MATHEMATICIANS

FAMOUS MATHEMATICIANS AND THEIR CONTRIBUTIONS

EUCLID •„Euclid of Alexandria‟ was a (325 BC-265 BC) Greek Mathematician. •Referred to as “Father of Geometry”. •His major contribution was „Elements of Geometry‟; a compilation of the most important mathematical facts.

Life and Works of Euclid • Euclid unified a collection of isolated discoveries into a single deductive systems based on a set of initial postulates, definitions and axioms. • His „Elements‟ is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry).

• He was the first mathematician who initiated a new way of thinking the study of geometry. • Euclid‟s „Elements‟ is a collection of 13 books:- 1-6 are of plane geometry, 7-9 are of no. theory, 10 is the theory of irrational no.‟s, 11-13 are of 3-D geometry. • His other major works include Data, Divisions, Optics, Phenomena.

Contributions • Euclidean Geometry states that the sum of the angles of a triangle is 180˚. • Formulated a method to find out HCF. • Gave a proof that prime no.‟s are infinite. • First who proved √2 as a transcendental no.

SRINIVASA RAMANUJAN (22/12/1887-26/04/1920) •Ramanujan was an Indian Mathematician who lived during the British Rule in India. •He made substantial contributions to mathematical analysis, number theory, infinite series and continued fractions. •He is known as an all-time great Indian Mathematician.

Life and Works • He was a self taught mathematician. • Expert in trigonometry at the age 12 and discovered theorems of his own. • Contributed a synopsis of Elementary Results in Pure and Applied Mathematics which acknowledged in awakening the genius of Ramanujan. • He was best known for Landau-Ramanujan Constant, Mock theta functions, Ramanujan Conjecture, Ramanujan‟s Prime etc. • He quoted that “An equation for me has no meaning unless it expresses a thought of god” (showing that he was deeply religious).

Contributions • Introduced the property of Ramanujan Number, 1729 . ( It is the smallest natural no. that can be represented in two different ways and a sum of two cubes:- 1729=13+123=93+103 It is also the product of 3 prime numbers; 7×13×19) • Ramanujan independently developed and investigated the Bernoulli numbers and calculated the Euler Mascheroni Constant upto 15 decimal places. • Ramanujan's other notable contributions include hypergeometric series, the Riemann series, the elliptic integrals, the theory of divergent series, and the functional equations of the zeta function. • December 22, being the birthday of Srinivasa Ramanujan has been declared as the “National Mathematics Day” to be celebrated every year.

ARYABHATTA •Aryabhatta was born in AD 476 at Kusumapura, India. •He was the first major Indian Mathematician and astronomer of the classical age. •His major contributions are Aryabhatiya and the Arya Siddhanta. (476 AD-550 AD)

Life and Works • His major work Aryabhatiya, a compendium of mathematics covers arithmetic algebra, plane trigonometry etc. • He worked on the „place value system‟ using letters to signify numbers and stating qualities . • He was the one to calculate the value if Pi, observed solar and lunar eclipses, he found out the length of the year and came up with heliocentric model and much more.

Contributions • He discovered the positions of the 9 planets and found that these planets revolve round the sun. • Calculated the value of Pi. • Calculated the summation of series of squares and cubes, • Determined the area of a triangle.

BRAHMAGUPTA (590 AD-668 AD) •He was born to Vishnu Gupta at Punjab and lived Ujjain. •He was the first Indian Mathematician and astronomer who introduce the concept about zero and gave rules to compute with zero. •He was the first Indian writer who applied algebra to astronomy. •He was known as „ Bhillamalacharya‟(teacher from Bhillamala)

Life and Works • He composed the first book „Brahmasphutasiddhanta‟ at the age of 30. • He introduced four different methods of multiplications namely, Gun Mantrika, Khanda, Bheda, Ista. • He explained the method of inversion for the first time. • He gave the method of squaring and cubing. • His works on arithmetic includes integer fractions, progressions, barter, simple interest, the mensuration of plane figures and problems on volumes.

Contributions • One of the most significant input of Brahmagupta to mathematics was the introduction of zero to the number system which stood for „nothing‟. • His major contribution „Brahmasphutasiddhanta‟ consists of 21 chapters and contains great knowledge on arithmetic, geometric, algebra and astronomy. • He found the formula for geometric progression a+ar+ar2+…n terns = a(rn -1)/(r-1)

RENE DESCARTES (31 March1596-11 February •He was a French Philosopher, 1650) mathematician and scientist who invented analytic geometry. •He is known as the Father of Modern Mathematics . •He was also the Founder of Modern Philosophy. •He ranks as one of the most important and influential thinkers of modern times.

Life and Works • He is famous for having made an important connection between geometry and algebra, which allowed for the solving of geometrical problems by way of algebraic equations. • His famous works includes Meditationes de Prima Philosophia . • He claimed that education except mathematics gave him little of substance; only mathematics had gave him certain knowledge. • He was the first major figure in the philosophical movement known as Rationalism ( a method of understanding the world based on the use of reason).

Contributions • His greatest contribution was developing analytical geometry, which is applying algebra to geometry. • He established coordinate plane system, which he developed to visualize and locate exact points. • He introduced a methodological scepticism (doubted everything but wants certainty in life. • He laid the foundation for the development of calculus. • He also did groundbreaking work in physics most prominently in the field of optics.

PYTHAGORAS (570 BC-490 BC) •Pythagoras of Samos was an ancient Greek philosopher and the eponymous founder of Pythagoreanism. •He is often described as the first pure mathematician. •His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy.

Life and Works • He founded a philosophical and religious school in Croton. • His followers were commonly referred to as Pythagoreans. • He made important developments in music and astronomy. • He was an accomplished musician at playing the lyre. • He was the head of the society with an inner circle of followers known as mathematikoi. They were taught by Pythagoras himself and obeyed strict rules. • Rather than to formulate of solve mathematical problems, he was interested in the principles of mathematics, the concept of number, the concept of a triangle or other mathematical figure and the abstract idea of proof

Contributions • His major contribution was the Pythagorean theorem (base2+altitude2 = hypotnuse2 for a right angled triangle) • His other contributions include Pythagorean tuning, the five regular solids, the Theory of Proportions, the sphericity of the Earth, and the identity of the morning and evening stars as the planet Venus. • Pythagoras was the first person to recommend music as a prescription. He connected music to craftsmanship, design, government, raising a family, fellowship, and self-improvement. He thought it was possible to align the souls to their perfect nature, and through music he performed what he called “soul adjustments.”

BHASKARACHARYA •Bhaskaracharya, was an Indian Mathematician and Astronomer. • His father Mahesvara was a mathematician, astronomer and astrologer, who taught him mathematics. •He was the only ancient mathematician who has been immortalized on a monument. •He had been called the greatest mathematician of Medieval India. (1114 AD-1185 AD)

Life and Works • He was the greatest mathematician of medieval India. • He was the leader of a cosmic observatory at Ujjain, the main mathematical centre of ancient India. • His main work Siddhanta-Siromani, divided into four parts called Lilavati, Bijaganita, Grahaganita and Goladhyaya. These four sections deal with arithmetic, algebra, mathematics of the planets and spheres respectively. • He was particularly known for the discovery of the principles of differential calculus and its application to astronomical problems and computations. • He also wrote another treatise named Karana Kautuhala.

Contributions • He gave a proof of the Pythagorean theorem by calculating the same area in two different ways and then cancelling out terms to get a2 + b2 = c2. • Solutions of quadratic, cubic and quartic indeterminate equations are explained. • In Siddhanta-Siromani, Bhaskara developed spherical trigonometry along with a number of other trigonometric results. • Calculated the derivatives of trigonometric functions and formulae. • H e was the first to gave a general method to solve the Pell‟s equations(x2 − ny2 = 1) • Stated Rolle‟s theorem.