Srinivasa Ramanujan (1887-1920): Mathematician of the Divine
"An equation means nothing to me unless it expresses a thought of God."
Background Story I accidentally stumbled upon Ramanujan years ago. I already forgot his name but he was quoted saying that mathematical expressions don't interest him unless they are an expression of God. That quote never left me for some odd reason - I don't know why. I'm not even a good mathematician. It would recur every now and then - it was almost haunting. It was about him and about the depth of his math that was beyond the understanding of even the most distinguished mathematicians. Finally, I decided to act on my excitement and learn more about this genius whose source is divine. But first, I had to find out who he was again before I could look him up. Googling "greatest Indian mathematician" ranked him #1 on the results.
Short Bio Ramanujan was born in Madras, India on Dec 22, 1887, to a poor family during the British rule. At an early age, he already showed signs of being gifted in mathematics. Because of this gift however, he was beyond the understanding of his friends - and thus defaulted to being by himself. He was highly regarded but hardly understood.
As a working adult, he wrote a letter enclosing his mathematical expressions to G. H. Hardy, a Trinity College (Cambridge) mathematician, who was impressed and invited him over to Cambridge. There, Ramanujan spent the next 5 years working on his math, impressing his colleagues and also earning their wrath. He suffered racism, isolation and nutritional starvation. Despite the resistance, Ramanujan became a Fellow of Trinity College, Cambridge. Moreover, he was elected to a Fellow of the Royal Society - a highly coveted distinction awarded to individuals with "substantial contribution to the improvement of natural knowledge, including mathematics, engineering science, and medical science". I surmise that Ramanujan's genius was too radiant and mesmerizing that it would cost the Royal Society its credibility if Ramanujan was simply ignored. After the war, Ramanujan returned back to India where he died a year later at age 32. Ramanujan has become a bigger-than-life genius now after his death, with movies, stamp, museum and awards named after him.
Srinivasa Ramanujan with his colleagues at Cambridge
Namagiri Thayar His childhood friends would anecdotally narrate how the young Ramanujan would spend extended time inside the temple and write down his mathematical formulas on the floor. He claims that he gets his knowledge from his diety, Namagiri Thayar - he would see in his mind's eye a scroll that would unravel and reveal the secrets of the universe in mathematical expressions. In short, he did not arrive at the results by any kind of mathematical computation or proofs - it's simply divine revelation. This is also the reason why he had a hard time complying with Hardy about proofing his results - Ramanujan didn't even have the mathematical training to learn the basics of math.
Genius Ramanujan had no formal training in mathematics - he was self-taught. But the work he produced astounded Cambridge mathematicians of the highest order. He was placed on the same level as the most renowned mathematicians to have ever lived - Euler and Jacoby. His works were ground-breaking and original, without using any of the known mathematical templates of the time. He provided solutions to mathematical problems that were considered unsolvable during his time. His approach to math was intuitive and thru insight instead of rigid formulaic proofs which was the norm of the time. Altogether, he produced 3900 theorems/results until his untimely death at age 32. The ramification of his highly sophisticated formulae was just becoming to be understood and appreciated now, a century after his death. His work was so rich and multi-layered that new directions of research were opened up even from what initially seemed benign byproducts of his work.
Racism I cannot help but feel strongly about the racism that Ramanujan endured in the UK. He was beaten-up for being Indian and left largely unlooked-after even by his hosts. To them, he was just a commodity that was useful in furthering whatever they already knew with math. If they simply looked after the basic needs of Ramanujan - his vegetarian needs, his declining health and being made to feel an outsider, I think Ramanujan would have lived longer. Even though years after his death, in 1994, it was concluded that he died of amoebiasis, I strongly contend that a person's mental, physical and emotional well-being are paramount in the healing process.
Even with the current material about Ramanujan, the racism and condescension are apparent. He is described as "Ramanujan as an accidental discovery" and "...tamed by G. H. Hardy". Ramanujan initiated the contact by writing G. H. Hardy. Hardy didn't just stumble-upon Ramanujan. Additionally, Ramanujan's mathematics was an original repertoire and beyond the full comprehension of Hardy - thus Hardy had to press upon Ramanujan to comply with proofing for Hardy's and his society's comprehension. Sure, Hardy was instrumental in getting Ramanujan published and known, but to say that he tamed Ramanujan is incorrect and again, condescending.
It was simply too much for the colonizing Brits to admit that a poor dark-skinned Indian guy with no formal mathematical training could possibly be smarter than their entire lot.
Quotations about Ramanujan's Work
G. H. Hardy - English mathematician at Trinity College, Cambridge who invited and hosted Ramanujan in the UK
"...[Ramanujan's theorems] defeated me completely; I had never seen anything in the least like them before" and that they "must be true, because, if they were not true, no one would have the imagination to invent them"
"Ramanujan was a mathematician of the highest quality, a man of altogether exceptional originality and power"
E. H. Neville - English mathematician who convinced Srinivasa Ramanujan to come to England and eventually authored a fictionalised portrayal of Ramanujan's life in the 2007 octel The Indian Clerk "not one [theorem] could have been set in the most advanced mathematical examination in the world".
Bruce Carl Berndt - American mathematician who was Michio Suzuki Distinguished Research Professor of Mathematics at the University of Illinois
"...over the last 40 years, as nearly all of Ramanujan's conjectures have been proven, there had been greater appreciation of Ramanujan's work and brilliance, and that Ramanujan's work was now pervading many areas of modern mathematics and physics."
J. E. Littlewood - English mathematician at Trinity College, Cambridge who worked on analysis, number theory, and differential equations
"Every positive integer was one of [Ramanujan's] personal friends."
1729: Hardy-Ramanujam Number When Hardy rode a cab to visit Ramanujan at the hospital, the cab number was 1729. As noted by Hardy, there was nothing remarkable about such number. Without missing a beat, Ramanujan quipped, "No, it is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways.".
The Lost Notebook Great excitement was stirred when a 'lost notebook' was discovered in 1976. This was apparently written by Ramanujan during the last year of his life in India (1919–1920). Not really a notebook, but over 100 pages of loose and unordered paper with 600 mathematical formulas listed consecutively. The discovery caused a stir within the math circle reminiscent of the discovery of Beethoven's Symphony #10. Some of the information helped in calculating the entropy of black holes - a concept incomprehensible during Ramanujan's time.
Ending Thoughts There are many languages transcending the spoken ones. Music has its own language. A musician can play a symphony inside his head just by looking at musical scores - something completely abstract to a non-musician. As a web designer, I can say that a website also has its own unique language that is gobblygook to anyone who doesn't understand HTML. I can look at a simple HTML code on a website and I could see the layout and formatting of the content. Same thing with math at varying levels. I can look at a simple fraction and see how many parts there are to a whole. But to some physicists, they see the inner workings of the quantum realm - like realizing there are 11 dimensions to our reality (not just 4) just by looking at the equation. But to Ramanujan, his math is even incomprehensible to the most eminent mathematicians. Now, a hundred years after his death, some of his works are beginning to make sense in understanding black holes. I am provoked and curious. When Ramanujan looks at his equations, what picture does he see? How does the universe unravel to reveal its secrets? I guess that is my fascination about Ramanujan and his math. I would like to get a glimpse of that unseen reality.
Ramanujan died at a tender age of 32. I wonder what else he could have uncovered had he lived a longer time. But for his legacy, the world is much more informed with a given peek at what might lie just around the bend. In the next 500 years, octbe another Ramanujan will be born.
I was devouring materials about Ramanujan, consumed by him in the last 3 days, researching, watching videos, reading articles and even stumbling upon other great lives in the process (e.g. Edward Witten). I begin to truly appreciate how privileged I am for having the time to devote to all this. If I have a family, a business or a job, I wouldn't have this luxury. Even rich people don't have this prerogative, let alone poor people. Trump, Putin or Xi Jinping couldn't do this. For a householder (because I am not a monk) this is truly freedom. I enjoy a state of being where I live in a luxury hotel room where the owner (a good friend) would not even take my loose change as token payment, where I don't pay for public transport because I have a sturdy bike, where I can see a complimentary movie and even bring a friend with me. All I need to keep afloat is loose change for the cheap and delicious street food of Chiang Mai (what I would fondly call my Khao Soi money), beer money for my Blues nights and provision money (because I invite friends for coffee, bread, cocoa, etc.). All this money need is met by the yoga class I teach. It's enough. That's all I need and all I want. For now. Gratitude permeates.
Ayn Vinyasa Krama by Srivatsa Ramaswami (Oct 29, 2020) The man who knew infinity
TheLoneRider (Oct 29, 2020) ...to have the gods open up the scroll of knowledge for you. How much revelation is that?
Ayn (Oct 29, 2020) I watched the movie at least 3x now
TheLoneRider (Oct 29, 2020) There is another full length movie about him, Ramanujan. But in Hindi and no subtitles
Jay Mark (Oct 29, 2020) I've seen the movie and watched the documentary... some groups even suggested that aliens were the reason for his genius and visions...🙂
(Nov 4, 2020) When the most brilliant physicists on the planet call you 'the smartest living physicist', by no small measure, you are beyond brilliant. When he talks, the most acclaimed of them all shut-up and listen, hanging by his every word. When the most distinguished award in mathematics (Fields Medal) is given to a physicist, and not to a mathematician, you have to be none other than Edward Witten.....more »»
Chiang Mai INFORMATION
Chiang Mai Map
Chiang Mai, Thailand
IMPORTANT PLACES
Bus Station Train Station Chiang Mai International Airport Nong Buak Hard Park - free yoga classes daily
HOTEL
Arun Dara Villa - 7 exclusive rooms, 1 swimming pool for every room, grand opening
Nawa Sheeva Hotel - big rooms, high ceiling, salt-water pool, restaurant, cafe
Nawa Saraan Hotel - low density (4 spacious rooms), stone garden setting, Koi fish pond, Old City location
Arun Suite - 3 bedrooms in a 3-storie guesthouse within Old City, ideal for families
MOTORBIKE RENTAL
Tawan Bike - motorcycle rental | +66 91 635 2863 | Si Phum, Mueang Chiang Mai District, Chiang Mai 50200
Chiang Mai FYI / Tips
crop-burning season in Chiang Mai is between late Feb to early April. But laws change everytime. This year, 2019, there is a 61-day ban on burning so the farmers started burning early. When my plane was approaching Chiang Mai on Jan 24, 2019, there was already a thick blanket of smog covering the entire city (and beyond). But within the city itself, you won't feel it (but that doesn't mean the air is healthy). To monitor air conditions in real time, refer to site: Chiang Mai Air Pollution: Real-time Air Quality Index (AQI)
hot season begins March and lasts until June
wet season begins July and lasts until September
best time to visit Chiang Mai is mid-September to mid-February - after the monsoon and before the burning
you have to try Khao Soi, this is north Thailand's culinary staple
the tourist area where most of the hotels, restaurants, ticket offices, tour operators are, is located in the Old City
to exchange your dollars to Thai Baht, the Super Rich Money Exchange give the best rates. There are many branches scattered around Chiang Mai
get a red cab (songthao) outside the train station for Baht 50 (instead of paying B100 if inside the train station) to Old City - if you haggle nicely enough...I did!
shared red taxi (songthao) - B30 standard fare plying all over Old City
for only B50/day, best to rent a bike to go around the Old City - it's a 2.5km2 with lots to discover
FREE daily yoga classes from 9:00am to 10:15am at Nong Buak Hard Park (southwest corner of Old City). Resident and passing-through teachers take turns conducting yoga classes.
Blues/Jazz Bars in Chiang Mai
North Gate Jazz Coop - at Chang Phueg Gate, great Tuesday jam session, Blues on Sundays at 11pm by the Chiang Mai Blues band
Boy Blues Bar - at the Night Bazaar. Mondays at 9:30pm is open mic
My Secret Cafe - near Wat Phra Singh. Tuesdays at 7:30pm for the changing front-act and 9:00pm for the Panic Band
Taphae East - 88 Thapae Rd. (just north of Night Bazaar). Fridays at 9:30pm by Chiang Mai Blues Band
Chiang Mai Cost Index
B60 Chiang beer
B250 1 hour drop-in yoga session
B200 one hour Thai body massage at WAYA Massage(highly recommended)
B50 noodle soup with meat
B50 coffee
B40 pad thai
B30/kilo wash-only laundry
B50/kilo wash+iron laundry
B100-150 dorm bed/night
B250 fan room/night
B30 internet cafe/hour
B170-190 Movies Sat-Sun and public holidays
B130-150 Movies weekdays
B100 Movies Wednesdays (movie discount day)
B750 1/2 day Thai cooking lessons
B900-1000 1 full day Thai cooking lessons
B400 Muay Thai boxing ticket
B2500 starting room rate at the luxury hotel, Nawa Sheeva(highly recommended)
Transportation
B450 bus, Chiang Mai to Bangkok
B160-180 bus, Chiang Mai to Pai
B1250 bus, Chiang Mai to Luang Prabang
B1650 slow boat, Chiang Mai to Luang Prabang
B210 bus, Chiang Mai to Chiang Rai, 3-4 hours
B360 Green VIP bus, Chiang Mai to Mae Sai (Thai border town for visa run to Tachileik, Myanmar)
B50 bicycle rental, 24 hours
B200 motorbike rental, 24 hours
B273 #51 sleeping train from Bangkok to Chiang Mai
Book Online - direct booking with State Railway of Thailand. Best to register first. If going to BKK from CNX, click "Northern Line".
note -- big difference between booking direct with the State Railway and booking with an online 3rd party agent. 12GO was charging B1330 for the same trip that only cost me B941 with the State Railway.
note -- Oct 2022, I took the #10 Train from CNX to BKK, upper berth, 2nd class, a/c, sleeper, B941. The train was clean, fast, comfortable and modern. If you have heavy luggage that will cost more money in flight checkin, I would suggest this train. Otherwise, the flight now is so much cheaper it doesn't even make sense to take the bus or train.
Bangkok to Chiang Mai by Train from Bang Sue Train Station
10:22pm - #51 Train, arrive Chiang Mai 12:10pm, sleeper, 3rd class B270 (non sleeper), 2nd class B438, B728 upper deck, B798 lower deck
Loei to Chiang Mai by Bus
From Loei town center, take a tuk-tuk ride to the bus station, B30. There is only one bus station.
As of June 28, 2020 (still on Covid schedule), there are only 3 night trips: 8:30pm, 9:30pm and 12 midnight. 9 hours, B470.
The bus makes the following stops at the following times from a 9pm Loei departure: Phu Ruea (9:50pm), Phitsanulok (12:40am), Uttradit (2:20am), Lampang (4:35am)
Final bus stop is at the Red Bus Arcade, Chiang Mai, 9 hour-trip, arriving 6am (from 9pm Loei departure).
Take a red songthaew to Old City, B50. They'll try to charge you B100, but they'll take B50 (just assure the driver you won't tell the other passengers).
How to Get a 60-Day Thai Tourist Visa and then Extend by another 30 Days
This process is BEFORE Covid 19. Not sure what it is now.
60-Day Thai Tourist Visa
NOTE: There is no need to go back to your country to get the Thai tourist visa. Any major city with a Thai Embassy will do. Apparently there is also no need to have an invitation from a Thai establishment to justify the visa.
Bring the following to the Thai embassy:
a) proof of money (bank statement will suffice)
b) flight booking to Thailand
c) onward flight back to your country from Thailand
d) filled-in tourist visa form
e) 2 passport pictures
f) hotel booking in Thailand (they didn't ask me for this but better be safe)
g) passport with at least 6 months validity
After handing over all the documents, they will ask you to come pick your passport with the visa the following day from 4 to 5pm. That's it!
NOTE: after 2 successful attempts, I was already questioned the 3rd time.
30-Day Extension
NOTE: When your 60-day visa is close to expiry and you want to extend your stay. No need to leave Thailand.
bring the following to the Immigration Office:
a) passport (make sure your Tourist Visa hasn't expired yet)
b) Baht 1900
c) photocopy of your passport + visa duration date stamp + TM6 card (white immigration card) and sign all the copies
d) completed TM7 visa extension form (available at the Immigration Office)
e) one 4cmx6cm passport picture
submit the above to the Front Desk. They will give you a stub with your number on it. Take a seat and wait for your number to be called
when your number is called, your picture will be taken. Then go back to your seat. They will call you again.
when they call you again, they'll give you your passport with your extended visa. That's it!
when there are no lines, the whole process can take only 10 minutes
arrive early - in case there is a snag (visa snag, documentation snag, transport ticket snag, etc.), you will have ample time to troubleshoot the problem if you arrive early (to the airport, to the bus terminal, etc.)
put detailed itinerary on the Calendar apps of your smart-phone according to timelines - this is where you do all your thinking and planning. Once written down, you don't have to think anymore while you are on the journey...you just follow the steps. This frees your mind for something else that might happen while you are already en route
avoiding scams - as a general rule, I ignore the touts or anyone I don't know who call out to me. The calling comes in many forms - "Hi! Where are you from?", "Excuse me! Excuse me!", "Where are you going?". I don't look them in the eye and I remain non-verbal with them. If you reply to them, you just gave them an 'in' to hound you. In order not to look rude, I smile and wave the 'not interested' hand to them, without looking at them.
power bank - hand-carry your power bank. Do not check it in. You can be called in when you are already inside the plane to go all the way to the loading dock so you can personally remove the power bank...and chances are, you'll have to surrender it to them. And you might delay the plane departure!