1
general::
An unpredictable person or thing, as in We don't know how the new pitcher will do? he's an unknown quantity. This expression comes from algebra, where it signifies an unknown numerical value. Its figurative use dates from the mid-1800s.
American Heritage Idioms
2
general::
Phrase(s): *an unknown quantity
Fig. a person or thing about which no one is certain. (*Typically: be ~; become ~.) • John is an unknown quantity. We don’t know how he’s going to act. • The new clerk is an unknown quantity. Things may not turn out all right.
McGrawhill's American Idioms And Phrasal Verbs