Arthur T Knackerbracket has processed the following story:
Ramanujan brings life to the myth of the self-taught genius. He grew up poor and uneducated and did much of his research while isolated in southern India, barely able to afford food. In 1912, when he was 24, he began to send a series of letters to prominent mathematicians. These were mostly ignored, but one recipient, the English mathematician G.H. Hardy, corresponded with Ramanujan for a year and eventually persuaded him to come to England, smoothing the way with the colonial bureaucracies.
It became apparent to Hardy and his colleagues that Ramanujan could sense mathematical truths — could access entire worlds — that others simply could not. (Hardy, a mathematical giant in his own right, is said to have quipped that his greatest contribution to mathematics was the discovery of Ramanujan.) Before Ramanujan died in 1920 at the age of 32, he came up with thousands of elegant and surprising results, often without proof. He was fond of saying that his equations had been bestowed on him by the gods.
More than 100 years later, mathematicians are still trying to catch up to Ramanujan’s divine genius, as his visions appear again and again in disparate corners of the world of mathematics.
The English mathematician G.H. Hardy, after receiving a letter from Ramanujan and recognizing his brilliance, arranged for him to study and work with him in Cambridge.
Ramanujan is perhaps most famous for coming up with partition identities, equations about the different ways you can break a whole number up into smaller parts (such as 7 = 5 + 1 + 1). In the 1980s, mathematicians began to find deep and surprising connections between these equations and other areas of mathematics: in statistical mechanics and the study of phase transitions, in knot theory and string theory, in number theory and representation theory and the study of symmetries.
Most recently, they’ve appeared in Mourtada’s work on curves and surfaces that are defined by algebraic equations, an area of study called algebraic geometry. Mourtada and his collaborators have spent more than a decade trying to better understand that link, and to exploit it to uncover rafts of brand-new identities that resemble those Ramanujan wrote down.
“It turned out that these kinds of results have basically occurred in almost every branch of mathematics. That’s an amazing thing,” said Ole Warnaar of the University of Queensland in Australia. “It’s not just a happy coincidence. I don’t want to sound religious, but the mathematical god is trying to tell us something.”
[...] In September, Ono and two collaborators — William Craig and Jan-Willem van Ittersum — published yet another application for partition identities. Rather than looking for a new source from which these identities would spring, they were able to use them for an entirely different purpose: to detect prime numbers.
They took functions that counted partitions and used them to build a special formula. When you plug any prime number into this equation, it spits out zero. When you plug in any other number, it instead spits out a positive number. In this way, the partition identities can give you a way to pick out the entire set of primes from the integers, Ono said. “Isn’t that crazy?”
“Partitions are about adding and counting,” he said. “Why would they be able to detect which numbers are prime or not, on the nose, which is a multiplication thing?”
By tapping into the rich mathematical theory of modular forms, he and his colleagues found that this formula was just a glimpse of a much larger class of prime-detecting functions — infinitely many, in fact. “That’s mind-blowing to me,” Ono said. “I hope people find it beautiful.” It indicates a deeper relation between the partitions and multiplicative number theory that mathematicians are now hoping to explore.
In some ways, it makes sense that partitions keep infiltrating every corner of mathematics. “The theory of partitions is so basic,” Andrews said. “Counting stuff and adding stuff up happens in almost every branch of mathematics.”
Still, the precise nature of those connections is hard to work out. “It’s really about getting the perspective right,” Ono said.
“This is the great thing about Ramanujan’s work,” Kanade said. “It’s not just one identity he discovered, and a dead end. It’s always the tip of an iceberg. You just have to follow it through.”
“Ramanujan is someone who can imagine things that someone like me cannot,” Mourtada said. But the development of new fields of mathematics has “given us the possibility to find new partition identities that Ramanujan could probably have found just by imagination.”
“That’s why mathematics is so important,” he added. “It allows ordinary people like me to find these miracles, too.”
(Score: 4, Troll) by VLM on Tuesday October 29, @12:42PM (16 children)
If you take away the flamboyant diversity fetish about the guy, the entire story of this guy boils down to "a mathematician wrote papers that are occasionally, although rarely, still cited today" As though the guy invented the idea of academia or the idea of citing prior work.
Its kind of funny to watch the outsiders get all flustered at the idea that someone in an academic field wrote papers that are cited in later academic papers, and this leaves them absolutely breathless with amazement solely because of the guy's race. Generally, the Indian's I've met have been reasonably competent, nothing special nothing awful, although the "budget" coders are clearly on a pretty low budget LOL, so I'm sure the smartest one a century ago was pretty smart, but the mass media loves to give them the "talking horse" treatment where its not amazing that a mathematician existed, but it's utterly astounding to the more racist journalists that a brown one once existed. How could it be? How could someone non-white do math, the expectations among lefty journalist types are just so low but it seems like he was a "real" mathematician, what a mystery!?! LOL.
I believe they call it the racism of low expectations. They just can't stop talking about how the only thing that's important about the guy is his skin color not being white. Fairly ridiculous.
(Score: 2) by Gaaark on Tuesday October 29, @01:07PM (3 children)
I guess the math is beyond me, but i don't get how 5+1+1=7 is less remarkable than 7=1+1+5.
Was this suddenly a great thing back then? Yeah, they seem to be all "rumbly in the tumbly" over this guy, but reading it makes me go "Wha?"
--- Please remind me if I haven't been civil to you: I'm channeling MDC. ---Gaaark 2.0 ---
(Score: 3, Interesting) by JoeMerchant on Tuesday October 29, @01:58PM (2 children)
5 + 1 + 1 = 7
3 + 3 + 1 = 7
3 + 1 + 1 + 1 + 1 = 7
1 + 1 + 1 + 1 + 1 + 1 + 1 = 7
How many ways can you "partition" 7 using only addition of odd numbers?
Notice first: the number of partitions are themselves only odd. This was the kind of thing I was pissing off my 3rd grade teacher with back in the 70s.
🌻🌻 [google.com]
(Score: 3, Insightful) by acid andy on Tuesday October 29, @02:33PM (1 child)
It intuitively seems right that any even number of odd numbers would always add up to an even number.
Welcome to Edgeways. Words should apply in advance as spaces are highly limite—
(Score: 4, Insightful) by JoeMerchant on Tuesday October 29, @04:22PM
My 3rd grade exercise was: for these math problems (like 57+23 or 84-28) if the answer is even color the square blue, if the answer is odd color the square red.
So, I started coloring the squares based on the oddness of the result. Teacher told me: you need to write down how you worked that out. I said: I'm not working it out, for addition and subtraction, two odds make an even, two evens make an even, even and odd make an odd. "What about multiplication?" well, there, if there's an even, it's even, takes two odds to make an odd. "What about division?" well, there's only like two division problems on the page and they're obvious when you look at them (like 80/4=20 even).
🌻🌻 [google.com]
(Score: 3, Informative) by Anonymous Coward on Tuesday October 29, @01:29PM (3 children)
> "a mathematician wrote papers that are occasionally, although rarely, still cited today"
IINAM (I am not a mathematician) but I'm pretty sure that Ramanujan was quite extraordinary...and would still be recognized today as such, independent of his origin story. Check his cite count: https://scholar.google.co.in/citations?user=iQqBns4AAAAJ&hl=en [google.co.in]
Averaging something like 500/year in the last 8 years shown in the bar graph.
Then there is the journal named after him, https://link.springer.com/journal/11139 [springer.com] dedicated to publishing papers is areas where he worked. A little searching will give you a better sense of his influence.
(Score: 2) by VLM on Tuesday October 29, @01:48PM (2 children)
We're running into all sorts of relative vs absolute comparison issues.
Consider Euler, Hilbert, Von Neumann, Gauss, Newton I guess ...
(Score: 0) by Anonymous Coward on Tuesday October 29, @01:56PM
Same AC. Yes, Ramanujan is compared favorably to all those greats that you mentioned.
(Score: 1) by khallow on Tuesday October 29, @02:56PM
My ordering: Gauss and Newton > Euler, Von Neumann, and Ramanujan > Hilbert.
Ramanujan's charm is that he came up with a huge number of insanely complex formulas that other mathematicians have spent a century explaining why they work and what connections those formulas have to other branches of mathematics. He's created a lot of work for others to follow up on. There are several mathematicians that if they had lived a long life would rank higher than they currently do. Ramanujan is one of those (Galois, Reimann, Poincare, and Turing are other examples).
(Score: 5, Interesting) by JoeMerchant on Tuesday October 29, @01:53PM (1 child)
Low expectations is a very damning thing in society. On the other hand:
doesn't sound like low expectations or hollow praise. Ramanujan got there first, and I'd submit it was his isolation from classical academia which enabled him to do so, race and wealth was just the mechanism by which he remained isolated from classical schooling until he was 24.
Diversity of thought (regardless of race, nationality, wealth or poverty) is what is important for discovery and invention. I'll go a step further to point out Einstein's relatively academically distant position while he was developing relativity. Not only working as a patent clerk, but also his apparently neuro-divervent "I don't care what you all think" physiology / intellectual development.
🌻🌻 [google.com]
(Score: 0, Informative) by Anonymous Coward on Tuesday October 29, @04:56PM
The meat behind DEI.
(Score: 4, Touché) by krishnoid on Tuesday October 29, @03:09PM (1 child)
Right, didn't brown people invent the decimal system and zero [britannica.com], and discover the pythagorean theorem [nasa.gov] (search for "many cultures") and the quadratic formula [mathnasium.com]? Maybe it's more of a modern/developed-nation era mystery.
(Score: 3, Informative) by bzipitidoo on Tuesday October 29, @03:52PM
How about Viswanathan Anand? World Chess Champion from 2007 to 2013.
(Score: 4, Interesting) by vux984 on Tuesday October 29, @06:22PM (3 children)
I disagree.
All mathematicians stand on the shoulders of giants, but he had almost no formal training, basically pulled himself up by his bootstraps (by comparison to his contemporaries and peers), and produced many highly advanced novel mathematics results that are still being proven out today. That all makes him quite extraordinary even among the ranks of other math geniuses.
And his background, from India, from that time in history, his nationality, and yes, even the color of his skin, I think, are part of his story. Is it of particular note that a genius was born in India and not in Britain? Of course not. But would it have been harder for a brown genius born in India in 1887, isolated from formal training, to have developed his theories and have his genius recognized by western established acedemia? Yeah. For sure.
Is it the single most important or noteworthy thing about him?
No, of course not. But people enjoy the trope of a "brilliant genius coming from nowhere" and "person overcoming adversity", these are good story elements.
Einstein initially worked in a patent office while he developed his theories -- same sort of thing. Einstein was culturly Jewish and fled the Nazi's, and had a small role to play in America pursuing nuclear weapons. None of that made him a good mathematician, but it does make for interesting story fodder; and few articles will miss the opportunity to mention it.
Journalists, at the end of the day are in the business of telling stories. So why get bent out of shape over them doing that?
(Score: 3, Informative) by JoeMerchant on Tuesday October 29, @10:06PM (2 children)
I'm not so sure about developing his theories, I think that's actually easier because he was isolated from formal training.
Now, having his genius recognized, _that_ is special. I believe it was the recognition and support of Hardy, and others, which made his general recognition possible. As Hardy said, his greatest contribution was the "discovery of Ramanujan." Hardy, seeing in Ramanujan's writings, the potential to relate them to the accepted formalisms of British academia, the potential to have their uniqueness integrated and accepted by his mainstream colleagues - and Ramanujan's ability to make that connection with Hardy and others, that's what's special here.
We need more things like this in our world.
🌻🌻 [google.com]
(Score: 2) by vux984 on Wednesday October 30, @04:07AM (1 child)
To a point, I can see where you'd be coming from, and even agree... to a point. There is value in the creative freedom that comes with not being "indoctrinated" by the established theory and methods of the day.
But in this century, and even the last one, if you didn't have any formal training even a genius would risk just independently rediscovering the things we already knew.
(Score: 2) by JoeMerchant on Wednesday October 30, @11:47AM
I'd say there's no risk in rediscovery of things already known the risk is in not discovering things that are there waiting to be seen, but formal training steers us away from them. Not only overt steering like Galileo experienced but subtle steering that just ridicules somebody who has found a novel fundamental truth into a corner of obscurity.
Geometry taught me that I have no love of formal proof. Complexity theory at University taught me that people tend to oversimplify descriptions of significant problems. In today's world, if you have internet access, you can teach yourself the formal methods necessary to communicate with the establishment. Hopefully we can still have people who figure things out for themselves first and then learn the formal methods to get noticed and accepted by the academic world.
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