Juan de Ortega (mathematician)

Juan de Ortega (c. 1480 – c. 1568) was a Spanish Dominican friar and mathematician known for his work on commercial arithmetic. He is considered one of the key figures in the popularization of mathematics for practical purposes during the 16th century.

Ortega's most influential work was "Tractado subtilissimo d'arismetica y de geometria" (A Most Subtle Treatise on Arithmetic and Geometry), first published in 1512. This book covered a wide range of topics relevant to merchants and traders, including:

• Basic Arithmetic: Addition, subtraction, multiplication, and division with integers and fractions.
• Commercial Calculations: Interest calculations, currency exchange, and the rule of three.
• Geometry: Basic geometric concepts and their application to practical problems.
• Algebra: Some elementary algebraic techniques.

Ortega’s "Tractado" was significant for several reasons. First, it was written in the vernacular (Spanish) rather than Latin, making it accessible to a wider audience. Second, it emphasized practical applications over theoretical mathematics. Third, it used a standardized notation and clear explanations, contributing to the development of mathematical literacy among merchants and artisans.

Later editions of "Tractado subtilissimo d'arismetica y de geometria" were published with revisions and additions by other authors, further extending its influence. Ortega's work helped to bridge the gap between academic mathematics and the everyday needs of the commercial world, contributing to the growth of trade and industry in the 16th century. He is considered an important predecessor to later writers on commercial arithmetic, such as Adam Ries.