Google Books Ngram viewer shows that in American English the use of the verbs “convince” and “persuade” narrowly tracked each other until around 1968, when “convince” soared and “persuade” fell far behind.*
In British English, however, “persuade” took a strong lead shortly after World War I and maintained it until around 2012, when use of “convince,” which had started to advance around 1968, surpassed it.
Our verb “convince” derives from Latin convincere to refute, convict, prove, from com- + vincere to conquer.
Our verb “persuade” derives from the Latin persuadēre, from per- thoroughly + suadēre to advise, urge.
These days I seem hardly ever to meet with “persuade,” either in journalism or in books written since the turn of the century. It’s convince, convince, convince everywhere.
Whatever happened to a little friendly persuasion? Is there perhaps a lesson here?