Link to current text
MATH.23:3 - Forces
| Force | Tension |
|---|
| Examples guide invention | Their generating rule may conceal a restriction that the conjecture omits. |
| Generality increases reuse | A broader claim can lose the construction that made the original case work. |
| Counterexamples improve understanding | Excluding a troublesome case can also discard the phenomenon the work needs to understand. |
| Computation expands exploration | Search quality depends on representation, tested cases and the property being evaluated. |
| A new problem opens work | Its first attainable result can be much smaller than the eventual theorem. |
| Results and methods develop together | An answer can be useful immediately while its construction opens further questions and transfers. |