55-2019 How a chance discovery saved a precious mathematical legacy.


Ramanujan’s last major contribution “mock theta functions” were almost lost forever, but for a fortunate discovery made years later. The story of the lost note book goes like this ::

Ramanujan’s lost notebook is the manuscript in which the Indian mathematician Srinivasa Ramanujan recorded the mathematical discoveries of the last year (1919 — 1920) of his life. Its whereabouts were unknown to all but a few mathematicians until it was rediscovered by George Andrews in 1976, in a box of effects of G. N. Watson stored at the Wren Library at Trinity College, Cambridge and were due to be incinerated in a few days. The “notebook” is not a book, but consists of loose and unordered sheets of paper — “more than one hundred pages written on 138 sides in Ramanujan’s distinctive handwriting. The sheets contained over six hundred mathematical formulas listed consecutively without proofs.The manuscript contains no introduction or covering letter. In fact, there are hardly any words in the manuscript. There are a few marks evidently made by a cataloguer, and there are a few remarks in the handwriting of G. H. Hardy.

After Ramanujan died on April 26, 1920, at the age of 32, his wife Janaki had given his notebooks to the University of Madras. On August 30, 1923, the registrar Francis Drewsbury sent much of this material to G. H. Hardy, Ramanujan’s mentor at Trinity College, where he probably received the manuscripts of the lost notebook.

Almost surely, this manuscript, or at least most of it, was written during the last year of Ramanujan’s life, after his return to India from England. Undoubtedly, the most famous objects examined in the lost notebook are the mock theta functions.

Some time between 1934 and 1947 Hardy probably passed the notebook on to G. N. Watson, who with B. M. Wilson started on the project of editing Ramanujan’s notebooks. However, Wilson died in 1935 and Watson seems to have lost interest in the project in the late 1930s. After Watson’s death in 1965, J. M. Whittaker examined Watson’s papers (which were a complete mess, due to be incinerated in a few days) and found Ramanujan’s notebook, which he and R. A. Rankin sent to Trinity College Wren library on December 26, 1968. The lost notebook George Andrews, following a suggestion by Lucy Slater, found the lost notebook in the spring of 1976 while on a visit to Trinity College. George Andrews and Bruce C. Berndt have published several books in which they give proofs for Ramanujan’s formulas included in the notebook. Bruce C Berndt says of the notebook’s discovery: “The discovery of this ‘Lost Notebook’ caused roughly as much stir in the mathematical world as the discovery of Beethoven’s tenth symphony would cause in the musical world.”

The “lost notebook” was published on December 22, 1987, by Narosa publishing house, India, 67 years after Ramanujan died !

Also see :: Remembering Ramanujan


54-2019 When a mother almost killed her own son ………

When a mother almost killed her own son …….

It is not known to many that the legendary Indian mathematician Ramanujan attempted suicide in 1918, by jumping before a train. Ramanujan was under mental depression, brought about by the harsh weather he was not accustomed to, strict and inappropriate dietary habits, very demanding and stressful research activity, poor health conditions, war related miseries, and above all, separation from his newly married wife Janaki. Luckily, he was saved just in time, because the driver slammed the brakes in time.

There is a saas-bahu twist to Ramanujan’s tale. When he returned to India in 1919, he was miffed at Janaki, his wife. Ramanujan rebuked her, “I wrote so many letters, at times once every week, but you chose not to reply even once”. Mystified, sobbing Janaki told him that she was writing letters frequently even when none were received from Ramanujan. She was handing over letters to her mother-in-law for posting, as she had no money for even postage. Both of them then realised the dirty game played by the mother-in-law in hiding letters from each other. Many years later, Dr S Chandrasekar recounted his conversation with Janaki Ammal, who apprehended that longing for loving words from his wife perhaps was one of the contributory factors for Ramanujan’s depression, which led to him to the attempted suicide. The selfish mother never thought of the consequences of her foolish and cruel act.

This episode has a sad and cruel climax. Just a few months later, the mother had to see with her own eyes, the painful death of her own son. The mother could not even repent the injustice she had done to her own son, and ask his forgiveness.

See Remembering Ramanujan

53-2019 Yet another filthy festival (#4)

53-2019 Yet another filthy festival (#4)

FirecrackerIt is time for yet another filthy festival celebrated in the name of religion. This jewel in the crown of religious madness is called “Diwali” or Deepavali, and is due in a few days. We will of course see all the filth and garbage which usually accompany such religious exhibitions. Add to all that, all the noise, smoke and poison showered generously using fire-crackers and explosives. Factor-in the number of accidents where people get hurt or property destroyed. You have the best reason to call Diwali the ultimate nonsense in religious freedom.

The only persons who seem to enjoy all this rubbish are the businessmen and shopkeepers. They allure you with cleverly-worded campaigns filled with dubious “festival offers” , and add insult to injury.

Long live religious liberty, to hell with commonsense and social responsibility.

  1. Filthy festival #1
  2. Filthy festival #2
  3. Filthy festival #3
  4. Filthy festival #4

Is there any way to save the planet ?

Stop celebrating such religion motivated festivals, and follow the example given by Greedy Greens.


52-2019 Made for each other and for தமிழ்

This is an update and sequel to my earlier post on my friend Shrinivasan and his wife Nithya . They continue to amaze everyone with their collaboration and achievements. Recently, they adopted a baby girl and gave her a தமிழ் name : இயல் . Their elder child (a boy) is called வியன் .The choice of two unusual, but pure தமிழ் names shows their respect and love for தமிழ். Their sustained contributions to தமிழ் did not go unnoticed or unrewarded.

I am blessed and proud to know Shrini and Nithya personally.

50-2019 Yet another filthy festival (#3)

We just crossed a filthy festival in India. It is time to drown in one more display of filth, noise, garbage and nuisance. durgaThis is called “Durga Pooja” (aka Durga puja) and was once celebrated, only in Assam and West Bengal states of India. It is now common to see it almost all over India. This time, it will be the goddess of strength/power who will be venerated with all the din and noise she deserves. Streets will be blocked, to erect pompous “pandals” . Blaring noise will be played on loudspeakers, austensibly to promote devotion and prayers. The grande finale will, as usual, include processions in the name of immersion, where all lakes, rivers and water bodies will be poisoned. Add all the filth and garbage which will fill our streets, and with anti-social activities of the muscle-men behind all this.

Long live “religious freedom”. Too bad for you, if you do not agree.

49-2019 Better light a candle than curse the darkness

I recently saw some cynical and illogical remarks from a learned friend about my
sunset webpage.

What should you do when someone says “Behold the beautiful sunset ” ? React with some cynical remarks about all that is not so beautiful around you ? Or complain about irrelevant and unrelated issues which people have not solved ? Why can’t people understand the value of appreciating the sunset ? Why don’t they learn to light a candle rather than curse the darkness ? Why do they criticise and belittle the person who lit a candle ?

In a way, this learned friend is much better than all the others whom I informed about this “sunset” web page, and who did not even care to give any signs of having seen it.

A big thank you to all others who watched and appreciated the sunset.

47-2019 Making-a-mockery-of-privacy — a sequel

The ridiculously shameful display I reported in my earlier post is not over. I discovered some more blunders in that site. For instance, that site does not mention anything about the Head of that institution. It does not display the name, official designation e.g. Dean/Principal/Director, contact details etc. Neither do we know his date of birth, qualifications if any etc., unlike the details given for all other faculty in this institution. Needless to talk about the numerous typos and linguistic gaffes. Ignoring all norms of decency and responsible behaviour, the website provides no “contact me” for giving feedback. There is no way you can report these blunders to anybody responsible, unless you use some public platform like this..

All this speaks a lot about the quality, competence and maturity of the people running this institution. Their website stands as proof of the saying , “where ignorance is bliss … ” Like Mark Anthony famously said “Oh judgement, thou art fled to brutish beasts …. “.

Take look at this web page

46-2019 Making a mockery of privacy and decency

See the actual web page now.

Recently, I came across a ridiculous display of violation of decency and privacy. I was shocked and ashamed to see that this blunder occurred in the website of my own alma mater, where I studied almost 50 years ago. The website displays a whole lot of academic information as well as some irrelevant information and misses out on some meaningful information. For instance, it announces the date of birth of all its teachers/faculty (including the ladies). Why should anyone know who is older / younger than who in the University ? Strangely, it does not give the date/place where the teacher acquired the qualifications listed against their names. Strange ! No one seems to have noticed this goof up or has any objection to the public display of personal, non-academic information.

If you don’t believe me, take a look at this faculty details webpage.

Notice that this is the webpage of the Professor and Head of Computer Science ! Is this what you teach your students ? What quality can we expect from students trained here ?