July 10, 2023

What Mathematicians/Scientist say about Indian Mathematics

1.

“India is, the cradle of the human race, the birthplace of human speech, the mother of history, the grandmother of legend, and the great grandmother of tradition. our most valuable and most instructive materials in the history of man are treasured up in India only.” – Mark Twain

2.

“Gravitation was known to the Hindus (Indians) before the birth of Newton. The system of blood circulation was discovered by them centuries before Harvey was heard of.”                                         – P. Johnstone

3

“We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made.” – Albert Einstein

4.

It is high time that the full story of Indian mathematics from Vedic times through 1600 became generally known. I am not minimizing the genius of the Greeks and their wonderful invention of pure mathematics, but other peoples have been doing math in different ways, and they have often attained the same goals independently. Rigorous mathematics in the Greek style should not be seen as the only way to gain mathematical knowledge. In India, where concrete applications were never far from theory, justifications were more informal and mostly verbal rather than written. One should also recall that the European Enlightenment was an orgy of correct and important but semi rigorous math in which Greek ideals were forgotten. The recent episodes with deep mathematics flowing from quantum field and string theory teach us the same lesson: that the muse of mathematics can be wooed in many different ways and her secrets teased out of her. And so they were in India … David Mumford 

5.

“After the conversations about Indian philosophy, some of the ideas of Quantum Physics that had seemed so crazy suddenly made much more sense.” – W. Heisenberg (German Physicist, 1901-1976)

6.

“Our present knowledge of the nervous system fits in so accurately with the internal description of the human body given in the Vedas (5000 years ago). Then the question arises whether the Vedas are religious books or books on anatomy of the nervous system and medicine.” – B G Rele (The Vedic Gods)

7.

"How great is the science which revealed itself in the Sulba, and how meagre is my intellect! I have aspired to cross the unconquerable ocean in, a mere raft." ---- B Datta 

8.

 The Vedic Hindu, in his great quest of the Para-vidya, Satyasya Sa tyam , made progress in the Apara-Vidya, including the various arts and sciences, to a considerable extent, and with a completeness which is unparalleled in antiquity." -----B Datta 

9.

The Indians have an extremely subtle and penetrating intellect, and when it comes to arithmetic, geometry and other such advanced disciplines, other ideas must make way for theirs. "I will omit all discussion of the science of the Indians, a people not the same as the Syrians; of their subtle discoveries in astronomy, discoveries that are more ingenious than those of the Greeks and the Babylonians; and of their valuable methods of calculation which surpass description."----- (Severus Sebokht in 662 AD) "

10.

"Indeed, if one understands by algebra. the application of arithmetical operations to complex magnitudes of all sorts, whether rational or irrational numbers or spacemagnitudes, then the learned Brahmins of Hindostan are the real inventors of algebra." ----- H Hanke

11.

"The intellectual potentialities of the Indian nation are unlimited and not many years would perhaps be needed before I ndia can take a worthy place in world Mathematics." ---(Andre Weil in 1936)

12.

"India has given to antiquity the earliest scientific physicians, and, according to Sir William Hunter, she has even contributed to modern medical science by the discovery of various chemicals and by teaching you how to reform misshapen ears and noses. Even more it has done in mathematics, for algebra, geometry, astronomy, and the triumph of modern science - mixed mathematics - were all invented in India, just so much as the ten numerals, the very cornerstone of all present civilization, were discovered in India, and, are in reality, sanskrit words." ----Swami Vivekananda

13.

The Hindus solved problems in interest, discount, partnership, alligation, summation of arithmetical and geometric series, and devised rules for determining the numbers of combinations and permutations. It may here be added that chess, the profoundest of all games, had its origin in India."--- F Cajori

14.

" ... it is remarkable to what extent Indian mathematics enters into the science of our time. Both the form and the spirit of the arithmetic and algebra of modern times are essentially Indian. Think of our notation of numbers, brought to perfection by the Hindus, think of the Indian arithmetical operations nearly as perfect as our own, think of their elegant algebraical methods, and then judge whether the Brahmins on the banks of the Ganges are not entitled to some credit."--- F Cajori 

15.

"Incomparably greater progress than in the solution of determinate equations was made by the Hindus in the treatment of indeterminate equations. Indeterminate analysis was a subject to which the Hindu mind showed a happy adaptation." --   F Cajori 

16.

"Unfortunately, some of the most brilliant results in indeterminate analysis, found in the Hindu works, reached Europe too late to exert the influence they would have exerted, had they come two or three centuries earlier." ---F Cajori

17.

"As I look back upon the history of my country, I do not find in the whole world anothercountry which has done quite so much for the improvement of the human mind. Therefore I have no words of condemnation for my nation. I tell them, 'You have done well; only try to do better.' Great things have been done in the past in this land, and there is both time and room for greater things to be done yet ... Our ancestors did great things in the past, but we have to grow into a fuller life and march beyond even their great achievement. " --- Swami Vivekananda (Complete Works Vol III p.195)

18.

"There is no question of the superiority of the Hindus over their rivals in the perfection to which they brought the science. Not only is Aryabhatta superior to Diaphantus (as is shown by his knowledge of the resolution of equations involving several unknown quantities, and in general method of  resolving all indeterminate problems of at least the first degree), but he and his successors press hard upon the discoveries of algebraists who lived almost in our own time!"
                                           - Sir Mountstuart Elphinstone (1779 - 1859)  

19.

 It is very important to note that some 2,500 years ago at the least Pythagoras went from Samos to the Ganges to learn geometry...But he would certainly not have undertaken such a strange journey had the reputation of the Brahmins' science not been long established in Europe..."

    - Francois Marie Arouet Voltaire (1694-1774) France's greatest writer and philosopher.

20.
     " It is more likely that Pythagoras was influenced by India than by Egypt. Almost all the theories, religions, philosophical and mathematical taught by the Pythagoreans, were known in India in the sixth century B.C., and the Pythagoreans, like the Jains and the Buddhists, refrained from the destruction of life and eating meat and regarded certain vegetables such as beans as taboo. "It seems that the so-called Pythagorean theorem of the quadrature of the hypotenuse was already known to the Indians in the older Vedic times, and thus before Pythagoras.”

Prof. H. G. Rawlinson 19th Century, British historian and author
21.

 “We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made.” -    Albert Einstein

22.

It is certain that the Vedic Indians knew something of astronomy and that it had a high utilitarian value for them as it did for all peoples of antiquity. The Vedic priests had to make careful calculations of times for their rituals and sacrifices, and also had to determine the time of sowing and harvest. Moreover, astronomical periods played an important role in Vedic thought for they were successive parts of the ever-returning cosmic cycle.”- Fritjof Capra (Physicist)

23.

It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.”

 Pierre-Simon Laplace

24.

The Indian system of counting is probably the most successful intellectual innovation ever devised by human beings. It has been universally adopted. ...It is the nearest thing we have to a universal language. --- John D. Barrow

        25.
        “Hindu cosmology  gives a time-scale for the earth and the universe which is consonant with that of modern scientific cosmology”, as opposed to the limited Biblical-Quranic cosmology, which was protected against more far-sighted alternatives by a vigilant religious orthodoxy. ---- Carl Sagan

        26.

        It is clear how much we owe to this brilliant civilization, and not only in the field of arithmetic; by opening the way to the generalization of the concept of the number, the Indian scholars enabled the rapid development of mathematics and exact sciences. The discoveries of these men doubtless required much time and imagination and, above all, a great ability for abstract thinking. These major discoveries took place within an environment which was at once mystical, philosophical, religious, cosmological, mythological and metaphysical.-       Georges Ifrah.

        27.

        I once heard, and I think it is true, that only one man in the world—some Indian mathematician—understood the mathematics of string theory in eleven-dimensional space, and he dreamed it. ---- Mullis, Kary B  

        28.

        In the Shulba Sutra appended to Baudhayana’s Shrauta Sutra, mathematical instructions are given for the construction of Vedic altars. One of its remarkable contributions is the theorem usually ascribed to Pythagoras, first for the special case of a square (the form in which it was discovered), then for the general case of the rectangle: “The diagonal of the rectangle produces the combined surface which the length and the breadth produce separately.” --- Elst, Koenraad

         29.

        I shall not now speak of the knowledge of the Hindus … of their suitable discoveries in the science of astronomy—discoveries even more ingenious than those of the Greeks and Babylonians, of their rational system of mathematics, or of their method of calculation which no words can praise strongly enough; I mean the system using nine symbols. --- Severus Sebokht

         

        30.

        When I read the Bhagavad Gita and reflect about how God created this universe everything else seems so superfluous. ---Albert Einstein

        31.

        “Modern physics has shown that the rhythm of creation and destruction is not only manifest in the turn of the seasons and in the birth and death of all living creatures, but is also the very essence of inorganic matter,” and that “For the modern physicists, then, Shiva’s dance is the dance of subatomic matter.”

        “Hundreds of years ago, Indian artists created visual images of dancing Shivas in a beautiful series of bronzes. In our time, physicists have used the most advanced technology to portray the patterns of the cosmic dance. The metaphor of the cosmic dance thus unifies ancient mythology, religious art and modern physics.”-       Fritjof Kapra

        32.

        Everything has come down to us from the banks of Ganges ---- Francois Voltaire

        33.

        If there is a country on earth which can justify the claim the honour of having been the cradle of the Human race or at least the scene of primitive civilization, the successive developments of which carried into all parts of the ancient world and even beyond the blessings of knowledge which is the second life of man, that country is assuredly India. -- Friedrich Creuzer - German philologist and archaeologist.

        34.  

        • Access to the Vedas is the greatest privilege this century may claim over all previous centuries.” --- Julius Robert Oppenheimer
        • 35.  
        • The Bhagavad Gita… is the most beautiful philosophical song existing in any known tongue. -- --- Julius Robert Oppenheimer - Inventor of Atom Bomb
        • 36.
        • A millennium before Europeans were willing to divest themselves of the Biblical idea that the world was a few thousand years old, the Mayans were thinking of millions and the Hindus billions ---Carl Sagan
        • 37.
        • That Hindu astronomical lore about ancient times cannot be based on later back-calculation, was also argued by Playfair’s contemporary, the French astronomer jean-Sylvain Bailly: “The motions of the stars calculated by the Hindus before some 4500 years vary not even a single minute from the [modem] tables of Cassini and Meyer. The Indian tables give the same annual variation of the moon as that discovered by Tycho Brahe - a variation unknown to the school of Alexandria and also the Arabs. - Jean Sylvain Bally French Astronomer
        • 38. 
        • Most of my ideas & theories are heavily influenced by Vedanta - Erwin Schrödinger









June 16, 2023

MATHEMATICS/SCIENCE EXAM - 2023 (NMTC / VVM)

 1. NMTC (National Mathematics Talent Contest) 2023 - An examination being conducted by AMTI (Association of Mathematics Teachers of India) 

STUDENTS FROM CLASS 5 -12 CAN APPLY FOR THIS EXAM




VVM (VIDYARATHI VIGYAN MANTHAN)
STUDENTS FROM CLASS 6 -11 CAN APPLY


REGISTRATION OF NMTC / VVM IS OPEN 

EXPECTED SYLLABUS

SYLLABUS OF OTHER SUBJECTS IS 90% NCERT TEXT BOOK. 


FOR MORE DETAILS CLICK THE FOLLOWING LINK-


DO APPLY 

May 8, 2023

JAGRAN MATHEMATICS SCREENING TEST

 Dear Students,

As you know that there is a difference between the syllabus taught in School and question asked in different competition examination. The gap of Syllabus is too high. In most of the competition, the question paper is prepared for two levels. 

Junior Group (6-8) and Senior Group (9-11). The questions are designed in such a way that only students who are very good at Mathematics, analytical and passionate in Mathematics can crack them.

1. VVM (Vidyarathi Vigyan Manthan

2. IOQM (Indian Olympic Qualifier in Mathematics)

3. NTSE (National Talent Search Examination)

4.  Aryabhata Examination ( By CBSE)

5. BMTSC (Bhaskaracharya Mathematics Talent Search Competition)

6. NMTC (National Mathematics Talent Contest)

7. All India Ramanujan Mathematics Olympiad

8. Aryabhata/Ramanujan National Math Challenge - (All India Council of Technical Skill Development)


 REGISTER YOUR SELF FOR THE TEST IN ADVANCE

 It is my initiative to train the students in Higher Mathematics so as the gap between the current syllabus and Syllabus of different Competitive Examination can be filled and they feel comfortable in facing the challenges. The test has been designed to select a group of students who are good at Mathematics and eager to learn something different and new,                                                                                                                                                                   

                                                      Link for Junior Group (6-8) and Senior Group (9-11) are different. Click the link carefully. There are 20 questions in all to be done in 60 minutes (maximum)                       

                                                  

                                          LINK FOR TEST (CLASS 6- 8)


                                      LINK FOR TEST (CLASS 9 -11)


Best of Luck to All
Dr Rajesh Thakur

April 16, 2023

WOMEN MATHEMATICIANS (OTHER COUNTRIES) - K Bhanumoorthy

 

WOMEN MATHEMATICIANS (OTHER COUNTRIES)

“A Mathematics knows no races or geographic boundary; For Mathematics, the cultural world is one country.” ---- David Hilbert, A German Mathematician.

 

INTRODUCTION:

Mathematics is the queen of all sciences. We can not imagine the branch of science where there is no influence of mathematics and its use in our daily life. One can see mathematics in nature too. The petals in a lotus flower form a sequence known as ‘FIBONOCCI Sequence’. One can see symmetry in flowers. We can see even honey comb in hexagonal shape where efficient use of space while using little wax. The hexagonal shape attracted the attention of the humans since long.

Here are the five women mathematicians from different countries:

        1.Ms Ada Lovelace

 2.Ms. Hypatia

   3.Ms. Dorothy Vaughn

   4.Ms. Katherine Johnson

         5.Ms. Maryam Mirzakhani

 I.                     Ms. ADA LOVELACE: She was born on 10th, December 1815. She is 19th century English Mathematician. She is considered to be the first computer programmer. Mr. Babbage was working as a professor in maths at Cambridge University. She became friend of him, interacted in his idea of designing a computing device. She described the machine by an article adding some details, step by step instructions on how the machine would work. Her notes on Babbage machine have been recognised as the first algorithm to be carried out by a machine. Lovelace had a vision, made a machine with symbols and rules to compute. Her vision has become a reality today. In brief, we could say, she has been a star child and she is an analytical engineer.


II.                   Ms. HYPATIA: She is the daughter of the great mathematician and philosopher, Theon of Alexandria referred in 350 AD. She got trained by her father and became the head of Platonist School in 400 AD. She believed in the spiritual aspect of maths and thought the numbers are the spiritual language of the Universe. She divided mathematics into four branches namely: Geometry, Arithmetic, Astronomy and Music. She also taught the writing of Plato and Aristotle. She extended/accompanied her father in creating version of Euclid’s Elements. She was known to be great teacher and counsellor. The work started by her father Theon was carried on by her daughter Hypatia.

III.                 Ms. DOROTHY VAUGHN: She was born 20th September 1910 at Kansas City, Missouri. She graduated at the age of 15. She is an American Mathematician and a computer programmer. She contributed to the US space program. She became a part of NASA (NATIONAL AERONAUTICS AND SPACE ADMINISTARTION). She got degree in maths in 1929 from Wilber Force University. She worked as a maths teacher in Virginia. During 1943, she worked for NASA computing unit, a group of African-American female mathematicians called as human computer, performed computations and data analysed for Aero Space engineering. She has been expert in Fortran, a computer programming language used for scientific and algebraic applications. In 2016  a  book by Margot Lea Shetterly wrote about the contributions by Vaughn. The book was made into an acclaimed film in 2016.

IV.                Ms. KATHERINE JOHNSON: She was born 26th August 1918. She is an American Mathematician. She was a NASA employee. She worked for the grand success of the first and subsequent US crewed Space Flight. She earned a reputation for mastering complex manual calculations and helped pioneer, the use of computers to perform the tasks. The space agency noted her’ historical role as one of the first African-American woman to work as NASA scientist’. She had a tremendous mathematical capabilities and abilities to work with Space Trajectories. In 2016, she was presented with the Silver Snoopy award by NASA astronaut, Leland D. Melvin. She is known as human computer. Her calculations were also essential to the beginning of space shuttle program. She worked on plans for Mission to Mars. The first job she did was teaching. Her knowledge of analytical geometry helped her grow professionally, and she was very assertive in her approach and all official dealings.


V.                  Ms. MARYAM MIRZAKHANI: She was born on 12th may, 1977 in Tehran. She is an Iranian Mathematician and a professor of mathematics at Stanford University. As a child, she attended Tehran Farzanegan School, part of National Organisation for Development of Exceptional Talents (NODET). She won the gold medal for mathematics in the Iranian National Olympiad. In 1994, she became the first Iranian woman to win a gold medal at the international maths Olympiad in Hongkong. She scored 41 of 42 points. In 1999, she obtained bachelors degree of science in maths from Sharif University of Technology, got Ph.D. in 2004 from Harvard University. Her work has been recognised by American Mathematical Society for the proof of the theorem of  ‘Schur’, contributed to the theory of Moduli Spaces of Riemann Surfaces. She described herself as a slow mathematician saying that ‘you have to spend some energy and effort to see the beauty of maths’. Sharif University of Technology where she graduated, named the library of the college on her name. She got many awards and rewards.



CONCLUSION: It is indeed a rich experience for me to know and be aware of the five women mathematicians of other countries (other than India) We do enjoy the outcome of selfless service, contributions made, for the cause of the society, the public in general and all nations as a whole.

“One important key to success is self-confidence. An important key to self-confidence is preparation.” --------------------------- a quate by Arthur Ashe.

 

Mr K Bhanumoorthy is a retired KVS Principal. He can be contacted at - bhanu_haresh@yahoo.co.in