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Answer:
sorry I write about only one mathematician because brainly can't expect more then 5000 word answer
Step-by-step explanation:
Here are concise but comprehensive profiles of two notable Indian mathematicians: Srinivasa Ramanujan and Bhāskara II.
Srinivasa Ramanujan (1887-1920)
Early Life and Education
Srinivasa Ramanujan was born on December 22, 1887, in Erode, Tamil Nadu, India. From a young age, he showed an extraordinary aptitude for mathematics. He excelled in mathematics in school but struggled with other subjects. At age 16, he discovered G.S. Carr’s book "A Synopsis of Elementary Results in Pure and Applied Mathematics," which fueled his passion for advanced mathematical concepts.
Early Career and Struggles
Despite his talent, Ramanujan faced significant challenges. He attended several schools but failed to secure a degree due to his focus on mathematics to the detriment of other subjects. He worked in various clerical positions while independently pursuing his mathematical interests.
Collaboration with G.H. Hardy
In 1913, Ramanujan sent a letter containing some of his mathematical results to G.H. Hardy at the University of Cambridge. Hardy recognized the brilliance of Ramanujan’s work and invited him to Cambridge. With support from the University of Madras, Ramanujan arrived in England in 1914.
Contributions to Mathematics
Ramanujan made significant contributions to various areas of mathematics, including number theory, continued fractions, and infinite series. Some of his notable contributions include:
- Ramanujan Prime and Ramanujan Theta Function: His work on prime numbers and theta functions.
- Partition Function: Counting the number of distinct ways of representing a number as a sum of positive integers.
- Mock Theta Functions: These functions later played a crucial role in the development of modern number theory.
Later Years and Legacy
Ramanujan’s health deteriorated in England. He returned to India in 1919 and continued his work until his death on April 26, 1920, at age 32. His legacy endures through the vast body of work he left behind, inspiring further research and discoveries in mathematics. The Ramanujan Journal and the annual Ramanujan Prize honor his contributions.
Bhāskara II (1114-1185)
Early Life and Education
Bhāskara II, also known as Bhāskarāchārya, was born in 1114 in Bijapur, Karnataka, India. He belonged to a lineage of scholars and received a comprehensive education under his father, Mahesvara, an accomplished mathematician and astronomer.
Major Works and Contributions
Bhāskara II is renowned for his seminal works in mathematics and astronomy, including "Lilavati," "Bijaganita," and "Siddhanta Shiromani." Each of these texts made significant contributions to their respective fields.
- Lilavati (Arithmetic): Deals with arithmetic and algebra, presenting problems and their solutions in a poetic form.
- Bijaganita (Algebra): Focuses on algebra, including solutions of quadratic, cubic, and quartic equations.
- Siddhanta Shiromani (Astronomy): Divided into four parts: Lilavati (arithmetic), Bijaganita (algebra), Grahaganita (mathematics of planets), and Goladhyaya (sphere). This work provides an extensive treatment of mathematical astronomy.
Contributions to Mathematics and Astronomy
Bhāskara II made numerous contributions, such as:
- Calculus Concepts: His work contains early ideas of calculus, such as differentiation and integration.
- Diophantine Equations: Solutions to certain types of equations that were later named after him.
- Astronomical Observations: He accurately described planetary motions and eclipses.
Legacy
Bhāskara II’s work influenced both Indian and Islamic mathematicians. His texts were studied and translated, impacting mathematical and astronomical thought for centuries. Today, his legacy is celebrated for the profound and lasting contributions he made to mathematics and astronomy.
These concise profiles provide an overview of the lives and contributions of Srinivasa Ramanujan and Bhāskara II, highlighting their impact on the field of mathematics.
Answer:
Srinivasa Ramanujan
Srinivasa Ramanujan (22 December 1887 – 26 April 1920) was an Indian mathematician who, despite having almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Born in Erode, Tamil Nadu, Ramanujan displayed a natural affinity for mathematics at a young age, developing complex theorems and solving problems that were considered unsolvable at the time.
His work caught the attention of British mathematician G.H. Hardy, with whom he began a famous collaboration. Ramanujan’s genius led him to produce groundbreaking new theories, including the properties of the partition function and the Ramanujan prime and theta functions. He also made deep contributions to the analytical theory of numbers and worked on elliptic functions and infinite series.
Ramanujan’s health deteriorated during his time in England, and he returned to India in 1919, where he died a year later at the young age of 32. His legacy continues to inspire mathematicians around the world, and his notebooks—filled with unpublished results—have been studied by scholars for decades after his death'.
Aryabhata
Aryabhata, also known as Aryabhata I to distinguish him from later mathematicians with the same name, was born in 476 CE in what is now Bihar, India. He is recognized as one of the first major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy.
His most celebrated work is the Āryabhaṭīya, written in 499 CE when he was just 23 years old. This work consists of 118 verses and describes the mathematics and astronomy of Aryabhata’s time. The Āryabhaṭīya covers a wide range of topics, including arithmetic, algebra, plane trigonometry, spherical trigonometry, and astronomy.
In mathematics, Aryabhata is credited with introducing the place value system and the concept of zero to the world. He worked on the approximation of pi (π), and his estimate—3.1416—is remarkably close to the actual value. He also gave methods for solving linear and quadratic equations.
In astronomy, Aryabhata proposed a heliocentric model where the Earth rotates on its axis daily and revolves around the Sun annually. He calculated the length of the sidereal year with remarkable accuracy at 365 days, 6 hours, 12 minutes, and 30 seconds.
Aryabhata’s work significantly influenced mathematics and astronomy in the medieval Islamic world. His texts were translated into Arabic, and his ideas were incorporated into Islamic knowledge, which later reached Europe.
Aryabhata’s legacy continues to be celebrated in India; his birth anniversary is observed as National Mathematics Day in India. The country’s first satellite, Aryabhata, launched in 1975, was named in his honor.
Brahmagupta
Brahmagupta (c. 598 – c. 668 CE) was an Indian mathematician and astronomer who authored two significant works: the Brāhmasphuṭasiddhānta (BSS) in 628 CE, which is a theoretical treatise, and the Khaṇḍakhādyaka in 665 CE, a more practical text.
His work in mathematics included defining zero for the first time and explaining how to use it in calculations. He also developed rules for dealing with negative numbers and operations involving zero. Brahmagupta’s rules governing arithmetic operations with zero and negative numbers are still in use today.
In astronomy, Brahmagupta made significant contributions by arguing that the Earth and the universe are spherical and not flat. He was among the first to use mathematics to predict the positions of planets and the timings of lunar and solar eclipses, which were major scientific advancements at the time.
Brahmagupta’s influence extended beyond India. His works were translated into Arabic and had a profound impact on Islamic and Byzantine astronomy. His texts were studied by scholars in the Islamic world, who used his mathematical rules and astronomical models.
Brahmagupta’s religious views, particularly the Hindu yuga system of measuring the ages of mankind, also influenced his astronomical work. Despite this, his mathematical and astronomical theories have stood the test of time and continue to be relevant.