/səˈluːʃən/
[noun] An answer to a problem or a way of dealing with a difficult situation. It can also mean a liquid mixture in which one substance has been completely dissolved into another.
Every time you dissolve sugar in water, you are performing the same action the Romans used to describe paying off a debt.
The word 'solution' reaches back to the Latin verb 'solvere', which meant to loosen, to untie, or to release. This root had a wonderfully physical sense to it — imagine fingers working free a knot in a rope. From 'solvere' came the noun 'solutio' (genitive: 'solutionis'), which the Romans used to describe the act of loosening or releasing, including the very practical business of paying off debts, since paying what you owe 'releases' you from obligation. This Latin noun passed into Old French as 'solution', and from there entered Middle English in the 14th century, carrying the same broad sense of releasing or dissolving.
In medieval English, the word first appeared primarily in medical and philosophical writing. Scholars and physicians used it to describe the breaking up or dissolving of something — a bodily swelling that 'dissolved', or the resolution of a contradiction in an argument. The idea of loosening was always at its heart. A problem, in this framework, was like a tangle or a knot, and finding a 'solution' meant working it free, returning things to a state of clarity and order.
The chemical and scientific sense developed naturally from this same root idea. When you dissolve salt into water, you are quite literally 'loosening' the salt, releasing its particles into the liquid. By the 17th century, as natural philosophy and early chemistry grew more sophisticated, 'solution' became a standard technical term for a liquid in which another substance had been uniformly dissolved. This meaning and the problem-solving meaning have lived comfortably side by side ever since, both reflecting the original Latin image of something being loosened or set free.
The Latin root 'solvere' has been extraordinarily productive in English, sending down a whole family of related words along different paths. 'Dissolve' came directly from Latin 'dissolvere' (dis- + solvere), meaning to loosen apart completely. 'Resolve' followed from Latin 'resolvere' (re- + solvere), meaning to loosen again or untie thoroughly — giving us both the sense of solving something and the sense of firm personal determination, as if one has 'untied' internal conflict. 'Absolve' came from Latin 'absolvere' (ab- + solvere), to loosen away from, hence to free from guilt. Each of these words carries the ghost of that original untying motion.
Perhaps the most surprising branch of this family is the word 'solve' itself, which did not actually appear in English until the 15th century — arriving after 'solution' had already been in use. English speakers had the noun before they had the verb, which is a relatively unusual situation. The financial echo also survived quietly into modern English: when a company cannot pay its debts, we call it 'insolvent' — literally 'unable to loosen' — from Latin 'in-' (not) + 'solvere'. The simple act of untying a knot has, over two thousand years, given the English language one of its most versatile and far-reaching word families.