Log in

Previous Entry | Next Entry

Ramanujan Syndrome

In the first of my recent posts on the technological singularity, I remarked on something I called the "Ramanujan Syndrome". Modern biographers of the famous Tamil mathematician Srinivasa Ramanujan have often noted that his spiritual devoutness was over-romanticized, as contemporaries such as G. H. Hardy observed. Equally, however, there has in recent decades been a tendency to view his lack of formal training before the age of about 25 (in 1914) as a distinction, almost glamorous.

M. T. Narayana Iyengar, editor of the Journal of The Indian Mathematical Society, wrote:
Mr. Ramanujan's methods were so terse and novel and his presentation so lacking in clearness and precision, that the ordinary [mathematical reader], unaccustomed to such intellectual gymnastics, could hardly follow him.

This reminded me of Abel's comment on Gauss, that he was like a fox who erased his tracks in the sand with his tail. Inscrutability, too, has been an over-romanticized trait of many mathematicians.

Wikipedia reports of Ramanujan's work with Hardy from 1914 - 1919:
Hardy had already received 120 theorems from Ramanujan in the first two letters [from 1913], but there were many more results and theorems to be found in [Ramanujan's] notebook. Hardy saw that some were wrong, some were already discovered and the rest were new breakthroughs. Ramanujan left a deep impression on Hardy and Littlewood. Littlewood commented, "I can believe that he's at least a Carl Gustav Jacob Jacobi", while Hardy said he "can compare him only with [Leonhard] Euler or Jacobi."

Ramanujan spent nearly five years in Cambridge collaborating with Hardy and Littlewood and published a part of his findings there. Hardy and Ramanujan had highly contrasting personalities. Their collaboration was a clash of different cultures, beliefs and working styles. Hardy was an atheist and an apostle of proof and mathematical rigour, whereas, Ramanujan was a deeply religious man and relied very strongly on his intuition. While in England, Hardy tried his best to fill the gaps in Ramanujan's education without interrupting his spell of inspiration.

(Emphasis added above.)

Hardy himself wrote:
The limitations of his knowledge were as startling as its profundity. Here was a man who could work out modular equations and theorems... to orders unheard of, whose mastery of continued fractions was... beyond that of any mathematician in the world, who had found for himself the functional equation of the zeta function and the dominant terms of many of the most famous problems in the analytic theory of numbers; and yet he had never heard of a doubly-periodic function or of Cauchy's theorem, and had indeed but the vaguest idea of what a function of a complex variable was...".
        - Dictionary of Scientific Biography. (1970-1980). New York: Charles Scribner's Sons.

I remarked:
You're not going to help Mozart emerge by not having Salieri and his ilk to teach him. That's just Ramanujan Syndrome in my book - the romance of the self-taught. Not everyone needs formal education, but good education never stifled anybody.

Ramanujan definitely faced strong culture shock and what we would today consider a kind of national chauvinism, but was it a good or bad thing that he remained "undiscovered" for so long? I think that nowadays, some of us tend to think of the rigid orthodoxy of academia in developed countries as a limiting factor.

I also think that this is a mistake of attribution. Sometimes, being self-taught can allow natural talent to unfold in an unprecedented way; but more often, lack of education (formal or otherwise) can cause it to collapse on itself. Just as it was an apocryphal legend that Ramanujan couldn't prove most of the astoundingly insightful theorems he came up with, it seems unlikely that his achievements would have diminished by coming to Cambridge earlier, or having the benefit of a thorough education in mathematics such as he began to receive, partially and belatedly, from the British system.

What do you think?



( 4 comments — Leave a comment )
Nov. 25th, 2008 10:41 am (UTC)
Incomplete sentence?
Equally, however, there has in recent decades been a tendency to view his lack of formal training before the age of about 25 (in 1914).

It looks as if there should be an 'as' phrase somewhere after 'view' ('view something as something'):
--- "a tendency to view as a positive"?
--- "a tendency to view as essential"?
--- "a tendency to view his lack of formal training before the age of about 25 (in 1914) as vital to his success as a mathematician"?
Nov. 25th, 2008 11:11 am (UTC)
"... as a distinction, almost glamorous."

Thanks for catching that!

Dec. 2nd, 2008 04:17 am (UTC)
Hardy and Littlewood were professors with lots of experience in teaching, and they were there--with Rama, who also had very serious emotional issues ( including a suicidal depression). I tend to stick with their evaluation of the situation.

When someone is a genius--things are different, then if one is just talented. If Albert Einstein had studied differential geometry seriously as a student, would that have helped him to invent General Relativity? Probably not, as "every schoolboy in Gottingen
knew more DG than he did", according to David Hilbert.

The question was not whether Rama would have done better if he had
been at Cambridge earlier, but whether it would de destructive to
hold up his research by sending him back to the basics. Hardy and Littlewood thought it was too great a risk to take.

Dec. 3rd, 2008 12:41 pm (UTC)
Too great a risk: the Natural and virtuosity
OK, I'll bite. Do you think it was "too great a risk" to take?

I think that, while it's possible to hold up someone's research by doing any number of things, it was more an admission of the fact that they had never encountered someone like Ramanujan before and didn't know how to deliver the basics to a "self-taught" virtuoso such as he was in a way that might not interfere with that virtuosity.

IMO, that doesn't mean that the basics can ever be bad for you, me, or a hypothetical genius, merely that we may respond to different teaching styles differently. You could even argue that this is just a reluctance to mess with a "winning formula". I hold, however, that the Golden Goose principle is fallacious when it comes to education, and that when it accompanies an excessive reverence, it's just another flavor of the romanticization of "The Natural".

( 4 comments — Leave a comment )

Latest Month

December 2008

KSU Genetic and Evolutionary Computation (GEC) Lab



Science, Technology, Engineering, Math (STEM) Communities

Fresh Pages


Page Summary

Powered by LiveJournal.com
Designed by Naoto Kishi