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I can almost see two branches of mathematics developing. One which is human-understandable, the other formally verified. I assume the latter is a strict superse
by jhrmnn 2mo ago
I can almost see two branches of mathematics developing. One which is human-understandable, the other formally verified. I assume the latter is a strict superset of the former?
- metahuman_crumb 2mo agoI suggest "Catching crumbs from the table" by Ted Chiang. Very short piece published in Nature (2000) and well worth a read. Depicts a scenario where modified humans produce science beyond ordinary scientists' comprehension.
- cfiggers 2mo agoThis is a theme in Blindsight by Peter Watts as well. In that setting, field experts working at the bleeding edge are so advanced that non-experts literally can't understand what they're saying at all. So there's a whole class of specialists, "synthesists", that specialize in gaining approximate understanding of the experts' work for the purpose of communicating it to outsiders—perhaps wrongly, according to the expert at least, but hopefully more productively vs the unmediated version.
- cfiggers 2mo agoWhat's amusing to me in this context is, summarizing emails and such has for a while been a supposed use case for AI—the LLM serving as the "synthesist" to explain long texts accessibly. But with this math question, a human "synthesist" would be needed to approximately understand the math discovered and programmatically verified by the LLM. So the roles reverse.
- Jblx2 2mo agoMochizuki enters the chat
- OhNoNotAgain_99 2mo ago[dead]
- JadeNB 2mo agoPresumably there's not much logical obstruction to all human-understandable math eventually being formalized, although the willingness and ability to commit the requisite enormous amount of time will probably be insurmountable. But definitely that hasn't happened already!