in Cambridge phrase, is one who has obtained a place in the highest mathematical tripos. The first man of this class is termed the senior wrangler, the rest are arranged according to respective merit, and are called second, third, fourth, etc., wrangler, as it may be. In the Middle Ages, when letters were first elevated to respectability in modern Europe, college exercises were called disputations, and those who performed them disputants, because the main part consisted in pitting two men together, one to argue pro and the other con. In the law and theological “schools” this is still done for the bachelor's and doctor's degrees. The exercise of an opponent is called an opponency. Wrangling is a word-battle carried on by twisting words and trying to obfuscate an opponent- a most excellent term for the disputations of school-men. The opponency begins with an essay on the subject of dispute.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894