Āryabhaṭa (c. 920 – c. 1000) was an Indian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and

astronomer An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galax ...

, and the author of the ''Maha-Siddhanta''. The numeral II is given to him to distinguish him from the earlier and more influential Āryabhaṭa I. Scholars are unsure of when exactly he was born, though

David Pingree David Edwin Pingree (January 2, 1933 – November 11, 2005) was an American historian of mathematics in the ancient world. He was a University Professor and Professor of History of Mathematics and Classics at Brown University. Life Pingree gra ...

dates of his main publications between 950–1100. The manuscripts of his ''Maha-Siddhanta'' have been discovered from

Gujarat Gujarat () is a States of India, state along the Western India, western coast of India. Its coastline of about is the longest in the country, most of which lies on the Kathiawar peninsula. Gujarat is the List of states and union territories ...

Rajasthan Rajasthan (; Literal translation, lit. 'Land of Kings') is a States and union territories of India, state in northwestern India. It covers or 10.4 per cent of India's total geographical area. It is the List of states and union territories of ...

Uttar Pradesh Uttar Pradesh ( ; UP) is a States and union territories of India, state in North India, northern India. With over 241 million inhabitants, it is the List of states and union territories of India by population, most populated state in In ...

, and

Bengal Bengal ( ) is a Historical geography, historical geographical, ethnolinguistic and cultural term referring to a region in the Eastern South Asia, eastern part of the Indian subcontinent at the apex of the Bay of Bengal. The region of Benga ...

, so he probably lived in northern India.

Maha Siddhanta

Aryabhata wrote ''Maha-Siddhanta'', also known as ''Arya-siddhanta'',

Sanskrit Sanskrit (; stem form ; nominal singular , ,) is a classical language belonging to the Indo-Aryan languages, Indo-Aryan branch of the Indo-European languages. It arose in northwest South Asia after its predecessor languages had Trans-cultural ...

language work containing 18 chapters. It summarizes a lost work attributed to Parashara, and is probably based on

Shridhara Śrīdhara or Śrīdharācārya (8th–9th century) was an Indian mathematician, known for two extant treatises about arithmetic and practical mathematics, ''Pāṭīgaṇita'' and ''Pāṭīgaṇita-sāra'', and a now-lost treatise about algebra ...

's work. The initial twelve chapters deal with topics related to

mathematical astronomy Theoretical astronomy is the use of analytical and computational models based on principles from physics and chemistry to describe and explain astronomical objects and astronomical phenomena. Theorists in astronomy endeavor to create theoretica ...

and cover the topics that

Indian mathematicians Indian mathematicians have made a number of contributions to mathematics that have significantly influenced scientists and mathematicians in the modern era. One of such works is Hindu numeral system which is predominantly used today and is likely ...

of that period had already worked on. The various topics that have been included in these twelve chapters are: the

longitudes Longitude (, ) is a geographic coordinate that specifies the east-west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter ...

of the planets, lunar and solar

eclipses An eclipse is an astronomical event which occurs when an astronomical object or spacecraft is temporarily obscured, by passing into the shadow of another body or by having another body pass between it and the viewer. This alignment of three ...

, the estimation of eclipses, the lunar crescent, the rising and setting of the planets, association of the planets with each other and with the stars. The next six chapters of the book includes topics such as

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

geography Geography (from Ancient Greek ; combining 'Earth' and 'write', literally 'Earth writing') is the study of the lands, features, inhabitants, and phenomena of Earth. Geography is an all-encompassing discipline that seeks an understanding o ...

and

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

, which were applied to calculate the longitudes of the planets. In about twenty verses in the treatise, he gives elaborate rules to solve the

indeterminate equation In mathematics, particularly in number theory, an indeterminate system has fewer equations than unknowns but an additional a set of constraints on the unknowns, such as restrictions that the values be integers. In modern times indeterminate equati ...

: by = ax + c. These rules have been applied to a number of different cases such as when c has a positive value, when c has a negative value, when the number of the quotients is an even number, when this number of quotients is an odd number, etc.

Other contributions to maths

Aryabhata II also deduced a method to calculate the

cube root In mathematics, a cube root of a number is a number that has the given number as its third power; that is y^3=x. The number of cube roots of a number depends on the number system that is considered. Every real number has exactly one real cub ...

of a number, but his method was already given by Aryabhata I, many years earlier. Indian mathematicians were very keen to give the correct sine tables since they played a vital role to calculate the planetary positions as accurately as possible. Aryabhata II played a vital role in it by constructing a sine table, which was accurate up to five decimal places.

Maha Siddhanta

Other contributions to maths

References

Further reading