'Algorithms' can be proved, 'implementations' necessarily need tests. Algorithms, are mathematically able to be proved, but any real implementation has to invo

'Algorithms' can be proved, 'implementations' necessarily need tests. Algorithms, are mathematically able to be proved, but any real implementation has to involve physical hardware at some level, these implementation details cannot (reasonably) be proven mathematically therefore need sufficient tests. In the absence of a proof, tests can cover both algorithms & implementations.