Sorry to butt in, but as a computer scientist who's seen this sort of thing unfold since at least the 1970's---recalling Doug Lenat's "Automated Mathematician" and the hype surrounding it---I find the notion of math PhD students becoming dependent on software automation alarming and thought I'd ask a question or two, if you don't mind.
Has anyone explored in a serious way the pedagogical implications of having PhD students use automation in their *reasoning* work? There is some evidence that use of generative AI degrades critical thinking and other cognitive skills, which is a good enough reason to ask. We could be doing a disservice to students by persuading them to use such tools. Speaking from personal experience, more than once in my life I've written a computer program to solve a puzzle I still had no idea how to solve after writing the computer program and studying its output. Computer mediation does something to the reasoning process, and I'm not so sure we fully understand the implications. People have been teaching math without such tools for thousands of years; why take on an unknown possible risk like this?
More broadly, I cannot help wondering: what's driving the urgency that demands automation in math of all things? Automating the provision of life-saving devices and medicines to people who need them has a justifiable urgency. But math? This is not to say people should tediously calculate every little thing when there are helpful tools available. It's simply to ask: is there a better rationale than variations of "avoid tedium", "avoid mistakes", "go faster" or "everyone else is doing it", which seem superficially appealing but in the end are incoherent justifications (in my view)?
Anthony
npub1j4…nt0rs
2026-07-24 15:22:56 UTC
in reply to nevent1q…jxah
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"content": "Sorry to butt in, but as a computer scientist who's seen this sort of thing unfold since at least the 1970's---recalling Doug Lenat's \"Automated Mathematician\" and the hype surrounding it---I find the notion of math PhD students becoming dependent on software automation alarming and thought I'd ask a question or two, if you don't mind.\n\nHas anyone explored in a serious way the pedagogical implications of having PhD students use automation in their *reasoning* work? There is some evidence that use of generative AI degrades critical thinking and other cognitive skills, which is a good enough reason to ask. We could be doing a disservice to students by persuading them to use such tools. Speaking from personal experience, more than once in my life I've written a computer program to solve a puzzle I still had no idea how to solve after writing the computer program and studying its output. Computer mediation does something to the reasoning process, and I'm not so sure we fully understand the implications. People have been teaching math without such tools for thousands of years; why take on an unknown possible risk like this?\n\nMore broadly, I cannot help wondering: what's driving the urgency that demands automation in math of all things? Automating the provision of life-saving devices and medicines to people who need them has a justifiable urgency. But math? This is not to say people should tediously calculate every little thing when there are helpful tools available. It's simply to ask: is there a better rationale than variations of \"avoid tedium\", \"avoid mistakes\", \"go faster\" or \"everyone else is doing it\", which seem superficially appealing but in the end are incoherent justifications (in my view)?",
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