Hopeless means there is no chance left. A search called off on the ninth day because it had become hopeless, a court case your own lawyer begs you to drop, three-nil down with four minutes to play.
The commonest use in speech is much lighter: hopeless at something means very bad at it — I am hopeless at maths, he is hopeless with money. It is said about yourself as much as about anyone else, and it lands as affectionate rather than cruel. The other side of the word is the feeling: a hopeless patient is one nobody can save, a hopeless person is one who has stopped believing anything will improve, and the sentence around it does the sorting. Watch the prepositions — hopeless AT a skill, hopeless WITH a thing or a person. Hopelessly slides further still: hopelessly lost, hopelessly in love, where it means nothing more than completely.
1adjectivehopelessWith no chance of success or improvement.
“By midnight the rescue looked hopeless.”
synonyms: futile, doomed, unwinnable
2adjectiveuselessVery bad at something.
“I am hopeless at remembering names.”
synonyms: useless, incompetent
3adjectivedespairingFeeling that nothing will ever get better.
“After the third rejection he felt tired and hopeless.”
synonyms: despairing, despondent
Too few real examples of this word to estimate which sense is commonest.
Middle English
hopen
English
hope
English, today
hopeless
From hope + -less. Compare Swedish hopplös. hope comes from Middle English hopen. From Middle English hopen, from Old English hopian (“hope”), from Proto-West Germanic hopōn; further etymology unclear. 2
Etymology from Wiktionary, CC BY-SA