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This entry of the Diccionario panhispánico de dudas explains the uses of the diéresis or crema (the ¨ mark) in Spanish (it is mandatory over a u to indicate that this vowel must be pronounced in the combinations gue and gui, as in vergüenza, lingüística), but it gives no hints on its origin.

I would like to know the historical origin of this sign.

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I always thought it was called trema! – hippietrail Jan 9 '12 at 8:53
@hippietrail: well, if you wear a Greek gown, you can also call it trema ;-) – Gonzalo Medina Jan 16 '12 at 20:48
up vote 2 down vote accepted

Wikipedia explains it pretty well. It was invented by the Greeks, to mark a vowel that shouldn't be combined with adjacent ones into a diphthong or new sound. With that sense it's been used ever since, even in English (although this usage is almost extint). The word diaeresis means separation; crema comes from trema, which is Ancient Greek for pip (of dice), another name given to this diacritic by the Greek.

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