Historically, up to the 18th century a single dot followed by short notes didn't necessarily mean "add exactly half the length", It could mean either more or less than half, depending on the style and tempo of the music (and the performers were expected to be able to judge that without any written instructions on the score). You often see "mathematically incorrect" notations like a dotted quarter note followed by three 32nd notes.
In the early classical period (up to early Beethoven) dotted notes were sometimes used instead of ties across barlines - for example a half-note at the end of a bar and the dot written at the start of the next bar, where the tied note would be in modern notation.
In the 19th century the usage corresponded closer with the mathematical "add half" rule. Double dots were often used, and three dots occasionally. I can't remember ever seeing more than three.
Modern scores, especially with time signatures that are not so "simple" as 2/4, 3/4, 4/4, or 6/8 (or no time signature at all), tend to use tied notes rather than multiple dots. Counting "beats" in a time signature like 11/16 is hard enough without having to read multiply-dotted notes.
Note also that dotted rests have never been used, except where they represent whole beats in compound times - i.e. dotted quarter-note rests in 6/8 and 9/8, and dotted half-note rests for half a bar of 12/8 - though in the 18th century the dots after the such rests were often omitted, since the absence of any notes was enough to make a common-sense interpretation of what the notation meant.
Of course new editions of old music often change the original notation to match current notation conventions - which can sometimes add a misleading sense of "mathematical accuracy" which the composer never intended.