Dorabella cipher
A short note from the composer Edward Elgar in 1897, written in tiny semicircles, that nobody has managed to read since.
Elgar sent it to the young Dora Penny, who never made sense of it. The text is 87 characters built from one, two or three arcs in eight orientations — 24 symbols, almost exactly an alphabet's worth, which points to a simple substitution cipher. But 87 characters give frequency analysis very little to chew on, and every proposed solution so far has needed assumptions about misspellings, private jokes or phonetic spelling.
Elgar was a keen amateur cryptographer who once cracked a cipher a magazine had declared insoluble. He later wrote Dora into one of his Enigma Variations (1899), a title with no connection whatsoever to the German machine, which cryptographers point out anyway.