4 entries
famous problems analytic number theory
Goldbach's conjecture has been confirmed for every even number up to 4×10¹⁸ and is still a conjecture. Number theory has an unusually exact account of what a checked range is evidence about, and it is not the length of the range.
mathematical logic computability
Finite examples can make a rule engine look complete even when no procedure can decide every case it will meet. Logic separates consistency, completeness and decidability; computability supplies the hard boundary.
A calendar can contain an observed feast day, a legal date and a settlement convention that move differently. Calendar rules and festival records make the authority behind each date part of the datum.
Opening, cleaning or reconstructing an object can erase the very context that made it interpretable. Archaeology and archive recovery built procedures around irreversibility before data work had version control.