The Kerala School (also called the Kerala school of astronomy and mathematics) was a tradition of mathematicians and astronomers active in the Malabar region of present-day Kerala, India, from roughly the late 14th century to the late 16th or early 17th century. Founded by Madhava of Sangamagrama (c. 1340 - c. 1425), the school produced a continuous line of scholars-including Parameshvara, Damodara, Nilakantha Somayaji, Jyeshtadeva, and Achyuta Pisharati-who worked on infinite series, trigonometry, and planetary astronomy within the framework of Sanskrit astronomical (jyotisha) treatises. The school's most important results, series expansions for trigonometric functions, were described in Sanskrit verse in a book by Nilakantha called the Tantrasangraha (around 1500), and again in a commentary on this work called the Tantrasangraha-vakhya. Some aspects of the school's place in the broader history of mathematics and astronomy, including the extent and significance of its planetary models, are subject to differing interpretations; see kerala-school-heliocentric-reading-viewpoint-debate and Heliocentrism - Hindu Viewpoint.
Historians of mathematics broadly agree that the Kerala School independently derived power-series expansions for sine, cosine, and arctangent centuries before equivalent results appeared in Europe, anticipating techniques later associated with calculus. Madhava was the first to use infinite series approximations for a range of trigonometric functions, a development that has been called the decisive step from the finite procedures of ancient mathematics toward treating limit-passage to infinity. In attempting to solve astronomical problems, the Kerala school independently discovered a number of important mathematical concepts.
A separate and more contested question concerns the school's astronomical models. Some scholars argue that 16th-century Kerala astronomer Nilakantha Somayaji modified earlier Indian planetary theory in a way that implies a partially heliocentric arrangement for the motion of the planets, while others read this work as a refinement within an essentially geocentric or Tychonic-style framework rather than a genuine departure from geocentrism. One account describes a 16th-century Kerala astronomer-mathematician presenting observational studies in geocentric terms that could nonetheless be transformed into a mathematical model with the sun at the center. This question of interpretation is treated further at Heliocentrism - Hindu Viewpoint.
For fuller historical background, including the chain of teachers and disciples through which the school's work was transmitted, see Kerala School History.
There is broad consensus among historians of mathematics, reached independently across multiple countries and institutions, that the Kerala School derived infinite-series expressions for several trigonometric functions substantially earlier than their independent discovery in Europe. See kerala-school-priority-consensus. No comparable consensus exists regarding whether the school's planetary models constitute a heliocentric or proto-heliocentric system; that question remains a matter of scholarly interpretation rather than settled agreement.