Juan de Ortega (born Palencia, Spain, c. 1480; died c. 1568),^[1] was a Spanish mathematician. He wrote some of the earliest works on commercial arithmetic, and discovered an improved method for calculating square roots.

Very little is known of Ortega's life.^[2] He was a member of the Dominican Order in Aragon,^[2] and he taught arithmetic and geometry in Spain and Italy.^[1]

For his work on arithmetic Ortega drew on that of Boethius and of 13th-14th century mathematicians.^[1]

A widely known^[3] publication among Ortega's works was Tratado subtilissimo de Aritmetica y de Geometria ("Most refined treatise on arithmetic and geometry") (Barcelona, 1512). The work was published in Spain, France and Italy, and translated into several languages.^[2] The Tratado was innovative^[3] in focusing on the practical, in particular commercial, application of arithmetical and geometrical techniques.^[2] In later editions^[4] this work also introduces a novel approximation method for calculating square roots,^[5] which appears to be largely based on the Pell equation and thereby the best available technique,^[6] even though no general solution of this equation is known to have been found until much later.^[1]

Another textbook by Ortega was Cursus quattuor mathematicarum artium liberalium ("Course of four mathematical arts") (Paris, 1516).^[1]

Another textbook by Ortega was "Conpusicion de la arte de la arismetica y juntamente de geometría"^[7]

• "Ortega biography". MacTutor archive. School of Mathematics and Statistics, University of St Andrews, Scotland.