xrchz comments on Superintelligence Reading Group - Section 1: Past Developments and Present Capabilities - Less Wrong
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Neither math research nor programming or debugging are being taken over by AI, so far, and none of those require any of the complicated unconscious circuitry for sensory or motor interfacing. The programming application, at least, would also have immediate and major commercial relevance. I think these activities are fairly similar to research in general, which suggests that what one would classically call the "thinking" parts remain hard to implement AI.
They're not yet close to being taken over by AI, but there has been research on automating all of the above. Some possibly relevant keywords: automated theorem proving, and program synthesis.