Aryabhata was one of the first Indian mathematicians and astronomers belonging to the classical age. He was born in 476 BC in Tarenaga, a town in Bihar, India. It is however definite that he travelled to Kusumapara (modern day Patna) for studies and even resided there for some time. It is mentioned in a few places that Aryabhata was the head of the educational institute in Kusumapara. The University of Nalanda had an observatory in its premises so it is hypothesized that Aryabhata was the principal of the university as well.

Aryabhata wrote many mathematical and astronomical treatises. It covers several branches of mathematics such as algebra, arithmetic, plane and spherical trigonometry. Also included in it are theories on continued fractions, sum of power series, sine tables and quadratic equations.

Aryabhata worked on the place value system using letters to signify numbers and stating qualities. He also came up with an approximation of pi ( ) and area of a triangle. He introduced the concept of sine in his work called ‘Ardha-jya’ which is translated as ‘half-chord’.

Sir William Rowan Hamilton, (born August 3/4, 1805, Dublin, Ireland—died September 2, 1865, Dublin) Irish mathematician who contributed to the development of optics, dynamics, and algebra—in particular, discovering the algebra of quaternions. His work proved significant for the development of quantum mechanics.

Hamilton was proficient in arithmetic at an early age. But a serious interest in mathematics was awakened on reading the Analytic Geometry of Bartholomew Lloyd at the age of 16. (Before that, his acquaintance with mathematics was limited to Euclid, sections of Isaac Newton’s Principia, and introductory textbooks on algebra and optics.) Further reading included works of the French mathematicians Pierre-Simon Laplace and Joseph-Louis Lagrange.

Born on January 4, 1643, in Woolsthorpe, England, Isaac Newton was an established physicist and mathematician, and is credited as one of the great minds of the 17th century Scientific Revolution. With discoveries in optics, motion and mathematics, Newton developed the principles of modern physics. In 1687, he published his most acclaimed work, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), which has been called the single most influential book on physics. Newton died in London on March 31, 1727.

In August 1684, Halley traveled to Cambridge to visit with Newton, who was coming out of his seclusion. Halley idly asked him what shape the orbit of a planet would take if its attraction to the sun followed the inverse square of the distance between them (Hooke's theory).

James Joseph Sylvester, (born September 3, 1814, London, England—died March 15, 1897, London) British mathematician who, with Arthur Cayley, was a cofounder of invariant theory, the study of properties that are unchanged (invariant) under some transformation, such as rotating or translating the coordinate axes. He also made significant contributions to number theory and elliptic functions.

In 1837 Sylvester came second in the mathematical tripos at the University of Cambridge but, as a Jew, was prevented from taking his degree or securing an appointment there. In 1838 he became a professor of natural philosophy at University College, London (the only nonsectarian British university). In 1841 he accepted a professorship of mathematics at the University of Virginia, Charlottesville, U.S.

Born on April 15, 1707, in Basel, Switzerland, Leonhard Euler was one of math's most pioneering thinkers, establishing a career as an academy scholar and contributing greatly to the fields of geometry, trigonometry and calculus, among many others. He released hundreds of articles and publications during his lifetime, and continued to publish after losing his sight. He died on September 18, 1783.

Leonhard Euler was born on April 15, 1707, in Basel, Switzerland. Though originally slated for a career as a rural clergyman, Euler showed an early aptitude and propensity for mathematics, and thus, after studying with Johan Bernoulli, he attended the University of Basel and earned his master's during his teens. Moving to Russia in 1727, Euler served in the navy before joining the St. Petersburg Academy as a professor of physics and later heading its mathematics division.

Pierre Simon Laplace was born at Beaumont-en-Auge in Normandy on March 23, 1749, and died at Paris on March 5, 1827. He was the son of a small cottager or perhaps a farm-labourer, and owed his education to the interest excited in some wealthy neighbours by his abilities and engaging presence.

Secure of a competency, Laplace now threw himself into original research, and in the next seventeen years, 1771-1787, he produced much of his original work in astronomy. This commenced with a memoir, read before the French Academy in 1773, in which he shewed that the planetary motions were stable, and carried the proof as far as the cubes of the eccentricities and inclinations. This was followed by several papers on points in the integral calculus, finite differences, differential equations, and astronomy.