this was given at LVK ,Almora....both presentation were presented in a lucid manner....which provide me Ist prise for twice....really it was a good experience...
History of Ramanujam And His ContributionsVamshi TG
This document provides biographical information about Srinivasa Ramanujan. It states that he was born in 1887 in Erode, India and died in 1920 in Chennai, India. Despite facing obstacles in his formal education, he was able to master advanced mathematics on his own and gained recognition for his works in number theory. He went on to work as a clerk but continued his mathematical research. He was later invited to study at Cambridge University in England, where he made significant contributions before his untimely death at age 32.
Shrinivasa Ramanujan was a renowned Indian mathematician born in 1887 in Tamil Nadu. He made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having little formal training in pure mathematics. Some of his key accomplishments included formulating the Ramanujan prime, the Ramanujan theta function, and pioneering work on mock modular forms and partition theory. He collaborated with English mathematician G.H. Hardy and produced nearly 3,900 results, though he unfortunately died young in 1920 at the age of 32. Ramanujan is celebrated annually in India and considered one of the greatest mathematicians of all time.
Srinivasa Ramanujan was a famous Indian mathematician who made significant contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having little formal training. Some of his key achievements include formulating the Ramanujan prime and the Hardy-Ramanujan number 1729. He worked with the mathematician G.H. Hardy at Cambridge University but suffered from illness and passed away at the young age of 32. His life and work have been celebrated through films, books, and National Mathematics Day in India.
Srinivasa Ramanujan was an Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions. Although he had almost no formal training, his natural talent for mathematics was recognized as being on par with legendary mathematicians such as Gauss, Euler, and Newton. During his short life, Ramanujan independently compiled nearly 3900 mathematical results, many of which have been proven correct and inspired further research. He made significant original discoveries such as the Ramanujan prime and theta function. India now celebrates Ramanujan's birthday as National Mathematics Day in recognition of his remarkable contributions.
Ramanujan was born in 1887 in India and showed extraordinary talent in mathematics from a young age through his notebooks of original mathematical discoveries. He met the mathematician Hardy, who helped bring Ramanujan's work to the attention of the wider mathematics community and invited him to study at Cambridge University in England. Although Ramanujan made many profound contributions before his untimely death at age 32, his work continued to inspire mathematicians for years to come through theorems, formulas, and the notebooks he left behind.
Ramanujan was a renowned Indian mathematician born in 1887 in India. He showed extraordinary talent and self-taught himself advanced mathematics. He struggled to get recognition in India and moved to Cambridge University in England in 1913 where he began collaborating with mathematician G.H. Hardy and made significant contributions before dying young in 1920 at age 32. Ramanujan made substantial unpublished contributions to mathematical analysis, number theory, infinite series, and continued fractions. India now celebrates his achievements and birthday annually with National Mathematics Day.
- Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions with almost no formal training.
- He initially developed his skills in isolation in India before gaining recognition from mathematicians. He then began a famous partnership with the English mathematician G.H. Hardy at Cambridge University in England.
- Ramanujan received a Bachelor of Science by research from Cambridge for his work on highly composite numbers. He was also elected a Fellow of the Royal Society, becoming one of the youngest Fellows in the society's history.
Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having little formal training in pure mathematics. He displayed remarkable talent and intuition for mathematical theories from a young age. Although he struggled with poverty and lack of education, Ramanujan's work attracted the attention of mathematician G.H. Hardy, who helped bring Ramanujan to Cambridge University. There, Ramanujan continued his groundbreaking mathematical research until his untimely death at age 32 from illness. His notebooks contained thousands of results that have inspired continued research by mathematicians seeking to understand his insights and theorems.
History of Ramanujam And His ContributionsVamshi TG
This document provides biographical information about Srinivasa Ramanujan. It states that he was born in 1887 in Erode, India and died in 1920 in Chennai, India. Despite facing obstacles in his formal education, he was able to master advanced mathematics on his own and gained recognition for his works in number theory. He went on to work as a clerk but continued his mathematical research. He was later invited to study at Cambridge University in England, where he made significant contributions before his untimely death at age 32.
Shrinivasa Ramanujan was a renowned Indian mathematician born in 1887 in Tamil Nadu. He made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having little formal training in pure mathematics. Some of his key accomplishments included formulating the Ramanujan prime, the Ramanujan theta function, and pioneering work on mock modular forms and partition theory. He collaborated with English mathematician G.H. Hardy and produced nearly 3,900 results, though he unfortunately died young in 1920 at the age of 32. Ramanujan is celebrated annually in India and considered one of the greatest mathematicians of all time.
Srinivasa Ramanujan was a famous Indian mathematician who made significant contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having little formal training. Some of his key achievements include formulating the Ramanujan prime and the Hardy-Ramanujan number 1729. He worked with the mathematician G.H. Hardy at Cambridge University but suffered from illness and passed away at the young age of 32. His life and work have been celebrated through films, books, and National Mathematics Day in India.
Srinivasa Ramanujan was an Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions. Although he had almost no formal training, his natural talent for mathematics was recognized as being on par with legendary mathematicians such as Gauss, Euler, and Newton. During his short life, Ramanujan independently compiled nearly 3900 mathematical results, many of which have been proven correct and inspired further research. He made significant original discoveries such as the Ramanujan prime and theta function. India now celebrates Ramanujan's birthday as National Mathematics Day in recognition of his remarkable contributions.
Ramanujan was born in 1887 in India and showed extraordinary talent in mathematics from a young age through his notebooks of original mathematical discoveries. He met the mathematician Hardy, who helped bring Ramanujan's work to the attention of the wider mathematics community and invited him to study at Cambridge University in England. Although Ramanujan made many profound contributions before his untimely death at age 32, his work continued to inspire mathematicians for years to come through theorems, formulas, and the notebooks he left behind.
Ramanujan was a renowned Indian mathematician born in 1887 in India. He showed extraordinary talent and self-taught himself advanced mathematics. He struggled to get recognition in India and moved to Cambridge University in England in 1913 where he began collaborating with mathematician G.H. Hardy and made significant contributions before dying young in 1920 at age 32. Ramanujan made substantial unpublished contributions to mathematical analysis, number theory, infinite series, and continued fractions. India now celebrates his achievements and birthday annually with National Mathematics Day.
- Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions with almost no formal training.
- He initially developed his skills in isolation in India before gaining recognition from mathematicians. He then began a famous partnership with the English mathematician G.H. Hardy at Cambridge University in England.
- Ramanujan received a Bachelor of Science by research from Cambridge for his work on highly composite numbers. He was also elected a Fellow of the Royal Society, becoming one of the youngest Fellows in the society's history.
Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having little formal training in pure mathematics. He displayed remarkable talent and intuition for mathematical theories from a young age. Although he struggled with poverty and lack of education, Ramanujan's work attracted the attention of mathematician G.H. Hardy, who helped bring Ramanujan to Cambridge University. There, Ramanujan continued his groundbreaking mathematical research until his untimely death at age 32 from illness. His notebooks contained thousands of results that have inspired continued research by mathematicians seeking to understand his insights and theorems.
Srinivasa ramanujan a great indian mathematicianKavyaBhatia4
Srinivasa Ramanujan was an Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. He developed his mathematical abilities largely through self-study and had a natural genius for mathematics. Ramanujan received recognition during his lifetime, including being elected as a Fellow of the Royal Society, but he died young at age 32. Even on his deathbed, he was working on theorems. His notebooks contained thousands of results without proofs that mathematicians have since worked to prove. Ramanujan's life and accomplishments have inspired biographies and films that highlight his brilliance in mathematics that was largely self-taught.
Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having no formal training in pure mathematics. He was born in 1887 in India and showed an extraordinary aptitude for mathematics from a young age. Ramanujan received recognition after sending letters containing his original mathematical ideas to G.H. Hardy of Cambridge University. Hardy arranged for Ramanujan to travel to Cambridge to pursue mathematical research. There, Ramanujan produced new theorems, continued fractions, and functions and worked with Hardy and Littlewood. He was elected a Fellow of the Royal Society and Trinity College, but his health declined and he returned to India, where he died at
Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having little formal training. He displayed remarkable talent and intuition for mathematical theories from a young age. Ramanujan received recognition after being invited to work with professor G.H. Hardy at Trinity College, Cambridge. Although he struggled with poor health in England, Ramanujan produced groundbreaking mathematical research and formulas before passing away at a young age in 1920. He is regarded as one of the greatest mathematicians and his contributions continue to have an impact.
Srinivasa Ramanujan Date Of Birth 22.12.1887Padma Lalitha
In last slide I have mentioned Srinivasa Ramanujan D.O.B. as
22.12.1987. I am extremely sorry for that. Please read it as 22.12.1887. Thanks to my friend Smt. Indira, who brought it to my notice.
Significant contribution of indian mathematiciansSAIVARSHINE
Srinivasa Ramanujan was an influential Indian mathematician who made important contributions to number theory, including the Hardy-Ramanujan-Littlewood circle method. He was largely self-taught and sent theorems he had discovered to Professor Hardy at Cambridge University, who invited him to study there. Ramanujan showed that any big number can be written as the sum of not more than four prime numbers and how to divide numbers into squares or cubes in multiple ways. Brahmagupta was significant for introducing the concept of zero to mathematics, representing nothing. The document goes on to discuss other influential Indian mathematicians like Aryabhatta, Shakuntala Devi, and Bhaskaracharya.
1) Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions.
2) He was mostly self-taught and discovered his talent for mathematics at a young age without access to formal education.
3) In 1913, he wrote a letter to G.H. Hardy including theorems and results that Hardy found extraordinary and helped arrange for Ramanujan to travel to Cambridge University where they collaborated until Ramanujan's death in 1920.
(1) Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having little formal training in pure mathematics.
(2) He was born in 1887 in India and showed an extraordinary aptitude for mathematics from a young age, mastering advanced mathematical concepts including trigonometry at age 13.
(3) Ramanujan received recognition for his genius and was invited to study at Trinity College, Cambridge in England. However, he struggled with the climate and culture in England and his health declined, and he ultimately returned to India where he passed away in 1920 at the young age of 32.
This ppt is on Srinivasa Ramanujan FRS was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical
Srinivasa Ramanujan was one of India's greatest mathematical geniuses, making substantial contributions to analytical number theory and working on elliptic functions, continued fractions, and infinite series. He was born in 1887 in Tamil Nadu, India and showed great mathematical aptitude from a young age. Some of his key works included discovering properties of cyclicity in numbers, identifying the number 1729 as the smallest number expressible as the sum of two cubes in two different ways, and constructing magic squares in which the sums of all rows, columns and diagonals are equal.
1) Srinivasa Ramanujan was one of India's greatest mathematical geniuses who made substantial contributions to analytical number theory, elliptic functions, and infinite series.
2) He was mostly self-taught and showed extraordinary talent from a young age, mastering advanced mathematical concepts from books he received.
3) Ramanujan struggled for recognition in India but eventually his work was brought to the attention of the English mathematician G.H. Hardy, who helped arrange for Ramanujan to travel to Cambridge University in 1914 where he spent five productive years collaborating before falling ill and returning to India, where he passed away in 1920.
Srinivasa Ramanujan was an Indian mathematician who made significant contributions to mathematical analysis, number theory, infinite series, and continued fractions. He developed his own theorems and ideas after discovering a book of mathematical results as a teenager. Ramanujan struggled to find employment due to pursuing mathematics instead of other studies. He gained recognition after publishing his first paper in 1911 and corresponding with the British mathematician G.H. Hardy. Despite religious objections, Ramanujan traveled to England in 1914 where he collaborated with Hardy and made further advances, especially in partitioning numbers. He was elected to the Royal Society of London but died in 1920 at the young age of 32, having made pioneering discoveries and being recognized as a mathematical genius.
Srinivasa Ramanujan was an Indian mathematician who made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions. Some of his key achievements include discovering the Ramanujan summation to assign values to divergent infinite series, deriving the Rogers-Ramanujan continued fraction, and finding remarkable infinite series for pi that enabled computing more decimal places with each term. He also made contributions to theories of numbers, elliptic curves, partition functions, and highly composite numbers. Despite having almost no formal training, Ramanujan made lasting contributions through his extraordinary intuition for mathematical objects and patterns.
Srinivasa Ramanujan Aiyangar was an Indian mathematician born in 1887 in India. He showed great talent and self-taught himself advanced mathematics from a young age. In 1913, he sent letters containing his original mathematical research to professors in Cambridge University. This led to him receiving a scholarship to study at Trinity College, Cambridge where he collaborated with professor G.H. Hardy and made significant contributions to mathematical analysis, number theory, infinite series, and continued fractions. Despite dying young at the age of 32, Ramanujan made substantial contributions to mathematical research.
Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite his lack of formal training. Some of his key achievements include formulating the Ramanujan prime and discovering the Ramanujan theta function. He worked closely with his mentor, G.H. Hardy, at Cambridge University where he was elected Fellow of the Royal Society. Unfortunately, Ramanujan's life was cut short at the young age of 32, but he left a lasting legacy as one of the greatest mathematicians of all time.
Srinivasa Ramanujan (1887-1920) was a renowned Indian mathematician who made extensive contributions to mathematical analysis, number theory, infinite series, and continued fractions. He had almost no formal training in pure mathematics but had a natural genius and aptitude in the field. Ramanujan's work attracted the attention of the English mathematician G.H. Hardy, who helped Ramanujan move to Cambridge University. There, Ramanujan continued his groundbreaking mathematical research before passing away at a young age. His work inspired entire new areas of mathematics and earned him recognition as one of the greatest mathematicians of all time.
Srinivasa Ramanujan FRS was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical
Srinivasa Ramanujan A great INDIAN MATHEMATICIANSchooldays_6531
We Indians are not too great but we have some GREATEST personalities like Aryabhatta -- Who gave the world ZERO
This is a small presentation on life history of Srinivasa Ramanujan.
Please LIKE and SHARE.
Great indian mathmatician -srinivasan ramanujanMahip Singh
Srinivasa Ramanujan was a mathematical genius born in 1887 in India. He showed great mathematical ability from a young age through self-study. Despite facing many struggles due to lack of funds and proper education, he gained recognition for his work. In 1913, he received a letter of support from mathematician G.H. Hardy, and was eventually brought to Trinity College, Cambridge in 1914, where he spent the last years of his life producing groundbreaking mathematical work before passing away in 1920 at a young age.
Srinivasa ramanujan a great indian mathematicianKavyaBhatia4
Srinivasa Ramanujan was an Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. He developed his mathematical abilities largely through self-study and had a natural genius for mathematics. Ramanujan received recognition during his lifetime, including being elected as a Fellow of the Royal Society, but he died young at age 32. Even on his deathbed, he was working on theorems. His notebooks contained thousands of results without proofs that mathematicians have since worked to prove. Ramanujan's life and accomplishments have inspired biographies and films that highlight his brilliance in mathematics that was largely self-taught.
Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having no formal training in pure mathematics. He was born in 1887 in India and showed an extraordinary aptitude for mathematics from a young age. Ramanujan received recognition after sending letters containing his original mathematical ideas to G.H. Hardy of Cambridge University. Hardy arranged for Ramanujan to travel to Cambridge to pursue mathematical research. There, Ramanujan produced new theorems, continued fractions, and functions and worked with Hardy and Littlewood. He was elected a Fellow of the Royal Society and Trinity College, but his health declined and he returned to India, where he died at
Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having little formal training. He displayed remarkable talent and intuition for mathematical theories from a young age. Ramanujan received recognition after being invited to work with professor G.H. Hardy at Trinity College, Cambridge. Although he struggled with poor health in England, Ramanujan produced groundbreaking mathematical research and formulas before passing away at a young age in 1920. He is regarded as one of the greatest mathematicians and his contributions continue to have an impact.
Srinivasa Ramanujan Date Of Birth 22.12.1887Padma Lalitha
In last slide I have mentioned Srinivasa Ramanujan D.O.B. as
22.12.1987. I am extremely sorry for that. Please read it as 22.12.1887. Thanks to my friend Smt. Indira, who brought it to my notice.
Significant contribution of indian mathematiciansSAIVARSHINE
Srinivasa Ramanujan was an influential Indian mathematician who made important contributions to number theory, including the Hardy-Ramanujan-Littlewood circle method. He was largely self-taught and sent theorems he had discovered to Professor Hardy at Cambridge University, who invited him to study there. Ramanujan showed that any big number can be written as the sum of not more than four prime numbers and how to divide numbers into squares or cubes in multiple ways. Brahmagupta was significant for introducing the concept of zero to mathematics, representing nothing. The document goes on to discuss other influential Indian mathematicians like Aryabhatta, Shakuntala Devi, and Bhaskaracharya.
1) Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions.
2) He was mostly self-taught and discovered his talent for mathematics at a young age without access to formal education.
3) In 1913, he wrote a letter to G.H. Hardy including theorems and results that Hardy found extraordinary and helped arrange for Ramanujan to travel to Cambridge University where they collaborated until Ramanujan's death in 1920.
(1) Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having little formal training in pure mathematics.
(2) He was born in 1887 in India and showed an extraordinary aptitude for mathematics from a young age, mastering advanced mathematical concepts including trigonometry at age 13.
(3) Ramanujan received recognition for his genius and was invited to study at Trinity College, Cambridge in England. However, he struggled with the climate and culture in England and his health declined, and he ultimately returned to India where he passed away in 1920 at the young age of 32.
This ppt is on Srinivasa Ramanujan FRS was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical
Srinivasa Ramanujan was one of India's greatest mathematical geniuses, making substantial contributions to analytical number theory and working on elliptic functions, continued fractions, and infinite series. He was born in 1887 in Tamil Nadu, India and showed great mathematical aptitude from a young age. Some of his key works included discovering properties of cyclicity in numbers, identifying the number 1729 as the smallest number expressible as the sum of two cubes in two different ways, and constructing magic squares in which the sums of all rows, columns and diagonals are equal.
1) Srinivasa Ramanujan was one of India's greatest mathematical geniuses who made substantial contributions to analytical number theory, elliptic functions, and infinite series.
2) He was mostly self-taught and showed extraordinary talent from a young age, mastering advanced mathematical concepts from books he received.
3) Ramanujan struggled for recognition in India but eventually his work was brought to the attention of the English mathematician G.H. Hardy, who helped arrange for Ramanujan to travel to Cambridge University in 1914 where he spent five productive years collaborating before falling ill and returning to India, where he passed away in 1920.
Srinivasa Ramanujan was an Indian mathematician who made significant contributions to mathematical analysis, number theory, infinite series, and continued fractions. He developed his own theorems and ideas after discovering a book of mathematical results as a teenager. Ramanujan struggled to find employment due to pursuing mathematics instead of other studies. He gained recognition after publishing his first paper in 1911 and corresponding with the British mathematician G.H. Hardy. Despite religious objections, Ramanujan traveled to England in 1914 where he collaborated with Hardy and made further advances, especially in partitioning numbers. He was elected to the Royal Society of London but died in 1920 at the young age of 32, having made pioneering discoveries and being recognized as a mathematical genius.
Srinivasa Ramanujan was an Indian mathematician who made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions. Some of his key achievements include discovering the Ramanujan summation to assign values to divergent infinite series, deriving the Rogers-Ramanujan continued fraction, and finding remarkable infinite series for pi that enabled computing more decimal places with each term. He also made contributions to theories of numbers, elliptic curves, partition functions, and highly composite numbers. Despite having almost no formal training, Ramanujan made lasting contributions through his extraordinary intuition for mathematical objects and patterns.
Srinivasa Ramanujan Aiyangar was an Indian mathematician born in 1887 in India. He showed great talent and self-taught himself advanced mathematics from a young age. In 1913, he sent letters containing his original mathematical research to professors in Cambridge University. This led to him receiving a scholarship to study at Trinity College, Cambridge where he collaborated with professor G.H. Hardy and made significant contributions to mathematical analysis, number theory, infinite series, and continued fractions. Despite dying young at the age of 32, Ramanujan made substantial contributions to mathematical research.
Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite his lack of formal training. Some of his key achievements include formulating the Ramanujan prime and discovering the Ramanujan theta function. He worked closely with his mentor, G.H. Hardy, at Cambridge University where he was elected Fellow of the Royal Society. Unfortunately, Ramanujan's life was cut short at the young age of 32, but he left a lasting legacy as one of the greatest mathematicians of all time.
Srinivasa Ramanujan (1887-1920) was a renowned Indian mathematician who made extensive contributions to mathematical analysis, number theory, infinite series, and continued fractions. He had almost no formal training in pure mathematics but had a natural genius and aptitude in the field. Ramanujan's work attracted the attention of the English mathematician G.H. Hardy, who helped Ramanujan move to Cambridge University. There, Ramanujan continued his groundbreaking mathematical research before passing away at a young age. His work inspired entire new areas of mathematics and earned him recognition as one of the greatest mathematicians of all time.
Srinivasa Ramanujan FRS was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical
Srinivasa Ramanujan A great INDIAN MATHEMATICIANSchooldays_6531
We Indians are not too great but we have some GREATEST personalities like Aryabhatta -- Who gave the world ZERO
This is a small presentation on life history of Srinivasa Ramanujan.
Please LIKE and SHARE.
Great indian mathmatician -srinivasan ramanujanMahip Singh
Srinivasa Ramanujan was a mathematical genius born in 1887 in India. He showed great mathematical ability from a young age through self-study. Despite facing many struggles due to lack of funds and proper education, he gained recognition for his work. In 1913, he received a letter of support from mathematician G.H. Hardy, and was eventually brought to Trinity College, Cambridge in 1914, where he spent the last years of his life producing groundbreaking mathematical work before passing away in 1920 at a young age.
Srinivasa Ramanujan (1887-1920) was a renowned Indian mathematician. He showed early signs of genius in mathematics as a child. He was self-taught and made significant contributions to mathematical analysis, number theory, infinite series, and continued fractions. Ramanujan developed his own theorems and results without any formal training. He was recognized by mathematicians in England and his work was found to be of extraordinary significance. However, he struggled with poor health and poverty, and ultimately died young at the age of 32 in India. Ramanujan is celebrated annually in India on his birthday as a brilliant mathematician who made major contributions despite facing disadvantages.
Aryabhata was an ancient Indian mathematician who made several important contributions to mathematics and astronomy, including developing an accurate approximation of pi and a system of astronomy called the aud Ayaka system. He also studied integer solutions to Diophantine equations of the form ax + by = c, helping to lay the foundations for later work in number theory.
S. Ramanujan was a renowned Indian mathematician born in 1887 in Tamil Nadu. He made extensive contributions to mathematical analysis, number theory, infinite series, and continued fractions. Some of his key achievements included developing new theorems regarding partition functions, elliptic functions, highly composite numbers, and discovering the Ramanujan prime and the Ramanujan theta function. Despite his untrained background, he was elected to the Fellowship of the Royal Society due to his exceptional genius and intuition for mathematical discoveries. He collaborated extensively with English mathematician G.H. Hardy and produced nearly 3,900 results, though most were without proof. Ramanujan passed away in 1920 at the young age of 32 due to illness.
Este documento presenta una actividad realizada con estudiantes de décimo grado para aprender sobre el número pi. Los estudiantes investigaron la historia de pi, obtuvieron su valor usando materiales como círculos de CD, y analizaron las diferencias en los resultados debido a limitaciones en la precisión de las medidas. La actividad les permitió comprender mejor la naturaleza irracional de pi y el concepto de error en mediciones.
Indian Mathematicians And Their Contributiondivyanshsngh
The document discusses several notable Indian mathematicians and their contributions, including:
- Srinivasa Ramanujan who made significant contributions to mathematical analysis, number theory, infinite series, and continued fractions.
- Aryabhata who proposed that the earth rotates on its axis and revolves around the sun. He also introduced trigonometric functions and the concept of zero.
- Brahmagupta who established rules for operations involving zero and developed concepts of addition, subtraction, multiplication, and division of negative numbers.
Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having no formal training in pure mathematics. He was born in 1887 in India and showed an extraordinary aptitude for mathematics from a young age. Ramanujan struggled to get recognition until he was introduced to the English mathematician G.H. Hardy through letters containing his original research. Hardy arranged for Ramanujan to work at Cambridge University where he spent the last years of his life conducting groundbreaking mathematical research before passing away in 1920 at the young age of 32. Ramanujan made substantial contributions to mathematical functions and analysis and continues to have a significant impact on mathematics despite his short life
Srinivasa Ramanujan was an Indian mathematician who made significant contributions to mathematical analysis, number theory, and continued fractions. He showed great aptitude for mathematics from a young age, mastering advanced concepts independently without formal training. Ramanujan struggled for recognition in India but eventually gained the support of G.H. Hardy in England. Working with Hardy, Ramanujan made advances in partition theory and the Riemann zeta function before dying at age 32.
Srinivasa Ramanujan was one of India's greatest mathematical geniuses, making substantial contributions to analytical number theory and worked on elliptic functions, continued fractions, and infinite series. He was born in 1887 in Tamil Nadu, India and showed great mathematical ability from a young age, though he was unable to complete a college education. Despite his lack of formal training, he gained recognition for his work in mathematics and was elected to the London Mathematical Society in 1918. Ramanujan made many advances in mathematical analysis, number theory, infinite series, and continued fractions. He passed away in 1920 at the young age of 32.
Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. He was born in 1887 in India and showed remarkable mathematical genius from a very young age, mastering advanced mathematical concepts on his own. Ramanujan received recognition after sending letters containing his original research to G.H. Hardy. He went on to collaborate with Hardy and others at Cambridge University. Despite his untimely death at age 32, Ramanujan made lasting advances in mathematical fields and unlocked new areas of research through his intuitive insights and discoveries recorded in his notebooks.
Srinivasa Ramanujan was a renowned Indian mathematician who made significant contributions to mathematical analysis, number theory, infinite series, and continued fractions. He had no formal training in pure mathematics but taught himself and made major discoveries. Despite facing doubts and struggles, he produced thousands of results and theorems. Ramanujan received honors including election as a Fellow of the Royal Society. He worked with English mathematician G. H. Hardy and brought Indian mathematical concepts to Western science before passing away at a young age.
National Mathematics Day Celebration 22 DecemberRakibulSK3
Srinivasa Ramanujan was a great Indian
mathematician . He was born on 22nd December
1887 in Erode (Tamil Nadu) during British
Government .His full name was Srinivasa Iyenger
Ramanujan . His father name was Kuppuswamy
Srinivasa Iyenger and his mother’s name was
Komalatammal. He was enrolled in the Town
higher Secondary School from 1897-1904 , Wherehe encountered formal mathematics for the first Time.
By age 11, he had exhausted the mathematical knowledge of two college students who were lodgers at his home .He was latter lent a book on advanced
trigonometry written by S.L.Loney. He completely mastered on this book by the age of 13 and discovered
Sophisticated theorems on his own . In July 1909,
Ramanujan married S.Janaki Ammal , who was then
Just 10 years old . The Cambridge mathematician
G.H. Hardy arranged for Ramanujan to visit Trinity
College in Cambridge .Ramanujan arrived in Cambridge in 1914 and He completed his graduation from Cambridge University ,London . He made a lot of his theories which are very popular in the world and That is why His theories still get used in lots of countries . He wrote many books Comprising his theories and formulas . He is famous for his contribution to number theory and infinite Series .His birthday is celebrated as National Mathematics Day in India every year .He was died on 26th April 1920 ,at the age of 32 years in Madras . He Worked for a very short period but his teaching are Still alive in many people’s mind and text books .His Contribution in the Field of mathematics has been immense and will be remembered forever.
During his short life, Ramanujan independently compiled nearly 3,900 results (mostly identities and equations).[6] Many were completely novel; his original and highly unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired a vast amount of further research.[7] Of his thousands of results, all but a dozen or two have now been proven correct.[8] The Ramanujan Journal, a scientific journal, was established to publish work in all areas of mathematics influenced by Ramanujan,[9] and his notebooks—containing summaries of his published and unpublished results—have been analysed and studied for decades since his death as a source of new mathematical ideas. As late as 2012, researchers continued to discover that mere comments in his writings about "simple properties" and "similar outputs" for certain findings were themselves profound and subtle number theory results that remained unsuspected until nearly a century after his death.[10][11] He became one of the youngest Fellows of the Royal Society and only the second Indian member, and the first Indian to be elected a Fellow of Trinity College, Cambridge. Of his original letters, Hardy stated that a single look was enough to show they could have been written only by a mathematician of the highest Ramanujan.
Srinivasa Ramanujan was a famous Indian mathematician who made significant contributions to mathematical analysis, number theory, infinite series, and continued fractions. He had a natural talent for mathematics and made many complex discoveries on his own. Despite coming from a poor background and having no formal training, he brought impressive theorems and results to the attention of Western mathematicians. Ramanujan collaborated with G.H. Hardy at Cambridge University, where he received his degree. He returned to India at age 32 and continued his research, but sadly died young from illness. Ramanujan's work inspired further research and he is celebrated in India for his mathematical genius.
This document provides biographical details about Srinivasa Ramanujan in 3 paragraphs:
1) It introduces Ramanujan, noting he was born in 1887 in India and showed extraordinary talent for mathematics from a young age, self-studying advanced mathematical concepts. He struggled in school due to focusing only on mathematics.
2) It describes Ramanujan's early life circumstances - he came from a traditional Brahmin family and had a close relationship with his mother. He excelled at mathematics but failed out of college due to poor performance in other subjects.
3) It outlines Ramanujan's path to recognition for his mathematical genius in India in the early 1910s, including gaining support and introductions
Srinivasa Ramanujan was a renowned Indian mathematician born in 1887 in India. He made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Despite lacking formal training, he independently compiled nearly 3900 mathematical results. Ramanujan received recognition from G.H. Hardy at Trinity College, Cambridge and was elected as a Fellow of the Royal Society. He worked with Hardy and others before passing away in 1920 at the young age of 32. Ramanujan's work inspired further research and he is regarded as one of the greatest mathematicians of all time.
Ramanujan was born in 1887 in India. He showed exceptional talent for mathematics from a young age, mastering advanced concepts by himself as a teenager. Though he lacked a formal degree, he made major contributions to mathematical functions and number theory. In 1909, he came to the attention of the mathematician G. H. Hardy, who helped get Ramanujan's work published. Ramanujan spent from 1914-1919 collaborating with Hardy at Cambridge University, but poor health forced his return to India, where he died in 1920 at age 32. Today he is remembered as one of the greatest mathematicians of all time for entirely original contributions.
Srinivasa Ramanujan was an Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, and infinite series. He had almost no formal training but was a natural genius who developed his own mathematical research in isolation in India. Some of his most notable work included discovering theorems on his own and re-discovering Euler's identity independently as a young boy. He is renowned for his work on Bernoulli numbers, the Euler-Mascheroni constant, and introducing several analytic functions and infinite series. Ramanujan demonstrated unusual mathematical skills from a young age and conducted his own research on advanced mathematical topics with no college education.
The document provides biographical information about the mathematician Srinivasa Ramanujan. It discusses that he was born in 1887 in India and showed early talent for mathematics without formal training. He independently discovered thousands of theorems. In 1913, he wrote a letter to G.H. Hardy including his work, which impressed Hardy. Ramanujan then went to Cambridge University where he collaborated with Hardy. He received recognition but struggled with health issues and returned to India, where he died in 1920 at a young age. His notebooks contained novel mathematical discoveries that have opened new areas of research.
Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having no formal training in mathematics. He was born in 1887 in India and showed an early aptitude for mathematics. Ramanujan's genius was recognized by English mathematician G.H. Hardy, who brought him to Cambridge University. There, Ramanujan continued his groundbreaking mathematical research but fell ill and returned to India, where he passed away in 1920 at the age of 32. Ramanujan made lasting contributions through theorems and results recorded in his notebooks that were studied by mathematicians for decades following his death.
Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having no formal training in mathematics. He was born in 1887 in India and showed an early aptitude for mathematics. Ramanujan's genius was recognized by English mathematician G.H. Hardy, who brought him to Cambridge University. There, Ramanujan continued his groundbreaking mathematical research but fell ill and returned to India, dying in 1920 at the age of 32. Ramanujan made major discoveries that have influenced mathematics and he is now celebrated as one of history's greatest mathematical minds.
Srinivasa Ramanujan was born in 1887 in Tamil Nadu, India. He was a gifted student who became fascinated with mathematics at a young age after obtaining a book compiling mathematical results. Despite failing his college exams due to focusing solely on mathematics, he gained recognition for his mathematical abilities and published his first paper in 1911. He struggled to find support for his work until he wrote to mathematician G.H. Hardy, who was amazed by Ramanujan's talents and helped bring him to Cambridge University in 1914. There, they had a highly successful collaboration, making discoveries like a formula for the partition function p(n), though Ramanujan's health suffered in the foreign climate and culture. He returned to India in
Srinivasa Ramanujan was born in 1887 in India and showed extraordinary talent in mathematics from a very young age. He mastered advanced mathematical concepts entirely on his own from books in his local library. Ramanujan's genius was further awakened after studying a book on 5000 mathematical theorems. He went on to make significant contributions to mathematical analysis, number theory, infinite series, and continued fractions. Despite having no formal training, Ramanujan was eventually recognized by mathematicians at Cambridge University, where he was elected as a Fellow.
Ramanujan was a renowned Indian mathematician born in 1887 in India. He showed extraordinary talent and self-taught himself advanced mathematics. He struggled to get recognition in India and moved to Cambridge University in England in 1913 where he began collaborating with mathematician G.H. Hardy and made significant contributions before dying young in 1920 at age 32. Ramanujan made substantial unpublished contributions to mathematical analysis, number theory, infinite series, and continued fractions. India now celebrates his achievements and birthday annually with National Mathematics Day.
Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having no formal training in pure mathematics. He was born in 1887 in India and showed an extraordinary aptitude for mathematics from a young age. Ramanujan struggled to find recognition for his mathematical genius in India but eventually his notebooks were sent to the English mathematician G.H. Hardy, who helped Ramanujan gain admission to Cambridge University. There, Ramanujan continued his groundbreaking mathematical research before falling ill and returning to India, where he passed away in 1920 at the young age of 32. Ramanujan made substantial contributions to mathematical fields and is regarded as one of the
Srinivasa Ramanujan was one of India's greatest mathematical geniuses. He was born in 1887 in a small village in India and showed a strong aptitude for mathematics from a young age, teaching himself advanced mathematical concepts from books. Despite facing health and financial issues that prevented him from attending university, he gained recognition for his brilliant work on mathematical theories and continued to make significant contributions on his own.
Ramanujan was a famous mathematician born in 1887 in Erode, India. He made contributions to analytical number theory and developed relations between elliptic modular equations. Despite difficulties, he received a scholarship to study mathematics and began solving problems in the Journal of the Indian Mathematical Society. Ramanujan went on to hold a clerk position and continued developing his mathematical ideas until his untimely death in 1920.
Srinivasa Ramanujan was a self-taught Indian mathematician who made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions. He was born in 1887 in India and showed an extraordinary aptitude for mathematics from a young age. Ramanujan's work attracted the attention of the English mathematician G.H. Hardy, and in 1914 Ramanujan traveled to Cambridge University in England, where he collaborated with Hardy and other mathematicians. However, Ramanujan's health declined in England due to illness and malnutrition, and he returned to India in 1919, dying there in 1920 at the age of 32. Ramanujan is regarded as one of the greatest mathematicians of his time.
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2. BIRTH & CHILDHOOD
Srinivasa Ramanujan better known as Srinivasa
Iyengar Ramanujan was one of India's greatest
mathematical geniuses. Ramanujan was born in his
grandmother's house in Erode 22 December
1887 , a small village about 400 km southwest of
Madras. His parents were K. Srinivasa Iyengar
and Komalatammal. When Ramanujan was a year
old his mother took him to the town of
Kumbakonam, about 160 km nearer Madras. His
father worked in Kumbakonam as a clerk in a cloth
merchant's shop.
3. PRIMARY EDUCATION
When he was nearly five years old, Ramanujan entered the
primary school in Kumbakonam although he would attend
several different primary schools before entering the Town
High School in Kumbakonam in January 1898. At the Town
High School, Ramanujan was to do well in all his school
subjects and showed himself an able all round scholar. In
1900 he began to work on his own on mathematics
summing geometric and arithmetic series. It was in the
Town High School that Ramanujan came across a
mathematics book by G S Carr called Synopsis of
elementary results in pure mathematics. This book, with its
very concise style, allowed Ramanujan to teach himself
mathematics
4. SCHOLARSHIP
Ramanujan, on the strength of his good school
work, was given a scholarship to the Government
College in Kumbakonam which he entered in 1904.
However the following year his scholarship was not
renewed because Ramanujan devoted more and
more of his time to mathematics and neglected his
other subjects. Without money he was soon in
difficulties and, without telling his parents, he ran
away to the town of Vizagapatnam about 650 km
north of Madras. He failed in English in
Intermediate .
5. STRUGGLE & HARDWORK
In 1906 Ramanujan went to Madras where he entered
Pachaiyappa's College. His aim was to pass the First Arts
examination which would allow him to be admitted to the
University of Madras. He attended lectures at
Pachaiyappa's College but became ill after three months
study. He took the First Arts examination after having left
the course. He passed in mathematics but failed all his
other subjects and therefore failed the examination. This
meant that he could not enter the University of Madras.
Continuing his mathematical work Ramanujan studied
continued fractions and divergent series in 1908. At this
stage he became seriously ill again and underwent an
operation in April 1909 after which he took him some
considerable time to recover.
6. He married on 14 July 1909 when his mother
arranged for him to marry a ten year old girl S
Janaki Ammal. Ramanujan did not live with his
wife, however, until she was twelve years old.
Ramanujan continued to develop his mathematical
ideas and began to pose problems and solve
problems in the Journal of the Indian Mathematical
Society. After publication of a brilliant research
paper on Bernoulli numbers in 1911 in the Journal
of the Indian Mathematical Society he gained
recognition for his work. Despite his lack of a
university education, he was becoming well known
in the Madras area as a mathematical genius.
7. In 1911 Ramanujan approached the founder of the
Indian Mathematical Society for advice on a job. After
this he was appointed to his first job, a temporary
post in the Accountant General's Office in Madras. It
was then suggested that he approach Ramachandra
Rao who was a Collector at Nellore. Ramachandra Rao
was a founder member of the
Indian Mathematical Society who had helped start the
mathematics library. He writes in ……….
“A short uncouth figure, stout, unshaven, not over clean, with one
conspicuous feature-shining eyes- walked in with a frayed notebook under
his arm. He was miserably poor. ... He opened his book and began to explain
some of his discoveries. I saw quite at once that there was something out of
the way; but my knowledge did not permit me to judge whether he talked
sense or nonsense. ... I asked him what he wanted. He said he wanted a
pittance to live on so that he might pursue his researches”.
8. Ramachandra Rao told him to return to
Madras and he tried, unsuccessfully, to
arrange a scholarship for Ramanujan. In
1912 Ramanujan applied for the post of
clerk in the accounts section of the
Madras Port Trust. In his letter of
application he wrote ……….
“I have passed the Matriculation Examination and studied
up to the First Arts but was prevented from pursuing my
studies further owing to several untoward circumstances. I
have, however, been devoting all my time to Mathematics
and developing the subject”.
9. Despite the fact that he had no university education,
Ramanujan was clearly well known to the university
mathematicians in Madras for, with his letter of
application, Ramanujan included a reference from E
W Middlemast who was the Professor of
Mathematics at The Presidency College in Madras.
Middlemast, a graduate of St John's College,
Cambridge, wrote ………….
“I can strongly recommend the applicant. He is a
young man of quite exceptional capacity in
mathematics and especially in work relating to
numbers. He has a natural aptitude for
computation and is very quick at figure work”.
10. On the strength of the recommendation Ramanujan was
appointed to the post of clerk and began his duties on 1
March 1912. Ramanujan was quite lucky to have a number
of people working round him with a training in
mathematics. In fact the Chief Accountant for the Madras
Port Trust, S N Aiyar, was trained as a mathematician and
published a paper On the distribution of primes in 1913 on
Ramanujan's work. The professor of civil engineering at the
Madras Engineering College C L T Griffith was also
interested in Ramanujan's abilities and, having been
educated at University College London, knew the professor
of mathematics there, namely M J M Hill. He wrote to Hill
on 12 November 1912 sending some of Ramanujan's work
and a copy of his 1911 paper on Bernoulli numbers.
11. Hill replied in a fairly encouraging way but showed that he
had failed to understand Ramanujan's results on divergent
series. The recommendation to Ramanujan that he read
Bromwich's Theory of infinite series did not please
Ramanujan much. Ramanujan wrote to E W Hobson and H
F Baker trying to interest them in his results but neither
replied. In January 1913 Ramanujan wrote to G H Hardy
having seen a copy of his 1910 book Orders of infinity. In
Ramanujan's letter to Hardy he introduced himself and his
work……..
‘”I have had no university education but I have undergone the ordinary
school course. After leaving school I have been employing the spare time at
my disposal to work at mathematics. I have not trodden through the
conventional regular course which is followed in a university course, but I
am striking out a new path for myself. I have made a special investigation of
divergent series in general and the results I get are termed by the local
mathematicians as 'startling”.
12. Hardy, studied the long list of unproved
theorems which Ramanujan enclosed with his
letter. On 8 February he replied to Ramanujan,
the letter beginning……
“I was exceedingly interested by your letter and
by the theorems which you state. You will
however understand that, before I can judge
properly of the value of what you have done, it
is essential that I should see proofs of some of
your assertions”.
13. Ramanujan was delighted with Hardy's reply and when he
wrote again he said…..
“ I have found a friend in you who views my labours sympathetically. ...
I am already a half starving man. To preserve my brains I want food
and this is my first consideration. Any sympathetic letter from you will
be helpful to me here to get a scholarship either from the university or
from the government”.
Indeed the University of Madras did give Ramanujan a
scholarship in May 1913 for two years and, in 1914, Hardy
brought Ramanujan to Trinity College, Cambridge, to begin an
extraordinary collaboration. Setting this up was not an easy
matter. Ramanujan was an orthodox Brahmin and so was a
strict vegetarian. His religion should have prevented him from
travelling but this difficulty was overcome, partly by the work of
E H Neville who was a colleague of Hardy's at Trinity College
and who met with Ramanujan while lecturing in India.
14. Ramanujan fell seriously ill in 1917 and his doctors
feared that he would die. He did improve a little by
September but spent most of his time in various
nursing homes. In February 1918 Hardy wrote
Batty Shaw found out, what other doctors did not
know, that he had undergone an operation about four
years ago. His worst theory was that this had really
been for the removal of a malignant growth, wrongly
diagnosed. In view of the fact that Ramanujan is no
worse than six months ago, he has now abandoned
this theory - the other doctors never gave it any
support. Tubercle has been the provisionally accepted
theory, apart from this, since the original idea of
gastric ulcer was given up. ... Like all Indians he is
fatalistic, and it is terribly hard to get him to take care
of himself.
15. Ramanujan died of tuberculosis in
Kumbakonam on April 26, 1920. He was only
32 years old. “It was always maths ... Four
days before he died he was scribbling,” said
Janaki, his wife……….
As Times Magazine rightly wrote: “There is
something peculiarly sad in the spectacle of
genius dying young, dying with the first sweets
of recognition and success tasted, but before
the full recognition of powers that lie within.
16. RESEARCH WORK
Ramanujan showed that any big number can
be written as sum of not more than four prime
numbers.
He showed that how to divide the number into
two or more squares or cubes.
when Mr Litlewood came to see Ramanujan in
taxi number 1729, Ramanujan said that 1729 is
the smallest number which can be written in
the form of sum of cubes of two numbers in
two ways, i.e. 1729 = 93 + 103 = 13 + 123
since then the number 1729 is called
Ramanujan’s number.
17. HONOUR
On 18 February 1918 Ramanujan was elected a fellow
of the Cambridge Philosophical Society and then three
days later, the greatest honour that he would receive,
his name appeared on the list for election as a fellow
of the Royal Society of London .He had been proposed
by an impressive list of mathematicians, namely Hardy
, MacMahon, Grace, Larmor, Bromwich, Hobson, Baker
, Littlewood, Nicholson, Young, Whittaker, Forsyth and
Whitehead. His election as a fellow of the
Royal Society was confirmed on 2 May 1918, then on
10 October 1918 he was elected a Fellow of Trinity
College Cambridge, the fellowship to run for six year .
18. The honours which were bestowed on Ramanujan
seemed to help his health improve a little and he
renewed his effors at producing mathematics. By the
end of November 1918 Ramanujan's health had
greatly improved. Hardy wrote in a letter….
I think we may now hope that he has turned to corner, and is
on the road to a real recovery. His temperature has ceased to
be irregular, and he has gained nearly a stone in weight. ...
There has never been any sign of any diminuation in his
extraordinary mathematical talents. He has produced less,
naturally, during his illness but the quality has been the same.
He will return to India with a scientific standing and reputation
such as no Indian has enjoyed before, and I am confident that
India will regard him as the treasure he is. His natural simplicity
and modesty has never been affected in the least by success -
indeed all that is wanted is to get him to realise that he really is
a success.
19. Prime Minister Manmohan Singh has declared
2012 ‘national mathematics year’ in honor of
maths wizard Srinivasa Ramanujan’s 150th
birth anniversary.
“Along with CV Raman and Subramanyam
Chandrashekhar (both Nobel laureates), he is
among the three great men of science and
mathematics that Tamil Nadu and India have
given to the world of modern times”, he said.