Picture stirring something into a glass of water. Sugar , spreads out and is gone; sand just sits there in grains, however long you stir. Insoluble is that second glass — whatever you do, it will not come apart. The same picture is what people reach for when a problem will not come apart either: you keep working at it, and it stays in one hard lump.
From the word’s history
From Latin insolubilis: in- plus solubilis, from a root meaning to loosen or undo. English kept both jobs of that root, which is why the same word covers a solid that will not loosen in water and a problem that will not come undone. The packet also records unsolvable and insolvable as words built from the same source.
來自拉丁文 insolūbilis：in-（不）加上 solūbilis，字根的意思是「鬆開、解開」。英文把這個字根的兩種工作都留了下來。所以同一個字既能講固體在水裡鬆不開，也能講問題解不開。同一個來源還長出了 unsolvable 和 insolvable。
Wiktionary etymology supplied in this packet (source_ref kaikki:3f6f69a190036ae4:1114415849): Latin insolubilis, in- + solubilis; piecewise doublet of insolvable and unsolvable
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