Over the centuries, numerous mathematicians have shaped our understanding of the subject with their innovations and inventions.

Below in this blog, we talk about 20 famous mathematicians in India and abroad and their inventions that have defined mathematics as we understand it today.

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**Mathematicians of foreign origin**

**Pythagoras****Euclid**:**Archimedes**:**Isaac Newton**:**Gottfried Wilhelm Leibniz**:**Carl Friedrich Gauss**:**Ada Lovelace**:**George Boole**:**John von Neumann**:**Albert Einstein**:

(Father of Numbers): He introduced the Pythagorean theorem. This theorem reveals the relationship between the sides of a right-angled triangle, influencing mathematics and shaping various scientific disciplines for centuries.

Also known as the Father of Geometry, he established five postulates forming the basis of Euclidean Geometry. His book, Elements, is a collection of all the knowledge developed in Greek mathematics spanning over 23 centuries of mathematics.

Archimedes established the foundation for calculus with the method of exhaustion and the measurement of a circle’s circumference and area. Archimedes also gave an accurate approximation to “Pi” and showed that he could approximate square roots accurately. He invented a system for expressing large numbers.

Co-inventor of calculus, Newton conceived the Laws of Motion, and the Law of Universal Gravitation, and developed the method of Fluxions, an early form of differentiation for complex calculations – hugely impacting physics and mathematics.

Leibniz invented the modern standard notation for differentiation and made significant contributions to many areas of mathematics like algebra, logic, and topology.

Gauss contributed extensively to number theory, algebra, statistics, and analysis. He is known for the Fundamental Theorem of Algebra and Gauss’s Law in electrostatics.

Known as the world’s first computer programmer, Lovelace devised an algorithm intended to be processed by Charles Babbage’s Analytical Engine, paving the way for modern computing. The example she wrote of one sequence was how to calculate Bernoulli numbers. This is regarded by computer historians as the first computer program.

Boole invented Boolean algebra, the basis of all modern computer arithmetic. This binary system of logic is essential in electrical engineering and computer science.

Notably contributed to the von Neumann architecture, an early model of computation, and the Game Theory, providing a mathematical framework for decision-making processes.

Although primarily known as a physicist, Einstein’s Theory of Relativity intertwines physics and mathematics. It includes the famous Mass-Energy equivalence equation (E=mc^2), which revolutionised mathematical physics.

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**Mathematicians of Indian origin**

**Aryabhata I****Brahmagupta****Bhāskara II****Madhava of Sangamagrama****Nilakantha Somayaji****Raj Chandra Bose****Srinivas Ramanujan****Harish-Chandra****Calyampudi Radhakrishna Rao****Manjul Bhargava**

(476-550): Regarded as the pioneer of Indian mathematics, Aryabhata I was a renowned mathematician and astronomer. His most famous work laid the foundation of algebra and significantly improved number systems. His advancements in astronomical theories remain influential.

(598–668): Brahmagupta was a celebrated mathematician and astronomer who expanded Aryabhata’s work. He is particularly credited for establishing critical rules of arithmetic involving zero and negative numbers. His work, Brāhmasphuṭasiddhānta, presented ground-breaking mathematical theories and astronomical deductions.

(1114–1185): Often known as Bhaskaracharya, Bhāskara II was an esteemed mathematician and astronomer whose work linked ancient and modern mathematics in India. His most famous work, Lilavati, contained comprehensive solutions to mathematics problems involving arithmetic, algebra, and geometry.

One of his most significant works is the “Siddhanta Siromani,” a treatise comprising four parts: Lilāvati (arithmetic), Bijaganit (algebra), Grahaganit (mathematical astronomy), and Golādhyāya (sphere). Bhaskara II is also recognized for his accurate approximations of certain mathematical concepts, including pi and the sine function.

(1350–1425): Founder of the Kerala School of Astronomy and Mathematics, Madhava Sangamagrama introduced infinite series expansions for various trigonometric functions. His works on infinite series, trigonometric functions and geometric series were centuries ahead before similar work was done by European mathematicians.

Madhava’s series of sine, cosine, tangent, and arctangent are significant because they brought in the advent of calculus.

(1444-1544): A disciple of the Kerala School of Astronomy and Mathematics, Somayaji authored several acclaimed works including the “Tantrasangraha,” which covered various aspects of astronomy, and “Aryabhatiyabhasya,” a commentary on Aryabhata’s Aryabhatiya.

Apart from his main focus on astronomy, Somayaji also made important contributions to mathematics, developing sophisticated mathematical techniques for astronomical calculations. His works, particularly the ‘Tantrasangraha,’ influenced later astronomers across regions and timelines.

(1901–1987): Raj Chandra Bose was a renowned Indian mathematician and statistician known for his work in design theory and the theory of error-correcting codes, which had significant implications for communication technology. His research on binary sequences and orthogonal arrays continues to be influential in computer and information science.

(1887–1920): Srinivas Ramanujan’s contributions were in mathematical analysis, number theory, and continued fractions.

His first paper published a 17-page work on Bernoulli numbers that appeared in 1911 in the Journal of the Indian Mathematical Society. Although Ramanujan lacked formal education in mathematics, his natural proficiency led him to formulate theories along with G.H. Hardy, a famous mathematician at Cambridge University.

Hardy and Ramanujan developed a new method, now called the circle method, to derive an asymptotic formula for this function. One significant result of the Hardy-Ramanujan collaboration was a formula for the number p(n) of partitions of a number ‘n’.

(1923–1983): Born as Harish Chandra Mehrotra, he simplified the representation theory of semisimple Lie groups and automorphic forms. His work in infinite-dimensional group representations remains impactful in theoretical physics.[8]

(1920-2023): An eminent statistician, C.R. Rao is renowned for his work in theoretical statistics and mathematics. His contributions, such as the Cramer-Rao inequality and Rao-Blackwell theorem, remain core concepts in statistical theory.

(1974- ): Manjul Bhargava, the first person of Indian origin to win the Fields Medal, is famous for his contributions to number theory. His most significant work includes generalisations of the Gauss composition and his 14 new Gauss-style composition laws.

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At EuroSchool, we believe, the inventions of these brilliant mathematicians have immensely inspired the present-day mathematical advancements in various sectors. From shaping the fundamental principles in traditional mathematics to laying the groundwork for contemporary mathematics, their contributions have substantially transformed the world of mathematics and numbers. Teaching about famous mathematicians is a fascinating and engaging way to introduce students to the world of mathematics and its historical significance.