Indian Mathematicians

Indian Mathematicians

Srinivasa Ramanujan

Srinivasa Ramanujan

Srinivasa Ramanujan was a brilliant mathematician who gets credited even today for his contributions in the field of mathematics.

Born in the year 1887 in Tamil Nadu, Ramanujan was an exceptionally brilliant child who would outshine other children of his age in solving equations. The circumstances of his family were not good and they lived in poverty for most part of their lives, thereby not giving the young Ramanujan an opportunity to pursue his passion-mathematics-due to lack of proper resources.

However the laborious Ramanujan found his inspiration in the book 'Synopsis of elementary results in pure mathematics' by George S. Carr. A brilliant mathematician, Srinivasa Ramanujan is credited today for his contributions in the field of mathematics.

It was due to sheer strength of determination and devotion that the immensely talented mathematician could  invent some of the most crucial equations for the field of mathematical studies- game theory and infinite series. The infinite series for π is used in arithmetical calculations even today.

The year 1914 was the turning point in the struggling life the genius mathematician. He was invited to Cambridge by the very eminent mathematician, G.H.Hardy. Hardy after going through Ramanujan's papers was perplexed by the geniousness of his work. The papers that the young mind had brought along, from home to  Cambridge, were written between the years 1903-14. While some equations had already been discovered, the remainder were entirely new for even G.H.Hardy. He was amazed at Ramanujan's insight into algebraical formulae, transformations of infinite series, etc. In the year 1916, he was awarded his Ph.D. by the university.

The story of this mathematical genius is truly inspiring as Ramanujan had to practice in circumstances that didn't even let him afford enough papers to practice the equations.  A slate and chalk were his most trusted aids. At a very young age, Ramanuj bid goodbye to the world in the year 1920 due to the dreaded disease, Tuberculosis.

Brahmagupta

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Brahmagupta was a seventh century Indian mathematician and astronomer, best known for his book 'Brāhmasphuṭasiddhānta'. The book was the first text that treated zero as a number and gave references for using it in calculations.

Born in the state of Rajasthan, most of his works were in the Sanskrit language, which was the prominent language then. Known also as Bhillamalacarya, the genius mathematician made immense contribution in the field of Arithmetic by not only explaining how to calculate cube and the cube-root of an integer but also providing rules for computation of square and square root.

Brahmagupta could not complete the use of zero in calculations relating to division but he offered other calculations, such as (1 + 0 = 1; 1 - 0 = 1; and 1 x 0 =0), for using the digit zero.

Interestingly, previously calculations such as 3-4 entailed the answer called meaningless. Brahmagupta gave such calculations a meaning by inventing the concept of negative numbers.

Brahmagupta made immense contributions in the field of geometry and trigonometry by establishing √10 (3.162277) as an approximation for π (3.141593).  The other contributions of the accomplished mathematician were the Brahmagupta's Formula and Brahmagupta's Theorem. The former provided a formula for the area of a cyclic quadrilateral while the latter related to the diagonals of a cyclic quadrilateral.

Bhaskara I

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Bhaskara I (c.600 CE-680) was a seventh century Indian mathematician and astronomer credited with the invention of Hindu decimal system. Born in Maharashtra,

Bhaskara's commentary Aryabhatiyabhasya, written in 629 CE, is the oldest known work, in Sanskrit language, on mathematics and astronomy. He was a follower of Aryabhat.

His most notable books were Laghubhāskarīya and Mahabhaskariya

The latter book, divided into eight chapters, dwells into mathematical astronomy. The book is also credited to have given the approximation formula for sin x. Relations between sine and cosine, and also between the sine of an angle >90° >180° or >270° to the sine of an angle <90°  have been given in this book.

The book also discusses about longitudes of the planets, conjunctions of the planets with each other and with bright stars, eclipses of the sun and the moon, risings and settings, and the lunar crescent. Bhaskara I is also known for the Pell Equation ( 8x² + 1 = y² ).

Not much is known about Bhaskara I except that he was born in Parbhani, Maharashtra and died in Andhra Pradesh. He is called Bhaskara I to distinguish from another 12th century mathematician of the same name. It is believed that Bhaskara I's father was his earliest teacher and the book,  Laghubhāskarīya, is an abridged version of his earlier book, Aryabhatiyabhasya. However Bhaskara I along with Brahmagupta is considered to be the greatest ancient Indian mathematicians of all time.

Shakuntala Devi

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Shakuntala Devi was a remarkable lady known for superfast calculations, something that had earned her the title of 'human computer'.

Born in Bangalore in the year 1929, Shakuntala's talent was first observed by her father when he was training her for remembering numbers on the card for the circuses. Shakuntala's father used to work in a circus. Soon after the father - daughter duo were traveling to do street shows based on a young Shakuntala's calculations' talent.

Shakuntala had by the end of year 1944 moved to London thereby traveling across the world doing shows. After all the young prodigy was known to solve the most complex equations within seconds. So much so that the professor of psychology at California University, Arthur Jensen, had called her to the university in the year 1988 to study her exceptional capabilities.

The world was stunned with Shakuntala Devi's talent. In the year 1980, her name was recorded in the Guinness Book of World Record for calculating thirteen digit numbers- 7,686,369,774,870 × 2,465,099,745,779- which were picked at random at the Computer Department of Imperial College, London. She gave the correct answer – 18,947,668,177,995,426,462,773,730- in just 28 seconds.

Shakuntala Devi was also a successful astrologer and author of several books on the subject. She also wrote texts on mathematics for children and puzzles. The immensely gifted mathematician bid her adieu to the world in year 2013.

Aryabhata

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Famously also called Aryabhata I (476-550 CE) or Aryabhata The Elder, in order to distinguish him from another tenth century mathematician of the same name, Aryabhata flourished in Patliputra during Gupta dynasty

Aryabhata was a Scientist, Mathematician as well as an Astronomer. This is so because not only had he discovered that the Earth is spherical, which revolves around the Sun but also that the number of days in a year is 365.

The two most prominent works composed by Aryabhata are Aryabhatiya and the Aryabhatasiddhanta.

The latter is a lost work now while Aryabhatiya was divided into three sections- Ganita (Mathematics), Kala-kriya (Time Calculations), and Gola (Sphere).

In Ganita, Aryabhata has named the first 10 decimal places and given algorithms for obtaining the square and cubic roots by using the decimal number system. Aryabhata had also developed using one of the two methods for creating the table of sines by using Pythagorean theorem. He also realized that second-order sine difference is proportional to sine.

In Kala-kriya Aryabhata discusses about astronomy such as planetary motions, definitions of various units of time, etc.

In Gola, Aryabhata has applied trigonometry to spherical geometry. This also became the apparent basis for prediction of solar and lunar eclipse. The equation in Gola was used by Aryabhata to explain that the rotation of the Earth about its axis was the reason for westward motion of the stars. He also referred to reflections from the Sun for luminosity of the Moon and the planets.

C.R. Rao

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Calyampudi Radhakrishna Rao, considered the doyen of Indian Statistics, has works that have influenced various fields from economics to demography to medicine.

Born in 1879 in Karnataka, Rao had developed interest in the subject mathematics from a very early age. Evident as this is from his earlier account narrating how his father brought for him to solve a book titled 'Problems for Leelavathi' that contained questions by a mathematician for his daughter Leelavathi to solve. He explains how his father would motivate the then eleven years old Rao to try solving five to ten problems every day.

Rao had always keen interest in the subject and this is the reason why he could win for himself the Chandrasekara Iyer Scholarship for both the years at intermediate level. Even M.A, he graduated with first class honours from Andhra University in the year 1940. However it was his year at the Indian Statistical Institute that proved to be a turning point in the life of young Roy. Here he got to publish six papers, jointly (with top researcher K.R. Nair) as well as indepently in the year 1941.

C.R. Rao received gold medal and a first class M.A. degree in Statistics from the Indian Statistical Institute (Kolkata) in the year 1943. Rao' work focussed on four areas- multivariate analysis, linear model, designs in experiments, characterisation of probability distributions- and this focus continued to be his area of specialisation for the rest of his career.

Rao has made important contributions to combinatorial mathematics and a number of  technical terms in statistics such as Cramér-Rao Inequality or Bound (CRB), Rao-Blackwell Theorem, Fisher-Rao Metric, and Rao Distance have been  named after him.

Rao score test  was also created by hi as an alternative to Pearson’s chi-squared test and Wald’s test. C.R. Rao was also instrumental in introducing the concept of ‘quadratic entropy’ — a diversity measure, which could be used to carry out an analysis of diversity of any order.

C.R. Rao under the guidance of his mentor P.C. Mahalanobis has  contributed to the establishment of  statistical bureaus across India. He was conferred the Padma Vibhushan by the Government of India in the year 2001, and the National Medal of Science by President George W Bush in 2002. Aside from the various other awards, the legendary C.R. Rao has been has been awarded thirty-three honorary degrees by universities in eighteen countries if the world.

C.P. Ramanujan

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Chakravarthi Padmanabhan Ramanujam was a gifted Indian mathematician, known for his works on number theory and algebraic geometry.

Born in the year 1938 in Madras (now Chennai), Ramanujan joined the prestigious Loyola college in Madras (now Chennai) for finishing intermediate and college studies after finishing his high school in the year 1952.

C.P. Ramanujan is well known for his rejection of promotion to the position of an Associate Professor at Tata Institute of Fundamental Research (TIFR), Mumbai. Believing this elevation to a higher  position to be  undeserving in nature, he later accepted this post after persuasions by several of his friends and colleagues.

Passionate about the subject mathematics, the young Ramanujan was appreciated well by his doctoral supervisor for in-depth knowledge of the subject.

Ramanujan's personal library had books based in other languages as he was trying to teach himself other languages such as French, German, Russian and Italian to study mathematics in their original forms.

During his stint as a professor at TIFR, Ramanujan published his first two papers in the year 1963, on Waring’s problem for algebraic number fields. The second paper was based on the algebraic half of Siegel’s problem. The paper provided such results that had never been proved. The brilliant mathematician also received great praises for  preparing lecture notes, for highly established mathematicians, that were to be imparted as notes for various courses at TIFR, Mumbai.

Ramanujam had also made significant contributions in the field of algebraic geometry, especially providing clarification on the Kodaira Vanishing Theorem.

Ramanujan had made remarkable contributions in the field of mathematics and these were well appreciated by the international community. However just like S.Ramanujan, C.P. Ramanujan died very early at the young age of only 37. Immediately after his death, a commemorative hall was named after him in the Institute of Mathematics at the University of Genoa.

P.C. Mahalanobis

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P.C. Mahalanobis was an Indian Mathematician, Statistician and Scientist. Not only is he considered the father of Statistics in India but also the hand behind the establishment of Indian Statistical Institute (ISI) in India in the year 1931. He was also instrumental in shaping up of the Planning Commission of India.

Prasanta Chandra Mahalanobis was born in Kolkata in the year 1893. After completing his school education, he received his B.Sc in Physics from Presidency College, Kolkata. Later he went to Cambridge for further studies in Mathematics and Physics.

Mahalanobis is best known for his Mahalanobis Distance or D2-statistic- measure of comparison between two different data sets. In simple words, it is a measurement used for studies in population distribution.

Indian Statistical Institute (ISI) credits all the major statistical work done up till the 1930s to P.C.Mahalanobis. Many  findings of his early studies were of great impact for agricultural development and control of floods.

For Mahalanobis, statistics was a kind of new technology that aided greatly in increasing the efficiency of human effort. The sixty years of flood data, in Odisha, so analysed and published by him in 1926, laid the foundation for installation of Hirakud dam on Mahanadi river, some three decades later.

So great was the influence of his work that not only Statistics was soon recognised as a key discipline but also students majoring in Physics had begun to take interest in Statistics.

S.N. Bose

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Satyendra Nath Bose was an Indian physicist and mathematician, known most famously for Bose-Einstein Condensate. Bose had worked directly with Albert Einstein for this project. A certain type of particle named 'boson' or the 'God Particle' was assigned to Bose in recognition of the contributions made by Bose. Bose is therefore often referred to as “The Father of the God Particle”.

Born in the year 1894 in Kolkata, Bose had always been an intelligent child excelling in education at every turn. By the years 1913 and 1915 respectively, he had finished his B.Sc and M.Sc in Mathematics while also at the same time outperforming his other classmates.

S.N.Bose enrolled himself at the University College of Science in the year 1917 for further studies. It is during his tenure as a student there that Bose got to study theories of Statistical Mechanics by American mathematician J.Willard Gibbs and theory of relativity by Albert Einstein. Bose in collaboration with another bright fellow from his batch started translating the works of Einstein into English from German and French languages. This of course only after getting permission from Einstein.

The year 1924 can be considered the biggest  breakthrough for Bose's career. During this year was published a paper in which Bose had derived Planck’s 'quantum radiation law' without making any reference to the classical theories of physics. This work got all the more importance because Planck’s law had yet not been proved. This paper was submitted by Bose to Einstein for a review. Einstein was impressed with Bose's research. A translated copy of the research, in German language, was submitted to the European Physics Journal by Einstein himself along with a letter of personal recommendation. Einstein soon used the basic concept by Bose for further research into the field of material physics.

Further research by Peter Higgs and Francois Englert, in the field of God particle so clearly set by Bose, led them to winning the Nobel Prize in physics in the year 2013. Though Bose was never awarded this honour, many noted scientists believe Bose rightly deserved the award.

From the years 1927, when Bose was made the head of the physics department in University of Kolkata, till 1945 Bose was working in his field of expertise. During later years Bose moved towards literature, philosophy and Indian independence movement.

Bose had received not only Padma Vibhushan for his notable works but also been appointed for various prestigious positions at different universities. For instance,  being an adviser to the Council of Scientific and Industrial Research or the presidentship of Indian Physical Society and the National Institute of Science. He was also awarded the fellowship for the Royal Society in London in 1958. Satyendra Nath Bose died in the year 1974.

Anil Kumar Gain

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Anil Kumar Gain was an Indian mathematician, statistician and educationist. Gain was the founder of Vidyasagar University, named after the social reformer, Ishwar Chand Vidyasagar.

Born in Bengal in the year 1919, Gain as a young learner had always had great interest in subjects mathematics and english. He was a gold medalist in M.A. from the University of Calcutta degree before getting a doctorate in mathematics in the year 1950, from the University of Cambridge.

Gain's most significant contribution is his works on Pearson product-moment correlation coefficient in the field of applied statistics, along with his colleague Ronald Fisher.

Gain was the president of the statistics section of the Indian Science Congress Association. He also served as the head of the Department of Mathematics at the Indian Institute of Technology, Kharagpur. The eminent mathematician was also was honoured by the Royal Statistical Society and the Cambridge Philosophical Society. He died in the year 1978 in Bengal.

Mahavira

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Mahavira was a ninth century Indian mathematician known for separating astrology from mathematics. No exact information is available as to where he was exactly born, but it is mentioned that it was probably the Mysuru state of Southern India.

Mahavira made significant contributions in the field of algebra. The book written by him, Ganitasarasangraha, is composed of mathematical procedures such as basic operations, reductions of fractions, miscellaneous problems involving a linear or quadratic equation with one unknown, the rule of three (involving proportionality), mixture problems, geometric computations with plane figures, ditches (solids), and shadows (similar right-angled triangles).

His work was highly acclaimed because of his contributions to the establishment of terminology for concepts such as equilateral and isosceles triangle; rhombus; circle and semicircle.

Mahavira was the first mathematician to explain that negative numbers don't have square roots.

The brilliant mathematician's works were highly recognised in Southern India and his texts were referred to by many scholars from southern India.

Ganesh Prasad

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Ganesh Prasad, an eminent Indian mathematician, specialised in the theory of potentials, theory of functions of a real variable, Fourier series and the theory of surfaces.

Born in the year 1876, in the state of Uttar Pradesh, Ganesh Prasad's notable works include 'A Treatise on Spherical Harmonics' and the 'Functions of Bessel and Lame'.

After obtaining his M.A. and D.Sc degrees from Allahabad University, he had, in the year 1899, moved to Cambridge for further research and training as a Government of India scholar. He returned to India in 1904 and that is when he started laying the foundations for developing a culture  of research in India.

This is the reason why Ganesh Prasad is also known as the "father of mathematical researches in India."

Ganesh Prasad had also served as professor at Banaras Hindu University, Muir Central College (Allahabad). In the year 1923, he went to Kolkata to occupy the chair of Hardinge Professor of Mathematics. He was also elected the president of Calcutta Mathematical Society in 1924 and vice-president of Indian Association for the Advancement of Science, Kolkata. He held both these offices till his last. Dr Ganesh Prasad was also the founder member of National Institute of Sciences, India (which is now Indian National Science Academy). He was also one of the founders of the Agra University. Dr Prasad died in the year 1935.

C.S. Seshadri

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C.S. Seshadri is an eminent mathematician, known for the Seshadri Constant (named after him). The well known Indian mathematician was awarded the Padma Bhushan in the year 2009 for his outstanding contributions in the field of mathematics.

Born in the year 1932, Chennai, Seshadri completed his graduation in the subject Mathematics in the year 1953, from Madras University before attending Bombay (now Mumbai) University for a Ph.D in the subject. He completed his doctorate in the year 1958 and later on got elected as a fellow at the Indian Academy of Sciences in 1971. From the years 1953-1984, Seshadri also worked as a research scholar and senior professor, in the later years, at Tata Institute of Fundamental Research (TIFR), Mumbai.

C.S. Seshadri's area of specialisation is algebraic geometry. The Narasimhan–Seshadri theorem, created in collaboration with M.S. Narsimhan, has held a great influence in the field of mathematical studies. Equally well recognised are his works on the Geometric Invariant Theory,  Schubert Varieties, and Standard Monomial Theory.

Seshadri, from the years 1957-1960, was sent to France by TIFR, Mumbai. There he was quite fascinated by French tastes in not just wine and cuisine but also mathematics. Influenced greatly by mathematical geniuses such as Chevalley, Cartan, Schwartz, Grothendieck and Serre, Seshadri returned to India only to become one of the pioneers for starting the School of Mathematics, Tata Institute.

In a career spanning around five decades, C.S. Seshadri has been not only an inspiring teacher for many but also a leader of a whole generation of mathematicians. His contributions have been considered highly critical for development of Moduli problems,  Geometric Invariant Theory as well as Representation Theory of Algebraic Groups. The widely acclaimed mathematician is also the recipient of several prestigious awards such as TWAS Science Award, Honorary D.Sc. from Banaras Hindu University,
Shanti Swarup Bhatnagar Award, Fellow of IAS, INSA and a Fellow of the Royal Society, Honorary degree, Université Pierre et Marie Curie (UPMC), Paris, Fellow of the American Mathematical Society, Srinivasa Ramanujan Medal from the Indian Academy of Sciences, etc.

Radhanath Sikdar

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Radhanath Sikdar is most famously known for his calculation of the height of Mt Everest. He was one of the first two Indians to read Newton’s Principia (the other Indian was Rajnarayan Basak). By the year 1932, the talented mathematician had studied Euclid’s Elements, Jephson’s Fluxion and Analytical Geometry and Astronomy by Windhouse.

Born in Kolkata in the year 1813, Sikdar's first job was conducting geodetic surveys under the then Surveyor General of India, George Everest. He got this job in the year 1931 at the Great Trigonometric Survey.

By the year 1852, Sikdar had started working at the Dehradun headquarters under the student of George Everest, Colonel Andrew Waugh. Here Sikdar was tasked with calculating the height of different peaks for different mountains in the Himalayas. How Radhanath Sikdar came across this reading for the highest peak is interesting. Till date Kanchenjunga was considered the highest peak but a study by James Nicolson had concluded that there might be a higher peak, called the peak XV. This study however had to be left midway as Nicolson contracted malaria.

Sikdar basing his readings on the above calculations calculated the distance of peak XV. It is said that when he found out the measurements, he burst into Waugh's office exclaiming, "Sir, I have discovered the highest mountain in the world."

The peak was later on named Mt Everest and the height, 29002 ft, so calculated by Radhanath Sikdar, was the official height till the year 1955 in India, before an Indian survey recalculated it to 29,092 ft.

George Everest had retired in the year 1843, but the letter he wrote to Radhanath's father back then in appreciation of his work was testimony to the brilliance and unique capabilities of the young Bengali mathematician.

Dattathreya Ramchandra Kaprekar

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Dattathreya Ramchandra Kaprekar (1905–1986), also known as 'Ganitananda', was a recreational mathematician. After receiving his  education from a school in Thane and later from Fergusson College in Pune, Kaprekar, in the year 1927, won the Wrangler R. P. Paranjpe Mathematical Prize for an original piece of work in mathematics.

Though he had received, from the University of Mumbai, his bachelor's degree in the year 1929, yet Kaprekar he could never get any postgraduate training in the subject for himself. He was a teacher at a school on Nashik (Maharashtra), and had worked tirelessly to publish extensively on topics such as recurring decimals, magic squares, and integers with special properties.

Due to his extensive publications he had become a well known in the recreational mathematics circles.

He had described in his works several classes of natural numbers as well as the Kaprekar, Harshad and Self numbers. The Kaprekar constant, named after him, was also discovered by Kaprekar. 6174 is the number, which is also called the Kaprekar Constant.


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