Story of An Unusual Intellectual Relationship Between Two Giant Minds
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14-06-2009, 09:38 AM
An Unusual Intellectual Relationship
Between Two Giant Minds
V P N Nampoori
Based on books
Man who knew infinity
The Indian ClerkPage 2
(AN elderly man at the podium â€œ right side of the stage â€œ the suthradharan( narrator)- he
himself will act as Hardy- spot light on him. Every where else it is dark)
Mathematics is a young manâ„¢s game- once Hardy wrote. This is a story retold- about a
brilliant mathematician who will not grow old- ever green at thirties- like a tropical tree:
This is about Ramanujan- Srinivasa Iyangar Ramanujan to be exact- had he lived longer
what he might have achieved â€œ Hardyâ„¢s opinion was that he wouldnâ„¢t have achieved
much- he left this world with his best work behind him- this is true about masters- Christ,
Sankara, VivekanandaÂ¦Hardy used to scale the Mathematical ability of his
contemporary mathematicians in 100 point scale. He himself assigned 25, Littlewood,
one of his famous collaborator 30, David Hilbert the most eminent mathematician of his
day 80 .And to Ramnujan he assigned 100!
In the whole history of human intellectual relations Hardy-Ramnujan bond is
This yearâ„¢s new year day, Hardy was under depression. He even tried to commit suicide
with failed attempt like his student Ramanujan . In that morning he made 6 new year
1) Prove the Riemann Hypothesis
2) Make 211 not out in a test match in the fourth innings of the last test match at
3) Find an argument for the non existence of God which shall convince the public.
4) Be the first man at the top of the mount Everest.
5) Be proclaimed as the 1
President of USSR, of Great Britain & of Germany.
6) Murder Mussolini.
Please forgive me â€œ I see the sign of impatience growing in the face of my friends.
Today , this last day of August 1936, at Harvard , you are here not to hear Hardyâ„¢s
work but to hear Hardy about Ramanujan â€œ or Hardyâ„¢s version of the story.
It is said that at that time England can boast of three great mathematicians- Hardy,
Littlewood and Hardy and Littlewood- of course it was before when Hardy discovered
light dims- light comes out- Hardy on the Podium
when Harward wanted me to talk on a subject of my interest, I took Ramanujan- the
subject which is closest to my heart. Ramanujan was my discovery. I did not invent him-
like other great men , he invented himself- but I was the first really competent person to
see some of his work- a treasure I had found- yes, a treasure- I suppose that I still know
more of Ramanujan than anyone else , and I am still the first authority on this particular
subject- well , some might dispute that- Eric Neville, for one-or, more to the point , Alice
Neville-I owe more to him than to anyone in the world with one exception, and my
association with him is the most romantic incidence in my life- ( scanning the crowd ) â€œ
My life in this world is of greatest satisfaction since I could collaborate with Ramanujan
and of course also with Littlewood-
It was a time in Trinity , Cambridge year 1913, the month of Februaryâ€œ
Light dims and light comes out .. Hardy fishes out a letter from his pocket.. surely-been
reading for many time..( the passage of time can be shown either in the body language or
slight change in the attire)
I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust
Office at Madras on a salary of only 20 pounds per annum. I am now about 23 years of
age. I have no University education. ..I am striking a new path myself . I have made a
special investigation of divergent series in general and the results I got termed by the
local mathematicians as startling.
Very recently I came across a monograph by you styled Orders of Infinity in page 36
of which I find a statement that no definite expression has been found for the number of
prime numbers less than any given number. I have found an expression which very nearly
approximates to the real result, the error being negligible
It means that the boy has done what none of the great mathematicians of the past sixty
years has managed to do. He has improved on the prime number theorem. Which would
no details, no proofs, just formulae, not the mathematics I have ever come across- what
to make of this!! 1+2+3+4+Â¦= -1/12 .. pure lunacy
+.. = 2/p Bauer already published in 1859 â€œ a
Then one never seen in my life â€œ a real poetry-
+.. = 2
.. what sort of imagination !( on his blackboard Hardy tests it)- it appears to be correct to
the extent I can test.
( Hardy light his pipe , begins pacing)
Nothing else to do-must consult Littlewood- ( makes a walk, goes out
Hardy is sitting in a chair â€œ on the table two dinner plates- one not touched â€œHardy
watching as Littlewood pushes his wheeled chair from the desk across the room â€œ without
averting his eyes from the Indianâ„¢s manuscript)
I have found a function which exactly represents the number of prime less than x
(littlewood reads aloud) .. too bad he does not give it
Hardy- ..he is enchanting me to write back to him- dangling the carrot..
LW- and will you?
GH- I am inclined to ,yes.
LW- I would. Hey, look what he is asking for? Help in publishing his stuff. We can- there
is something- and should â€œ help him- provided gives more details
GH- and some proofs
LW â€œ and see , what do you think of the infinite series, by the way?
GH- either they came to him in a dream- or keeping something much up his sleeve.
LW rolls back to his desk GH rises- reaching for the Indianâ„¢s letter
LW- May I keep it tonight- to look it over more carefully
Gh- of course.
LW- we will talk in the morning- I will be up most of the night-
Â¦..Turns to go out
LW- ( suddenly with raised voice) Hardy, maybe, we should think about bringing over-
GH-( turning ) I was thinking the same
LW- ( prophetic)He may be the man to prove Reimann hypothesis
GH- ( Jealousy?)really?
LW- who knows? Because if heâ„¢s done all this on his own.. well, goodnight Hardy
( shaking hands- depart)
Light dims. When the stage brightens-
LW and Hardy are busy in deciphering Ramanujanâ„¢s Mathematics .. been working late
GH- OK . now the reply. Why donâ„¢t you draft it?
LW- You please. You are good at it. With your classifications of people, things and even
natural phenomena. I am sure that you have classified Ramanujanâ„¢s mathematics also.
GH- Yes. Class 1Those already known or easily deducible from known theorems.
2. Those that are new , but interesting because they are curious or difficult and 3 those
that are new, interesting and important.
LW- Perfect classification. Now the letter
GH- I already drafted it.
LW goes through it reads.
LW- The last sentence â€œ You always state your results in such peculiar forms that it is
difficult to be sure about this- This peculiar might put Ramanujan off.
GH- let us put it odd forms- instead of peculiar forms-
LW- no â€œ Thinks- let us put it in less startling way â€œ particular forms
GH- great- then let it be particular forms.
Modifies the letter. While completing the formalities of the letter writing..
GH- Here goes the reply to our future mathematician who will prove Reimann
Hypothesis . You know as a child I thought that the letters we put in the post box grow
limbs and run through the underground tunnels connecting the input box to reach the
output box- limbs disappears to be picked up by the post man..
LW- wonderful imagination! Give me the letter. I will post it. Let it run through
underground passages in England crossing Mediterranean and the Suez Canal tirelessly
trudging until it reaches the address : Accounts Department, Port Trust, Madras , India
Now they have to wait.. light dims.
GH is lecturing presumably to a group of School Children
George Friederich Bernard Riemann had conjured a famous hypothesis concerning the
distribution of the prime numbers â€œ yes- the Riemann hypothesis- still unproven.
It is probably the most important unproven hypothesis in mathematics.
There is Gaussâ„¢s method to calculate number of primes up to a certain number n. The
theorem over estimates the number of primes up to n. I call it error term.
Reimann found a link between distribution of Primes and something called zeta function
?(x) = 1/1
If x is complex number and if you plot a graph with imaginary part along y axis and real
part along x axis you get points in complex plane. Now the Zeta function will be zero for
a given complex number and is called the zero of the zeta function. Reimann Hypothesis
is this: The zeros of the Zeta function will be for a complex number when the real part is
Ã‚Â½. Or all the zeros will line up along the line at x=1/2. If I can prove at least one point off
the critical line then I have disproved Reimann hypothesis
A student ( voice)- How many such zeros are there?
GH- Oh! I proved there are infinite number of such zeros
Another student- means you proved Reimann Hypothesis?
GH- no, I simply proved that there are infinite zeros along the so called critical line x =
Ã‚Â½. It doesnâ„¢t mean that there are not infinite zeros not along the critical line.
Another student- you have a sentence with three negation. Difficult to grasp.
GH- no problem your language teacher, my sister , Gertrude will take care of.
Another student- Why the difficulty? Just look at Reimannâ„¢s books
GH- that is the sad story. He died of tuberculosis at the age of 38. His house keeper
cleaned his room . Afraid of infections. She burned everything and there went the proof
Student â€œ foolish maid!
GH- I will stop it here. Thank you all.
Standing ovation to GH with clapping of the students.
When light comes Bertrand Russell and LW are on discussion
BR- that is all about liars paradox. Now try this. Imagine a barber who each day shaves
every man in his town who doesnâ„¢t shave himself. Does the Barber shave himself?
LW- I should think so
BR- All right, then the barber is one of the men who does not shave himself.
BR- but you just said he did shave himself
LW- I did?
BR- Yes. I said the barber shaved every man who did not shave himself. If he does shave
himself, then he does not shave himself.
BR- All right, then he does not shave himself.
BR- But you just said he did
LW- Hardy, come save me. Russell is trying me to a spit and is about to roast me
BR- AH, Hardy, yesterday LW was telling me about your Indian, it is quite exciting. On
the brink of proving Riemann! When will you bringing him over ?
GH-( looking at LW on exposing some secret) I am not sure we will.
BR- Hardy, couldnâ„¢t it be some joke by some Cambridge man trapped in an observatory
in the wilderness of Tamil Nadu, trying to while away the hours by playing tricks on you.
GH- even if so, the man is genius
BR- or you are a fool.
LW and Hardy prepare to leave
We will meet tomorrow. Shake hands
LW- (Walking to exit) speaking of paradoxes, Brettie, Hardy will be a client of your mad
barber. Look at the cuts on his chin.
When stage brightens
Hardy sits upright on a chair.. reading a letter. LW enters. At the sight of him Hardy
GH- where were you? I was searching for you all day
LW- I was to the country. My train delayed. Why? Whatâ„¢s the matter?
GH- It has come
GH-this morning. That was why I was in search of you.
Take off your coat and sit down. I will get you some coffee.
He takes coffee in two glasses, hands over one to LW. Reads aloud
Dear Sir, I am very much gratified on perusing your letter of the 8
February 1913. I
have found a mentor in you who views my labours sympathetically.
LW- does he gives proof for that 1+2+3+ Â¦ = -1/12 stuff?
GH-Reads-He says it is under the new theory. The proof may not convince you since you
may not follow my method in a single letter.
I want from eminent professors like you to look for any worth in me . I am already a half
starving man. To preserve my brain I want food and it is my first consideration.
LW- do you really think that he is starving?
GH- you judge- just 20 pounds per annum.- and then ten pages of mathematics- he says I
shall have them published
GH- I have atleast worked out1+2+3+ Â¦ = -1/12
GH- I will show you.- goes to the blackboard .it simply says
1+2+3+4 = 1/1/1 +1/1/2 + 1/1/3 + 1/1/4+Â¦.= 1+1/2
LW- My God! This is Reimann calculation for zeta function with x = -1
GH- exactly. Only I donâ„¢t think he even knows itâ„¢s the zeta function. I think he came up
with it on his own.
LW- Do you mind if I borrow this?
GW- be my guest. Likely youâ„¢ll have more luck than I have
GH- Youâ„¢re the one who was senior wrangler.
LW- ( raises his eyebrows)show this to Mercer then( handles the letter)
GH-( as though just been slapped) I am sorryÂ¦look ,just take the letter
LW â€œ(reluctantly accepts it No hard feelings) Very good sir. thank you sir. Good night
GH- Good night. ( shuts the door)
Light dims.. then slowly brightens. Goddess Namagiri is seen in meditation pose .A
special seat is there in the room. Leave it to the directorâ„¢s imagination on the role of
Namagiri. Heavy rain. Close to midnight. Hardy watches the rain through the window.
Hardy relaxing on the chair. Dozes. Slowly rises and turns to bed room. Suddenly
knocking on the door- startled Hardy-thinking- who might be the visitor at this hour-
opens the door. LW dripping and umbrellaless
LW- the stuff about primes is wrong
LW- Oh! I am sorry. Have I woken you?
GH- It does not matter .come in
LW- I could not sleep- went through the scribbling. He takes everything legitimate on
operations he is doing on the divergent series. Theorem may be true for initial numbers.
May be upto even thousand. Unfortunately, he does not know that primes misbehave
once they get larger.
LW- but Hardy when you consider about the other stuff on continued fractions and
elliptic functions.. he is at least a Jacobi.
GH-( raises his eyebrows.) This is high praise.
GH- and the rest..?
LW- did not complete. Hardy just call him here.
GH_ he did not say about coming to England.
LW- of course he wants to come. Should come. Let not get him rot as a clerk in Madras
GH- how to start?
LW- Neville is going to Madras on December. Lecture tour. Let him persuade
GH- ideal emissary. Will he cross the ocean?
LW- Neville can handle it. If Mohammed cannot be brought to Mountain, bring
Mountain to Mohammed
GH- Wrong religion
LW- let it be ..Vishnu then ( laughing as he goes out )
Neville wrote Hardy from Madras . He met Ramanujan . First question he raised was
whether he will be forced to give some examination like Tripos. I said that Hardy will
take care of it so that no need to take examination. Then he relaxed .Ramanujan used to
say that all his results are due to his goddess , Namagiri who writes on his tongue the
correct answers and even correct questions .Neville succeeded in getting Ramanujan
good fellowship also and some money to his family during his absence from Madras.
Finally Ramanujan agreed to come to Cambridge along with Neville. In 1941, in a radio
talk on Ramanujan, Neville will say Â¦ of all Indians, Ramanujan was the first whom
the English knew to be innately the equal of their greatest men. The mortal blow to the
assumption, so prevalent in the western world , that the white is intrinsically superior to
black, the offensive assumption that has survived countless humanitarian arguments and
political appeals and poisoned countless approaches to collaboration between India and
England, was struck by the hand of Srinivasa Ramnujan.
At last Hardy succeeded in bringing a gem , uncut and unpolished, from India to
transform it to refined , dazzling and more valuable one.
Yes, Hardy was thrilled and of course Little wood also
LW enters. GH and LW discuss some Mathematics
LW- I heard from a German Indologist about some recently unearthed Manusctipt in
India describing the decimal system way back in centuries before Christ. Solving
indeterminate equations even by 6
Century by some tongue twisting name
Brahmagupta .. the same class as Pellâ„¢s equations of 16
GH- He may be brain-twisting also like our Ramanujan.
LW- Point is may be mathematics is in their blood.
GH- I thought that they are as behind us as we are behind Germans. Now your Indologist
changes the order?
Hurried steps outside then knock
GH is tense. LW volunteers to take the call brings Neville and Ramanujan. Ramanujan is
more nervous than Hardy. Sweating forehead- milk blended coffee colour- face fitted
with small pox pits- shadow of nose looks like a moustache-ill fitted tweed suit-collar too
tight to strangle his throat- Jacket â€œ full buttoned- strains to cover his belly- even shoes
clamp his feet â€œit seems- heavy lidded eyes-thick eyebrows-
GH- Thank you Neville for all the trouble you took. And Ramanujan, how was the trip?
Nev- he is quite uncomfortable. He uses shoes for the first time while boarding the ship.
SR- oh not. I am alright. Especially after welcome stay with Neville.
N- You know, Alice is now an expert in Indian cookery- rasam and pancake like item..
SR- Iddly and dosa
N- we didnâ„¢t get NV when Ramanujan was with us- strict veg- even my maid Esther now
can make rasam and rice.
GH- nice that Alice took care of you Ramanujan
N- He did not close his door last night. Alice reminded me , in India, people never close
their doors. I am afraid- she is going to be another Indologist-
GH- Ramanujan, may I ask, why donâ„¢t Indians close the doors?
SR- in our dwellings we do not have the doors to close. We even sleep outside â€œon the
LW- where as we English do every thing behind closed doors.
N- Harold, I have to be off- will see you later.
Take care Ramanujan- jam as Alice calls- For any Indian cookies, come to us Alice and
Esther will be happy
SR- Thank you Sir.
GH- why donâ„¢t you be comfortable Ramanujan? I have some coffee- One of my Indian
friends cricketer Chatterjee- made especially for you
GH- how do you like?
Ramanujan nods. Hardy is not sure whether it is yes or no What a sign language. GH
studies Ramanujan- Namagiri appears
LW- what are you working on Ramanujan?
SR- on highly composite numbers
LW- what are they?
SR- a number that is as far from a prime as a number can be. Some sort of anti prime
GH- raising eye borws- fascinating- can you give an example?
SR- I did it in the ship. ( grabs an imaginary pencil and starts writing..)
LW- just wait-goes out of the room- brings a blackboard on his legs and chalks
Awkwardly SR stands besides the BB.
SR- ( write on the BB) say 24. 20 has 6 divisors- 1,2,4,5,10,20 â€œ 21 has 4- 22 has 4 but
24 has 8- 1,2,3,4,6,8,12,24. So I define highly composite number as a number that has
more divisors than any number that comes before it.
LW_ what a strange mind! What a strange ranging mind! And how many of these
numbers have you calculated?
SR- I listed every highly composite number up to 6,746, 328, 388, 800
GH- Have you drawn any conclusions?
SR- You can work out a formula . Well, if N is highly composite number, then the
following formula can be written for NÂ¦
Hardyâ„¢s discomfort evaporates- heated discussions- as heat goes on in some strange
language of symbols and logics- Namagiri disappears , light dims.
Suthradharan: Ramanujan was not the first Indian to come to England for an Education
and feel isolated from the alien world around him. Mohandas K Gandhi , the future
apostle of nonviolence arrived in England in 1887, the year of Ramanujanâ„¢s birth. He
wrote I would continually think of my home and country. My motherâ„¢s love always
haunted me. At night the tears would stream down on my cheeks, and home memories of
all sorts made sleep out of question. Here, every thing was strange- the people, their
ways, and even their dwellings. I was a complete novice in the matter of English etiquette
and continually had to be on my guard. Ramnujan was lucky to find friend and
sympathizer in Mrs Alice Neville..
Ramanujan in his room in Trinity , Bishopâ„¢s Hostel. Ramnujan in his dhoti , loose shirt,
religious sandalwood mark on the fore head. He is reading a Panchangam, taking some
notes. Footsteps on the stair case and then the knock on the door. Ramnujan startled.
Hears the knock. Goes out to reply
R- Mrs Neville!
A- Hello, I hope , I am not disturbing you
R- Oh, no. Please come in
A-Hope, I am not interrupting you.
R- not at all. May I offer you some tea?
A- That will be wonderful. Indian tea?
(Ramanujan nods, goes to the makeshift kitchen. There is a trunk on the corner, a desk, a
chair and an old arm chair. A statue ( photo) of Namagiri on the desk.)
A- Eric has some work in Trinity. I also just accompanied him. Your rooms are very
A- I understand that you moved recently.
(Alice inspects the book . )
A- What are you reading? Some mathematics?
R- No, it is called Panchangam, a type of Almanac
A- and what is it used for?
R- It is only an old tradition. The Panchangam charts postions of stars and the moon.
Back home they consult it to know auspicious days for .. important events - such as?
R- Weddings, funerals, travelÂ¦
A- like some good days to go to London, changing rooms..?
( Ramnujan doesnot reply. Ramnujan enters with two cups of tea on a tray. Alice
looks directly on his eyes. His eye lids flutters. But does not look away)
A-Oh, I must sound terrible, as if questioning you. Mr Srnivas Ramanujan, I really
want to know
R- (Smiles, hands over the cup to Alice) Please sit
A- ( sitting on the chair) where will you sit?
R- Here.( sits on the floor, cross legged, almost at the knees of Alice)
A- ( sipping tea). Very nice. And do you always wear your dhoti in your rooms?
R- Not when I am expecting some visitors
A- Then it was not good that I came unannounced.
R- No, no . not at all ( he smiles)
A- would you wear dhoti when you go and visit say, Hardy?
R- Oh, no, it would not be correct.
A- You are welcome to wear it when you visit me.
R- Oh, I am sorry I havenâ„¢t visit you lately. I have been very busy.
A- I know. Eric told me. You are working hard. Of course that is for that you are
here. Will you teach me to read the stars?
R- I am not an expert. I am fascinated by the mathematics . that is all.
A- It is not an idle curiosity. The war , they say may come. Does not guarantee
anything any more. .. But if you can read the stars and if you could read the future..
R- It is not something you can teach.
A- ( raises from the chair and sits near Ramanujan. With child like enthusiasm) Tell
me about the first time you had the dream
R- What dream?
A- When Namagiri wrote on your tongue all those complicated mathematics.
Without u namagiri may feel lonely I feel.
R- no she is every where. may be even here now.
(Alice looks around .She doesnot see Namagiri appearing in meditating pose.)
R- But the first time it was not Namagiri in the dream. It was Narasimha
A- Who is Narasimha?
R- He is the Lion faced avatar of Vishnu. An interesting story . I will tell you on some
A- what did he do in your dream?
R- ( like telling a story ) My mother told that sign of Narasimhaâ„¢s blessing is drops of
blood seen in dreams. That was the first time. The drops of blood fell, and then it was
as ifÂ¦ as if scrolls before me, containing the most beautiful and complex
mathematics. Endless scrolls. Endless formulae. And then , when I woke, I hurried to
A- How old were you?
R- I was ten. It was always like that. What I see in the dreams is boundless. The
scrolls never cease.
A- It must be beautiful. Scrolls unfolding
R- Oh, no, it was terrible. What I can bring into the world is only the smallest
fragment of what I read on the scrolls. Each time it is being torn to shreds. Yes , it is
a terrible dreaming ( looks down as he says these words)
A- You suffer, donâ„¢t you?
( she stands up. Ramanujan too stands up thinking that she is leaving.
A- you are not much taller than I am. An inch at most.
( Comes nearer. Intimacy is created for a fraction of a second. Ramanujan doesnot
move .. suddenly she turns to depart. Ramanujan opens his mouth to say something.
She puts her mouth to her lips. And he does not speak. He doesnot move even. Alice
walks away slowely, nothing left to hurry for, slowly opens the door.. the flights of
step on the stair case. Ramaujan has not yet moved. Frozen.. Light fades)
Spot light . Soothradharan on the dias. He describes how Ramanujan makes rasam.
The recipe is his motherâ„¢s. First he soaks the tamarind pulp in boiling water. Then
smashes the pulp with his fingers to squeeze all the liquid out of it. Into the pot he
puts lentils and turmeric powder and water and let them cook until the lentils have
broken apart until it become some yellow gruel. He stirs the lentils, adds more water
and let the broth rest . solids sink to bottom. He strains the broth, leaving aside the
solids which will be used to make sambar. To this broth he adds coriander , cumins
powder, chilli poder, sugar, salt and tamarind juice. He cooks it for further fifteen
minutes and rasam is ready- after finishing it off with a garnish of mustard seeds
fried in ghee. Ramanujan makes rasam at the beginning of the week and it lasts for
one whole week. Reheating whenever he uses it. Sometimes offering it to his visiting
friends. Rasam corrodes the silvering of the brass pot, leaching out the lead-
Ramanujan note tasting the lead due to the spiciness of the rasam. Today he is
making the rasam in his kitchen. Middle of January. Ramanujan dressed to fight the
Full stage brightens. Namagiri in Abhaya mudra
Ramanujan is busy in making rasam. He takes some lentils in hands, he spills a few
on the table top. As he sweeps he counts( as if in trance)
1,2,3,4,5,6,7. How many ways 7 can be partitioned or divided these 7 lentils?
7groups of 1 each, 1 of 6 and 1 of 1, 1 of 5 and 2 of 1, 1 of 5 and 1 of 2, one of 4 and
one of 3, one of 4 and one of 2 and one of 1, three of 2 and 1 of 1, orÂ¦yes15 in all
And if there are 8 lentils?
Takes one lentils from the bowl and put it on the table along with 7.
Eight of 1, 1of 7 and one of one Â¦Â¦22 ways.
And nine lentils? 30 ways ( Namagiri disappears)
Keeps going through out night. Do not eat or sleep
Stage is completely decorated with lentils
Suthradharan on the dias..
And on that day Ramanujan did not sleep. He was drowned in the ocean of lentils
when he came up to 20 lentils. By then there were lentils everywhere. Some migrated
into bed, stick to the fibres of his muffler.. in 1994 an engineering student from
Jakarta , while trying to retrive a lost contact lens, will exacavate one from the gap
between two floor boards.. not knowing that it belonged to one of the partition group
made by famous Ramanujan escaped from cooking rasam. Yes that night rasam
Light brightens. Hardyâ„¢s place. Hardy is busy doing some mathematics. Ramanujan
enters with bulging three bags. Wishes Hardy. Looks around to keep the bags.
Finally finds a place. When he takes off the coat, some lentils fall off.
H- from where these lentils come?
R- Oh, I was cooking rasam. In fact for the last couple of days trying to..
H- what happened?
R- Partition of composite numbers. It occurred to me that there should be some
formula to calculate it.
H- please go on
R- partition of a number n that is, (p) n is easy to calculate when n is 5 or 7. but when
n increases, (P) n increases at astonishing rate
H- such as?
R- when n is 7 it is 15, for 15 it is 176, and partition number for 176 is
H- when n is 476,715,857,290?
R- that is what I am arriving at . to find a general formula for any n
Hardy cleans off the board.
H- it is all for you
Ramanujan starts drawing diagram, dots representing lentils. Writes the theta series.
Hardy mentions a generating function due to Euler. Ramnujan uses it. He writes
oh my God! Both are related
R- This is most exciting. I have some other business to attend. I have to prepare rasam
H- I thought you made it the night before.
R- I meant to, but the lentils..
H- I donâ„¢t see why this particular rasam is turning out to be such a lengthy production
( Hardy says by wiping the black board)
R- But this is no ordinary rasam. It is very special and refined rasam. With tomatoes.
And I must make it in large quantity. I forgot to invite you for a dinner party in
honour of Mr Chatterjee who is going to get married. Miss Chattopadyaya will be
there. Also Mahalanobis
H- And the Nevilles?
R- No. I donâ„¢t think that Mrs Neville will enjoy it
H- ok. I will come to taste your special rasam
Stage is lighted. Ramanujanâ„¢s place is jammed with guests. A table with white cloth is
filled with utensils , plates . Mahalanobis, Chatterjee, Ramanujan, Miss
Chattopadyaya, Ms Rudra are on intimate conversation. Knocks on the door.
Ramanujan goes out and enters with Hardy. Pin drop silence.
R- Professor Hardy, may I present Miss Chattopadhyaya?
C- ( reaches out her hand) how do you do?
H- Very well, thank you. And you?
C- Very well, thank you
R- This is Mr Mahalanobis, an upcoming Statistician.
M- ( bowing his head) Very much glad to meet you Sir.
H- Me too to meet another bright Indian. A nice head-gear you have.
R- Chatterjee you know
H- Ah, my Indian cricketer. Glad to meet you
C-( patting on the back of Hardy) Very nice of you to be here Professor Hardy. This
is Ms Rudra. We are going to get married by the next month end
H- I am Harold for you Mr Chatterjee. Glad to meet you Ms..Rud.. What type of
tongue twisting names you Asians have! What are you doing Ms in England
Ru- ( Just bows, in namaste post) I am a student at teachersâ„¢ college.
Ramanujan goes to kitchen section. Hardy also accompanies him . Table is crowded
with food items
H- What have you got! All these items !
R- rasam, pongal, rice, samosas, yogurt with cucumber and tomatoes, fried potatoes,
H- and you prepared all this on a single gas ring! No wonder youâ„¢ve been working
hard for several days. It smells delicious. You have done a remarkable job,
R- Hardy, I am not a good cook. I expected one of my Indian friend from London.
Unfortunately he has fallen ill. I have burned the pongal
H- It doe not matter. No one will mind
R- I laboured for to make it. And the rice is overcooked.
H- I tell you, Ramnujan, we are among friends. The important thing is the company
R- Well, it canâ„¢t be helped. We must go on.
Ramanujan and Hardy back in the midst of guests.
R- The meals is ready. Shall we sit?
Guests take their seats. Ramanujan brings rasam. Serves to all. Hardy tastes.says
Good. My compliments, says Ms chattopadyaya. Rudra nods. Chatterjee eats fast.
Mahalanobis is indifferent . Ramanujan watches all. Does not eat. Oh I forgot
pappadam. Jumps out and brings a basket full of papadam.Now thay are cold. Never
mind, says Hardy. He has fiished Rasam. Asks for one more round. Ramnujan serves.
Talks on cricket, Culcutta maidan, Bradman..
R- Who cares for the third round of rasam?
H- I would not say no.
Ramanujan extends to Ms Chattopadhyaya. She declines. Ms Rudra? She nods no,
covering her mouth. Hurted Ramanujan mutters I see, very well. Goes back to
kitchen. Few seconds silence. Cautiously Hardy looks over his shoulder to kitchen.
They hears a door opened and shut
M- has he gone out?
C-Perhaps he wanted some thing from the college kitchen.
They wait. No sign of him. Uneasy silence.
Ms C-Shouldâ„¢t some one go downstairs to the toilets? He might need help
C-I will go
M- I will go with him
Few minute later, they returns. He is not in the toilet
Ru-what might have happened?
Leaving ladies behind all goes out again. Conversations are heard
Have you seen Ramanujan? No Sir. I came just now. Oh I saw him heading towards
Kingâ„¢s Parade. Hardyâ„¢s sound- I looked up and down the street. No sign of him
They enters back
C-He has gone.
M- What else is there to do?
Dilemma about food. What to do. No one is sure. One by one they go out.
Out side, Hardyâ„¢s sound to porter: Hey why donâ„¢t you take the food to the college
kitchen?Porter: Sir, they are strange food what he eats, nobody will like. Hardy: yes
as strange as Ramanujan, but very tasty- hot and spicy, I really wanted one more
bowl of rasam. Let me know when he comes back. Porter: Yes sir. After all he is a
student, genius but immature.
Empty stage with untouched food darkens
Slowly stage brightens. Hardy is busy in doing some mathematics. Pipe in his mouth
unlit. Hurried steps outside. Alice Neville breaks in. Hardy is startled and astonished to
H- How nice to see you Mrs Neville. How is Eric?
Al-( without listening) Harold, I cam to know from Eric about the unfortunate dinner
party. I am deeply distressed.
H- we all are, Alice. Friends are alert
Al- Friends? Didnâ„¢t it occur to you that he might have taken ill? Fallen somewhere on
road side? Needs help?
H- Alice, calm down. If that so some body might have cautioned us.
Al- if he is in some strange land? Didnâ„¢t it occur to you Harold that Police is to be
H- Police? What are you talking Alice! That will be an insult to Ramanujan.
Al- ( now getting cool) Harold, You mathematicians are alike, no milk of human
consciousness. You suck the life out of poor Ramanujan- making him to work hard.
Why donâ„¢t you give him some break- to go to London, or he can spend some time
H- Ramnujan does not want a break. His Namagiri takes care of him, he says
Al- you believe in those nonsense?
H- He says that even if you do not believe it will work.
Al- Harold, please be serious. One week has gone. No news about the Indian boy.
And you, his mentor is cracking jokes! Mind you Harold , If I do not get any news on
Ramanujan within two days, I myself will put a complaint to the Police.
( Alice turns to go. Chatterjee breaks in almost in collision with Alice)
GH- Mr. Chatterjee, this is Mrs Neville. Nevilles were instrumental in bringing
Ramanujan to Trinity. Any news about Ramanujan?
Ch-Oh, glad to meet you Mrs Neville. ( to Hardy) I just had a telegram from
Al- ( almost spontaneously )Where is he? How is he?
Ch- He is in Oxford. he just wants 5 pounds to be send
GH- why donâ„¢t you..
Ch- I donâ„¢t have 5 pounds to spare. See , expenses for the wedding arrangement..
Al- Here, take it. I can spare 5 pounds ( fishes out the money and gives to Chatterjee.
Chatterjee is not ready to this reaction) or give me the address , I will send it by
GH is not happy that Alice is intruding into the affair.
GH- No Alice, I will send the money . I am responsible for him. He needs money for
the lodging at Oxford and expenses for returning to Trinity
Alice is hurt. She goes out
Ch- OK sir, Please inform me as soon as he is arrived. In fact Rudra is quite upset.
GH- Sure. I will take care of the situation.
When stage brightens, stage is empty. GH enters reading a book, settles down in a
chair, without taking eyes off the book
Ramnujan enters as though nothing has happened. As though he met GH just
R- Hardy, I got some formula for the partition problem. You knowÂ¦. ( He is holding
a news paper page from Daily Mirror started unfolding it..)
H- Excellent. I am eager to see it.
R- He spreads the soiled news paper on the table. It is far from complete. Still for low
values of n, I get fairly close values of p(n) , about 5% off.
GH- Indeed, I got the same result while you were gone.
R-(dispirited) well, then..
GH- Where were you Ramanujan? You just disappeared! We were all worried. Even
Alice was here scolding me for not complaining to police. Tell me, why did you go to
R- ( nervous, looks into his hands, rubs the hands..) It were the ladies..
R- They insulted me by not taking third round of rasam
GH- Oh! My God, again the rasam! But they did accept it
R- but they did not accept the third round. I felt hurt and insulted and I went out in
despair. I did not want to come back. Not while they were there. I got some money in
my pocket. So I caught the first train to Oxford..
GH-( trying to console Ramanujan) See Ramanujan, they accepted two rounds of
rasam. I do not know how it is in India. But here in England ladies like us to think,
well, that they have smaller stomachs. They feel it impolite, unfeminine, to eat too
R- I worked hard for more than one week in preparing the meals. They insulted me.
GH- Still you could have informed me. The fact is, it was quite an inconvenience,
your being away..
R- I was not idle. I improved upon my formula. In fact the lentils for ..rasam
GH- Please Ramanujan, no more rasam.
While discussing Mathematics
GH- You know, Ramnujan, Russell has been dismissed. For talking about antiwar.
R- I thought that he was going to Harvard
GH- He was refused a passport, even, by the foreign office. This means, he cannot go
to Harvard, for the position offered
R- what will happen to him?
GH- Lord Mayor put a fine of 100 pounds. He refused to pay. All his goods in Trinity
has , therefore, been auctioned
R- He would to every inch, a martyr. What about our Littlewood?
GH- He has been commissioned. In France..
R- Yes, this is the final resultÂ¦
Stage is dim.. they still work
Suthradharan- By the end of 1916, they got partition formula.
What an extra ordinary creature! It is like one of those circus bears trained to balance
a motor car on its nose, or some such thing. It went as one of the joint publications of
Hardy and Ramanujan. In fact, absence of Littlewood was filled up by Ramanujan, as
far as Hardy was concerned. He was distressed that his wife janaki doesnâ„¢t write. At
last after two years, he gets a letter from Janaki Requesting some money to purchase a
sari. She is in Karachi for some two months with her brother. Later on Ramanujan wil
find that his mother stood in between him and his wife as a wall not transmittion any
correspondence between them. One day Mahalanobis came to Hardy..
Stage darkens completely. When brightens, Hardy in his chair reading. Mahalanobis
M- Good morning sir. Sir, Mr Ramanujan is taken ill and is admitted in a nursing
GH- What happened?
M- Ramanujan, Ananda Rao and me were talking on some mathematical puzzles,
suddenly Ramanujan just fell down with acute pain in his stomach.
GH- but I saw him yesterday..
M- I feel that he might have been hiding the symptom from all of us from some time
GH- (puts on the coat)Let us go
Stage dims. When stage brightens, Hardy and Mahalanobis are in discussion. With
Ramanujan who is lying on a bed.
R- Matron said that Dr`Wingate will be here within five minutes to examine. Mahal,
did you bring the book?
GH- Which book?
R- the Carr, A synopsis of Results in pure and applied Mathematics
GH- But that is obsolete! Why do you want it?
R- Still I want to read it, like you people read Bible every day or we read Bhagavad
M- I think it is a source of comfort to him. He used to go through the numbered
equations in it when he cannot sleep at night..
GH- strange Ramanujan
M- I will bring it after the Doctorâ„¢s visit.
Doctor enters followed by the Matron
Doctor â€œ Hallo there. ( Matron signals Hardy to get up. Hardy gets up. Doctor
examines Ramanujan) What is your name mister?
Doctor now looks at Hardy. I wonâ„¢t try to pronounce it. So what is the trouble?
GH- A pain in the stomach
Doctor- Mister let the patient talk
Hardy is hurt
Doctor- I see. Here? Here? ( presses hard, at one point Ramnujan lets out a cry.
Triumphant doctor- there is the trouble spot
What brings you to Trinity young man? What are you studying?
Doctor- How interesting. I once had a mathematician patient. I said, sir, you have a
distinctly odd sense of humour. And he said, how do you mean odd? 3,5,7..?
( Ramanujan is disinterested. Others also are bored)
I again said, even if you are feeling better, you should take medicine. He said. How
do you mean even? 2,4,6..?
R- When may I go home?
D- not soon
R- but my work..
D â€œ ( to GH) by the way, who are you?
Gh- G H Hardy
D- what is your relation with the patient?
(for a moment Hardy is perplexed. He is not prepared for such a question)
M- Professor Hardy is a Don at Trinity. Mr Ramanujan is his pupil.
D- I see. A word with you. He is suffering from gastric ulcer. Has he been under
GH- I donâ„¢t know.. he has been working hard..
D- anxieties over war? Family trouble?
GH- not that I..
D- well , keep an eye on him ( stretches his hands) A Mathematics Don. Beastly stuff,
mathematics. My brother was better at it than me
Gh- I remember a Wingate
D- do you? Well, god day Hardy
GH- good day
Doctor goes out. Hardy goes to Ramanujan
GH- Take rest. Doctor suspects gastric ulcer. Due to strain. Take rest. I have a lecture
now. I shall come back in the afternoon ( Hardy goes out. Stage darkens)
Spot light on suthradharan â€œ One month passed . Ramanujan is still in the hospital.
One day Dr`Wingate told Hardy that Ramanujan may be suffering from Tuber
culosis. Hardy replied that his lungs are clear as you suggested yesterday. Yes,
doctor replied , we have to wait for symptoms to appear. Summer came to a close. No
sign of problem with the lungs. Ramanujan became a puzzle to Dr`Wingate. SO what
is he suffering from? Some mysterious oriental germ? He says he cannot go further.
He suggested Hardy to take Ramanujan to London and consult the lung man Dr Batty
Dr Betty Shawâ„¢s clinic in London.
Mahalanobis, Hardy and Chatterjee with Dr Shaw
Sh- I have made detailed examination of Ramanujan. Dr Wingate reports nightly
pyrexia, steady abdominal pain with no link to digestion, weight loss and low white
GH- I didnâ„¢t know about the blood count.
Sh- Oh, only usual procedure. Further examination showed enlargement of liver,
which is tender to the touch. I speculate metastatic liver cancer.
Gh- are you sure that it is cancer?
Sh- nothing is definitive. This is by my many years of experience..
Ch- no cure?
Sh- Neither treatment nor cure. But time will test and within few weeks condition will
Gh- are you sure that there is no hope?
Sh- no hope. I am very sorry. He may survive up to six months..
Doctor excuses and goes out.
GH- When symptoms match a diagnosis, the diagnosis is correct.. what a logic of
doctorsâ„¢! No student of mathematics will get away with such sloppy logic. Let us
Sh- ( to Hardy)Sir, shall I have a word in private?
They are on the other side of the stage â€œ even off stage
Sh- If you donâ„¢t mind my asking, I was wondering about the bill..
Gh- What about it?
Sh- to whom it should be addressed?
GH- to Ramanujan , of course.
Sh- But can he afford the expense?
GH- All his medical bills are being paid by the Trinity. I will guarantee that..
Sh- I see. ( he is impressed) He did not tell anything about himself, you see. What is
GH- He is the greatest mathematician of the last hundred years. Possibly last five
GH- Really. ( GH comes back to the anxiously waiting group)
When stage illuminates we see Ramanujan on the bed. Reading Carr. Hardy enters
GH- how are you now Ramanujan?
R- no change from the first day we came here.
GH- Nevilles are coming tomorrow. Alice is quite upset that we did not inform her
about your illness.
R- Please tell them not to come. I do not want to face them in this condition
GH- OK, I will try and no promise. By the way the taxi I took to come here has the
number 1729. It seemed to me rather a dull number.
R- ( smiling) no Hardy. It is an interesting number. It is the smallest number which
can be expressed as the sume of two cubes in two different ways
GH- Oh! You are right. 1729 can be expressed as 12
your Namagiri is so quick?
Dr Batty Shaw enters and signals Hardy to come to him. .Ramanujan turns back to
Carr. Notes down on a piece of paper
Sh- You are right. There appears no change in the condition of lungs
GH- does it alters your diagnosis?
Sh- Well, perhaps. But cancer is not my specialty. So I consulted with Dr Lees, the
( Mahalanobis enters. Wishes GH and Doctor. Goes to Ramanujan. Ramnujan
smiles. Mahalanobis goes through the scribbling of Ramanujan. )
SH- But Lee was also not helpful. He suggested Dr Frobischer. He suspected Malaria
GH- did he made the confirmative tests?
Sh- Yes. It turned out to be strange. Test is negative. And then he suspected
GH- but there is no symptom
Sh- Yes, we may wait more. As of now it is tuberculosis then.. Good day Hardy
( doctor exits)
GH-( reaching to Ramanujanâ„¢s bed) Medicine, what a sloppy science!
Mahalanobis give Ramanujanâ„¢s notes to Hardy.
GH â€œ Theory of Reality.
0= the absolute, nirguna Brahman, the reality with no qualities â€œ or negation of all
attributes ( Ramanujan nods)
infinity = the totality of all possible attributes, saguan Brahman â€œ and hence is
inexhaustible ( Mahalanobis smiles looking at Ramnujan who is in a meditation pose)
0X infinity= the set of finite numbers.
Each act of creation is a particular product of 0 and infinity from which a particular
individual emerges. Thus each individual may be symbolized by the particular finite
number that is the product in his case.
Ramanujan, is it some of your special type of short hand? Or philosophy tan
Mathematics? I am not good at Philosophy. We will give to Bretiie
Ramanujan â€œ Every mathematical equation should reveal the thought of God. How is
GH- finally, he went to Harvard.
M- what does the doctor say?
GH- they cannot make anything out of their wisdom.
R- I think I will die without proving Reimann
M- Hey, donâ„¢t be upset
GH- Ramnujan, I doubt whether even Reimann had proved it.
R-What do you mean?
GH- I will tell you a secret known only to three or four . I was visiting Bohr in
Copenhagen The younger , the Mathematician Bohr who was under the shadow of
his physicist Brother Niels. We were trying to prove Riemann without success. While
returning I got only a small boat and weather was grim. I thought that I may not
survive the journey. I went to the shop in the deck and purchased a view card in
which I wrote, I proved Reimann- GH and send to Littlewood, Bohr and possibly to
Russel. My idea was if I die, world will know that I proved Reimann and will be
remembered as the second man to prove Riemann and unluckily the proof drowned
with me. And your God did not stand for this undue glory to G H Hardy and the boat
reached England safely. Then I said it was a practical joke.
R&M- what a practical joke!
GH- There is no point for Ramnujan to be lying here idle.
R- I want to go home- Trinity
GH- You already made Trinity your home? Why donâ„¢t you call Janaki here?
R- I wrote . no reply!
M-OK, then we will go back to the Hostel.
GH- Yes. Trinity will take care of the bills. And by the way, you are , most probably ,
going to be the youngest FRS
R- My God!
M- what a happy news to hear!
Ramanujan reading in his room. Alice Enters.
R- Mrs Neville, what a pleasant surprise!
Al- ( taking hands of Ramnujan) You did not close the door? Or keeping it open like
your Indian custom? You are expecting some one?
R- No. Why?
Al- You are in the formal dress and not in dhoti.
R- Oh, I feel cold. Any way, I got a visitor now.
Al- Oh! I forgot. (She takes a rose flower from the bag and gives to Ramanujan.)
Congratulations to the youngest FRS.
R- Ah! Thank you. How is Dr Neville? I heard that he is getting a position in
Al- Yes . We are moving to London. I have to complete some work here for Eric.
How are you? You were not well and Harold did not inform us the correct picture.
Eric was in Paris and he contacted Harold as soon as he came back.
R- I was in the nursing hostel for several months. Better now. And back in Bishopâ„¢s
Al- you are working hard. I feel that Hardy is a vampire, sucking life out of you.
What does the doctors say?
R-Now I have to go to Mendip Hills. Near wells.
Al- But that is a sanatorium for tuberculosis.
R- Yes. My symptom fit no other diagnosis, and so by the process of elimination, it
has been concluded that it must be tuberculosis.
Al- But you donâ„¢t cough
R- No lung trouble. Just pain and fever. Illness is very boring, Mrs Neville. In fact I
once went to Railway station and jumped in front of a train. But the train stopped and
Al- (Moved by emotion) Do not think of such thing again. Think of janaki and your
R- Yes, I am trying. Hardy also told the same thing. He also advised me to take a
break and go to India for a couple of months. By that time the war also will end.
Al- I in fact came to tell you the same thing. Eric is also of the same opinion.
Littlewood was here . He did not find you . He went back , now somewhere in
R- may be I was in London at that time to consult the doctor.. Shall I make a coffee?
No milk or sugar. Rationing .
Al- No thank you. I am getting late. Take care Ramanujan.
R- Good day Mrs Neville. Give my regards to Dr Neville.
( Alice exits. Ramanujan goes back to his reading. Dozes and slowly slips to sleep)
Suthradharan : In his Introduction to the History of Mathematics, Howard Eves
chronicles the seminal moments in mathematics. The year 1906 marked the work of
Frechet, the year that of Brouwer. Then came a long dry spell with nothing for nine
years which was over in 1916 with Einsteinâ„¢s General Theory of Relativeity. Then in
1917, Evesâ„¢ entry shows Hardy and Ramnujan ( analytical number theory)Â¦..
stage brightens . Namagiri and her seat is vanished- emptiness
Hardy is reading. Littlewood enters
LW- Goodmorning, Harold.
GH- Ah! Littlewood, how nice to see you
LW- I am for a short break. Been to country. My mother was not well. I am on my
way back to the front.
GH- Where are you now?
LW- in Austria . How is Ramanujan? Did he reach India?
GH- Yes. He is now under the care of his wife janaki
LW- Funny person. I heard about his fellowship amount.
GH- yes. He send me a copy. He says out of 250 pounds fellowship amount per
annum. He says 50 pounds per annum to be paid to his parents. The surplus after the
expenses of Ramanujans are met, should be used for educational purpose , reduction
of school fees for poor boys and orphans and provision of books in school.
LW- glad to hear about Ramanujan. I should be off. Good day Harold.
GH- Good day Littelwood. I am waiting for you return. Ramanujan has kept a
vacuum in my life. I want you to fill it up.
Focus on suthradharan
Upon his return, India greeted Ramanujan as a hero. The youngest FRS. University
authorities put him in a luxury , in a villa on the banks of Cauvery. His wife Janaki
nursed him during his twilight . India wept on his demise.
Quite an ending to a story that began modestly, and would in all likelihood still be
going on, modestlyÂ¦ had Harold Hardy did not intervene. How many such gems are
lost, is loosing and will be lost without such interventions!!!
How many registrarâ„¢s in India today, for that matter how many vice chancellors of
today , 120 years after Ramanujan was born, would give a failed pre university
student a research fellowship --- this is after 60 years of independence, when we can
no longer blame the colonial power for not encouraging Indian Talent. Of course not
to forget Dr P K Iyengar as chairman of Science and Technology Committee of
Kerala who showed the courage to give research grant to a Pre degree failed boy
from Trivandrum and that too for Mathematics.. even though the academics do not
the boyâ„¢s papers gets published in international mathematical
journalsÂ¦Â¦rare are such gestures like those of Hardy and Iyengar.
over the years Ramanujan was never forgotten.. there were 105 papers published on
Ramanujanâ„¢s work since his death including about 10 by Hardy. One of Ramanujanâ„¢s
Conjuctures on partition function was proved by the Belgian mathematician, Pierre
Deligne for which he was awarded the Fields Medal, the Nobel Prize counterpart for
mathematics. Mathematician G M Watson compared Ramanujanâ„¢s identities to
Michelangeloâ„¢s beautiful sculpture the Day and Night. Several theorems of
Ramanujan are now being widely used in subjects like particle physics, statistical
Mechanics, computer science, cryptology, genetic engineering, strings theoryÂ¦.
Ramanujan was resurrected through George Andrewâ„¢s discovery of Ramanujanâ„¢s
Lost Notebook in 1976.
Ramanujan had come to this world and lives of some revolved around him like
planets around a star, discerning only the weakest of the penumbra of this star.. even
now dreams of Ramanujan pulled Hardy from sleep each morning with light reflected
off from a varnished cricket bat or from the fragment of a page from Ramanujanâ„¢s
notebooks Â¦ yes , from the NoteBooksÂ¦..
Had Ramanujan stayed in India- had he survived â€œ he would now on the brink of
fifty. Instead he died at thirty three. Tuberculosis was given as the cause. One is not
sure. However, there should be some cause to the effect.. yes some causeÂ¦ may be
tuberculosis. Or Namagiri or Narasimha declaring that we received the bloody
scrolls to the extent destined for usÂ¦Â¦ scrolls of which we still know only a tiny
part Â¦.. just a touch on the fragment of that Vast Mind
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