My brother recently asked me how to use pairs of words like historic/historical, mathematic/mathematical, and problematic/problematical. The typical usage advice is pretty straightforward—use historic to refer to important things from history and historical to refer to anything having to do with past events, important or not—but the reality of usage is a lot more complicated.
According to the Oxford English Dictionary, historic was first used as an adjective meaning “related to history; concerned with past events” in 1594. In 1610, it appeared in the sense “belonging to, constituting, or of the nature of history; in accordance with history”; sometimes this was contrasted with prehistoric. It wasn’t until 1756 that it was first used to mean “having or likely to have great historical importance or fame; having a significance due to connection with historical events.” The first edition of the OED called this “the prevailing current sense”, but the current edition notes that the other senses are still common.
The history of historical isn’t much clearer. It first appeared as an adjective meaning “belonging to, constituting, or of the nature of history; in accordance with history” (sense 2 of historic) in 1425, though there aren’t any more citations in this sense until the mid- to late 1500s, about the same time that historic began to be used in this sense. Also in 1425, it appeared in the sense of a work that is based on or depicts events from history, though this sense also didn’t appear again until the late 1500s. In the broader sense “related to history; concerned with past events”, it appeared in 1521, several decades before historichistoric appeared in this sense.
In other words, both of these words have been used in essentially all of these senses for all of their history, and they both appeared around the same time. It’s not as if one clearly came first in one sense and the other clearly came first in the other sense. There is no innate distinction between the two words, though a distinction has begun to emerge over the last century or so of use.
Other such pairs are not much clearer. The OED gives several senses for mathematical beginning in 1425, and for mathematic it simply says, “= mathematical adj. (in various senses)”, with citations beginning in 1402. Apparently they are interchangeable. Problematic/problematical seem to be interchangeable as well, though problematical is obsolete in the logic sense.
But rather than go through every single pair, I’ll just conclude with what
There is no rule or consistent pattern governing the formation of adjectives ending in -ic and -ical. . . .
When you’re in doubt about which form is preferred or whether an -ic/-ical word pair has differentiated, the only way to know for sure is to check a dictionary or other reference source.