.

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But well, the degree of excitement is my own bias. From other people I spoke to recently: - Risk-assessment diagnostics in medicine. There are a bunch of tests that are expensive and complex to run and need a specialist to evaluate. Deep learning is increasingly used to make it possible to do risk assessments with cheaper automated tests for a large population and have specialists focus on actual high-risk cases. Progress is slow for various reasons, but it has a lot of potential. - Weather forecasting uses a sparse set of inputs: atmospheric data from planes, weather baloons, measurements at ground stations, etc. This data is then aggregated with relatively stupid models to get the initial conditions to run a weather simulation. Deep learning is improving this part, but while there has been some encouraging initial progress this needs to be better integrated with existing simulations (purely deep learning based approaches are apparently a lot worse at predicting extreme weather events). Those simulations are expensive, they're running on some of the largest supercomputers in the world, which is why progress is slow.