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?
  • Physics
    • What actually happens when a quantum system is measured?
    • When a black hole evaporates, is the information about what fell in preserved (and how) in the Hawking radiation, or destroyed?
    • Why does the universe have a strong entropy increase toward the future but not the past?
  • Computer science
    • Is P really equal to NP?
    • Can fault-tolerant quantum computers actually be built?
    • Can we really achieve AGI with computation?
  • Finance
    • Do asset prices track underlying value or market narrative / noise?
    • Why is the historical US equity premium (~6%) so high that it implies a ~30–40x risk aversion?
    • Is financial instability inevitable in capitalism, or is it due to external shocks?
  • Psychology
    • Are emotions hard-wired (hence discovered) or constructed from more primitive ingredients?
    • Does trauma hide the memory that we recover later, or are these recovered pieces fabricated?
    • In psychotherapy, do specific techniques work? Or is it just the relationship?
  • History
    • Were the atomic bombings of Japan militarily necessary?
    • Was the Holocaust planned from the start, or did it emerge from bureaucratic chaos?
    • Did the Industrial Revolution raise or lower living standards for ordinary workers?
  • Geography
    • Does physical geography cause big changes to human outcomes in the long run?
    • Are places about a geographic location or about the flow of capital, people, and power that flow through?
    • Are local, regional, national, … really nested ways of organizing society, or an ineffective way of thinking about geography?