Taleb vs. the Gaussian crowd on 20% market crashes
Claude contrasts the normal-distribution models that call a 20% S&P drop a 'once per 10^86 years' event with Taleb's fat-tailed, unknowable-risk view.
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A tangled family river-crossing puzzle, solved and checked
The user brings a family river-crossing puzzle with tricky safety rules, gets a 15-step solution animated in React, then catches a flawed alternate solution.
Catching a real error in a Journal of Economic Theory proof
Claude verifies a published proof, misses a subtle continuity gap, gets corrected by the user, and confirms it matches the authors' own corrigendum.
Chasing a Counterexample to the Jacobian Conjecture
Claude runs a disciplined symbolic search for a map that would refute the eighty-year-old Jacobian conjecture, and the hunt turns up something startling.
Comparing four car insurers by their actual rate filings
Regulator filings for four large California carriers are mined into an eight-tab workbook, exposing one insurer pricing mileage across a fivefold factor spread.