The new versus the old method of computation as portrayed in an early encyclopaedia, the MARGARITA PHILOSOPHICA of Gregor Reisch (Strassbourg, 1504).

The illustration symbolizes the culmination of a four-hundred year rivalry. The abacists had fought to retain Roman numerals and the abacus for calculation. The algorists advocated the use of the Hindu-Arabic system, along with its algorithms for calculation, the methods having been popularized in Europe via a 12th century translation of the great arithmetic textbook of al-Khwârizmî .

The central figure in the woodcut, holding books on the two methods of calculation, is Arithmetica, representing one of the seven "liberal arts" comprising the university curriculum of the time. The abacists are represented by the Greek mathematician Pythagoras, who is calculating on a counting-board, whereupon pebbles are pushed along lines (the Latin word for pebble is calculus). The algorists are represented by the Roman philosopher and arithmetician Boethius, who is employing algorithmic methods to compute with Arabic numerals.

By the early 16th century, Western Europe had universally adopted the efficient algorithms.

Eugene Luks