1580s, originally religious, "a Protestant;" from reform + -ist. Political sense of "one who proposes or favors reform to the order of society," with varying specifics, is from 1640s. Related: Reformism (1904), which was specifically the theory that socialism might be established gradually via a nation's own institutions rather than only by revolution.
1820, "member of the progressive and reformist political party of Great Britain, an anti-Whig," from liberal (adj.). General meaning "person of liberal political principles or tendencies" (without reference to party) is by 1832; in reference to persons of a political ideology not conservative or fascist but short of socialism, from c. 1920. Also used from early 20c. of ministers from less-dogmatic Christian churches.
Conservative, n. A statesman who is enamored of existing evils, as distinguished from the Liberal, who wishes to replace them with others. [Ambrose Bierce, "Devil's Dictionary," 1911]
late 14c., "originating in the root or ground;" of body parts or fluids, "vital to life," from Latin radicalis "of or having roots," from Latin radix (genitive radicis) "root" (from PIE root *wrād- "branch, root"). The basic sense of the word in all meanings is "pertaining or relating to a root or roots," hence "thoroughgoing, extreme."
The figurative meaning "going to the origin, essential" is from 1650s. The political sense of "reformist" is by 1817, of the extreme section of the British Liberal party (radical reform had been a current phrase since 1786), via the notion of "change from the roots" (see radical (n.)). The meaning "unconventional" is from 1921. U.S. youth slang use is from 1983, from 1970s surfer slang meaning "at the limits of control."
The mathematical radical sign, placed before any quantity to denote that its root is to be extracted, is from 1680s; the sign itself is a modification of the letter -r-. Radical chic is attested from 1970; popularized, if not coined, by Tom Wolfe. Radical empiricism was coined 1897 by William James (see empiricism).