- Arithmetic (from Ancient Greek ἀριθμός (arithmós) ’number’, and τική [τέχνη] (tikḗ [tékhnē]) ‘art, craft’) is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms, which are highly important to the field of mathematical logic today.