A teenager has just done what dozens of seasoned mathematicians could not: they toppled a conjecture that quietly steered harmonic analysis and ...

For example, 9 = 2 (1 2)+7, and 15 = 2 (2 2)+7. This week's GeekDad Puzzle of the Week is simple: what are the two smallest counter-examples that disprove this conjecture?

So the example is not a counterexample to causal decision theory. Nevertheless, the example shows that causal decision theory can recommend unratifiable acts (acts that once decided upon appear ...