Oh snap!

Is this the case in the US?

PS I recall you saying you would return back to regional languages after you did Ajit Cour, but I never saw it.

1. Actually, I am questioning whether he should be remembered as a human calculator at all – even if, at a popular level, his contemporaries may have thought so (and even that I am not sure of).

2. Secondly – as far as independence of the abilities themselves – while they are different abilities, and in the extreme they do not coincide (Shakuntala Devi is no mathematician) – it is possible for mathematicians of the highest rank to have a very high level of computational skill – as a consequence of their superb mathematical intuition – but this then would pale against people like Devi. I am saying that if Ramanujan was indeed a computational genius, then that ability came because he could see special cases of his general results pretty quickly.

That’s all on that, from me, here. BTW, Dev Benegal is making a movie about Ramanujan.

I don’t think there is any dispute that his reputation as a mathematician is completely independent of his ability as a human calculator. If anything, it is the human interest story (“rags-to-riches”, dying young, exotic oriental savant-type genius) that is more compelling in the public mind.

This one incident keeps coming up in all stories of his life. There may have been others like it – but it seems to me that Ramanujan saw them as special cases (or the first non-trivial case) of his phenomenally more general results in number theory. So his calculation ability may pale beside Shakuntala Devi, though admittedly non-trivial in itself – and he could still be the greatest mathematician of the 20th century – or all time.

There is the famous anecdote that Hardy narrates about the time he visited Ramanujan on his deathbed. Hardy made a throwaway remark that his cab number was 1729, to which Ramanujan immediately responded, “Interesting. It is the smallest number that can be expressed as the sum of two cubes in two different ways.” (1729 = 9^3+10^3 = 1^3+12^3) This is a combination of both some amazing feel for numbers, and prodigious calculation ability.

Also, one of the most amazing things about Ramanujan was his intuition. He would come up with the most abstruse formulae, seemingly purely because he intuited them, and without any rigorous proof technique. This contributed to quite a bit of skepticism about the veracity of his results. In fact, when Ramanujan wrote Hardy from India with his results (many of which were independent rediscoveries of previous theorems), Hardy was so stunned by some of the new results (usually listed without proofs) that he said something to the effect that he couldn’t believe somebody could come up with them (My memory is hazy on the exact remark and quote, so I could be wildly mistating). I believe that his habit of listing theorems alone also made understanding and deciphering his notebooks difficult (some of his theorems were wrong too, but it was difficult to figure that out in the absence of proofs).

As for his contributions in number theory themselves, his major results about theta functions and partition theory are pretty mathematically sophisticated and don’t fall into the realm of pop mathematics, by any means. It is Ramanujan’s diamond-in-the-rough story (combined with the “white man’s burden” subtext) that really captured the popular imagination.

(I just saw that one of your links is to the 1729 incident. Sorry for rehashing it, but in any case, I do think the incident is evidence of significant calculation ability).

Is this true, or was it that one of the branches of math that he contributed so solidly to – was number theory, some of the more simple of whose results can be appreciated by the mathematically naive (occasionally, even by the innumerate), and the naive are then (mis)led to think they came from a human calculator?

Interestingly, Ramanujan was both a superb calculator and a mathematical genius. But the newspapers of the time were a lot more enamored of his calculating skills than his mathematical achievements: he was the famed ‘hindoo calculator’.

I won’t hold it against the book as Lalwani might well be aware of the difference, though she makes it so that her characters may not. A little girl may not realize that feats of calculation do not imply mathematical insight, and I can’t tell from the excerpt what the background of Jaggi Bhaiyya is.