Category Archives: mathematicians

Who wants to be a mathematician

I wish that there were official programmes like the following in India too:

Genius of Srinivasa Ramanujan

  1. In December 1914, Ramanujan was asked by his friend P.C. Mahalanobis to solve a puzzle that appeared in Strand magazine as “Puzzles at a Village Inn”. The puzzle stated that n houses on one side of the street are numbered sequentially starting from 1. The sum of the house numbers on the left of a particular house having the number m, equals that of the houses on the right of this particular house. It is given that n lies between 50 and 500 and one has to determine the values of m and n. Ramanujan immediately rattled out a continued fraction generating all possible values of m without having any restriction on the values of n. List the first five values of m and n.
  2. Ramanujan had posed the following problem in a journal: \sqrt{1+2\sqrt{1+3\sqrt{\ldots}}}=x, find x. Without receiving an answer from the readers, after three months he gave answer as 3. This he could say because he had an earlier general result stating 1+x=\sqrt{1+x\sqrt{1+(x+1)\sqrt{1+(x+2)\sqrt{1+\ldots}}}} is true for all x. Prove this result, then x=2 will give the answer to Ramanujan’s problem.

Try try until you succeed!!

Nalin Pithwa.

Women in mathematics

Happy International Women’s Day. I would like to re-blog the following :

The Porter Lecture — Interview with Prof. Erik Demaine

Education gives strength: Anand Kumar tells Maoist youngsters

I reproduce this highly inspirational news from The DNA, Mumbai, Thursday, February 23, 2017: 

Raipur: Super 30 founder Anand Kumar has exhorted the youth in Maoist areas to shun the gun and embrace pen to script a new tale of peace and prosperity through real empowerment which, he believes, only education can ensure.

Kumar was addressing students at the education city in Jawanga village of Chhattisgarh’s insurgency-hit Dantewada district at a programme on Tuesday.

State Chief Minister Raman Singh and Rajya Sabha MP Dr. Subhash Chandra were also present on the occasion.

Stressing that education was the only way to bridge the gap in the society, Kumar said, “Education can lend you strength in the real sense. It can bring about generational change.”

Technology should also be increasingly used to make quality education accessible to all, which is another prerequisite for an egalitarian society and tackling poverty effectively said Kumar, who runs a residential and free-of-cost “Super 30” programme for the last 15 years for talented students from the underprivileged sections.

Narrating his “Super 30” experience, he  gave examples of students from the most underprivileged sections and how they reached the Indian Institutes of Technology (IITs) through their hard work.

“All the problems in the world originate basically because of four-five reasons, like illiteracy, ignorance, poverty, lack of opportunities, unemployment, mindless violence etc. And, if we look at them closely, all have their genesis in lack of education. It is the lack of education that breeds inferiority complex and later manifests itself in different ways,” Kumar said.

Chief Minister asked the students to set a goal in their life and work hard with honesty to achieve it.

“Bastar is changing rapidly. The students (of education city) will play a key role in the development of Bastar. The day when maximum students of Bastar will sit on higher administration posts, that day will be memorable for me,” he said.

“With the efforts of the government, several children of Bastar have qualified for IIT, engineering and medical colleges. These children are not only future of Chattisgarh but the country too,” he said.

The Chief Minister also released Halbi-Gondi-English dictionary for students. –PTI.

Hats off to Mr. Anand Kumar and his “Super 30”!

From Nalin Pithwa

Donald Knuth, mathematician and computer scientist

Donald Knuth, American mathematician, computer scientist (born 1938):

(based on his brief biography presented in “Discrete Mathematics and its Applications by Kenneth H. Rosen):

Knuth grew up in Milwaukee, where his father taught book-keeping at a Lutheran high school and owned a small printing business. He was an excellent student, earning academic achievement awards. He applied his intelligence in unconditional ways, winning a contest, when he was in the eighth grade by finding over 4500 words that could be formed from the letters in “Ziegler’s Giant Bar.” This won a television set for his school and a candy bar for everyone in his class.

Knuth had a difficult time choosing physics over music as his major at the Case Institute of Technology. He then switched from physics to mathematics, and in 1960 he received his bachelor of science degree simultaneously receiving a master of science degree by a special award of the faculty who considered his work outstanding. At Case, he managed the basketball team and applied his talents by constructing a formula for the value of each player. This novel approach was covered by Newsweek and by Walter Cronkite on the CBS television network. Knuth began graduate work at the California Institute of Technology in 1960 and received his Ph.D. there in 1963. During this time, he worked as a consultant, writing compilers for different computers.

Knuth joined the staff of the California Institute of Technology in 1963, where he remained until 1968, when he took a job as a full time professor of Stanford University. He retired as Professor Emeritus in 1992 to concentrate on writing. He is especially interested in updating and completing new volumes of his series, The Art of Computer Programming, a work that has had a profound influence on the development of computer science, which he began writing as a graduate student in 1962, focusing on compilers. In common jargon, “Knuth” referring to The Art of Computer Programming has come to mean the reference that answers all questions about such topics as data structures and algorithms.

Knuth is the founder of the modern study of computational complexity. He has made fundamental contributions to the subject of compilers. His dissatisfaction with mathematics typography sparked him to invent the widely used TeX and Metafont systems. TeX has become a standard language for computer typography. Two of the many awards Knuth has received are the 1974 Turing Award and the 1979 National Medal of Technology, awarded to him by President Carter.

Knuth has written for a wide range of professional journals in computer science and in mathematics. However, his first publication in 1952, when he was a college freshman, was a parody of the metric system called “The Potrzebie Systems of Weight and Measures,” which appeared in MAD magazine and has been in reprint several times. He is a church organist, as his father was. He is also a composer of music for the organ. Knuth believes that writing computer programs can be an aesthetic experience, much like writing poetry or composing music.

Knuth pays USD 2.56 for the first person to find each error in his books and USD 0.32 for significant suggestionss, if you send him a letter with an error (you will need to use regular mail because he has given up reading e-mail), he will eventually inform you whether you were the first person to tell him about this error. Be prepared for a long wait, because he receives an overwhelming amount of mail. (The author Prof Kenneth H. Rosen received a letter years after sending an error report to Knuth, nothing that this report arrived several months after the first report of this error.)

With regards to Prof. Donald Knuth,

Nalin Pithwa



Edmund Landau mathematician

Edmund Landau (1877-1938)

Edmund Landau, the son of a Berlin gyanaecologist attended high school and university in Berlin. He received his doctorate in 1899, under the direction of Frobenius. Landau first taught at the University of Berlin and then moved to Gottingen, where he was a full professor until the Nazis forced him to stop teaching. Landau’s main contributions to mathematics were in the field of analytic number theory. In particular, he established several important results concerning the distribution of primes. He authored a three volume exposition on number theory as well as other books on number theory and (mathematical) analysis.

In particular, I like his classic, Foundations of Analysis, AMS Chelsea Publishing:

-Nalin Pithwa

Blaise Pascal (1623-1662)

Blaise Pascal exhibited his talents at an early age, although his father who made discoveries in analytic geometry, kept mathematics books away from him to encourage other interests. At 16 Pascal discovered an important result concerning conic sections. At 18 he designed a calculating machine, which he built and sold. Pascal, along with Fermat, laid the foundations for the modern theory of probability. In this work, he made new discoveries concerning what is now called Pascal’s triangle. In 1654, Pascal abandoned his mathematical pursuits to devote himself to theology. After this, he returned to mathematics only once. One night, distracted by a severe toothache, he sought comfort by studying the mathematical properties of the cycloid. Miraculously, his pain subsided, which he took as a sign of divine approval of the study of mathematics.

PS: The programming language, Pascal, was, of course, named after Blaise Pascal!

-Nalin Pithwa.

Alexandre-Theophile Vandermonde (1735-1796)

Because Alexandre-Theophile Vandermonde was a sickly child, his physician father directed him to a career in music. However, he later developed an interest in mathematics. His complete mathematical work consists of four papers published in 1771-1772. These papers include fundamental contributions on the roots of equations, on the theory of determinants, and on the knight’s tour problem. Vandermonde’s interest in mathematics lasted for only 2 years. Afterward, he published papers on harmony, experiments with cold, and the manufacture of steel. He also became interested in politics, joining the cause of the French revolution and holding several different positions in government.

More stories of mathematicians are everywhere, including the web, printed books, journals and my mind !! 🙂

Nalin Pithwa

PS: One of the best source of stories of mathematicians is, of course, the famous “Men of Mathematics” by E. T. Bell.


Frank P. Ramsey, Cambridge mathematician

Frank Plumpton Ramsey(1903-1930), son of the president of of Magdalene College, Cambridge, was educated in Winchester and Trinity College. After graduating in 1923, he was elected a fellow of King’s College, Cambridge, where he spent the remainder of his life. Ramsey made important contributions to mathematical logic. What we now call Ramsey theory began with his clever combinatorial arguments, published in the paper “On a Problem of Formal Logic.” Ramsey also made contributions to the mathematical theory of economics. He was noted as an excellent lecturer on the foundations of mathematics. His death at the age of 26 deprived the mathematical community and Cambridge University of a brilliant young scholar.

PS: The reader interested in Ramsey numbers should consult references like the following:

J. G. Michaels and K. H. Rosen, Applications of Discrete Mathematics, McGraw Hill.


Nalin Pithwa