I asked Claude: “What are the most effective and impactful ways you can help me?” One of its ideas was to ask it: What are the three questions this field has not resolved, where the disagreement is substantive and not just semantic? Who represents each position most forcefully?" So I posed this question about several subjects. This is a great way to discover the frontiers of knowledge in a field. Mathematics Are mathematical objects (numbers, sets, complex numbers) real, independent of human minds? Or useful fiction? Do we discover or invent them? Is there one true set theory or a multiverse of equally valid set theories, e.g. where the continuum hypothesis is true vs false? Are theorems true or false, even if we can’t prove them? Biology Does natural selection operate at a gene, individual, or group level? Does evolution proceed through gene mutation + selection, or do we need to add epigenetics, niche construction, and developmental bias? Which came first - RNA or mitochondria?…
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