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In the spirit of openness which is the hallmark of FOSS such as GNU/Linux, would this book be scanned and published for all to see? That would be great. Like FOSS, math too belongs to the world. I heard someone say that the university has not published many of his works. That would be sad. If published someone like Terrence Tao could write formal proofs for them like he and his team did some improvements for the work by Yitang Zhang.
The notebook (like Ramanujan's three previously known notebooks) has already been published, in 5 volumes by Bruce Berndt and George Andrews, with extensive annotation (e.g. just flipping at random, in the third volume Chapter 6 is called "Theorems about the Partition Function on Pages 189 and 182", and occupies 24 pages, and indeed contains formal proofs etc). A raw scan of the notebook(s) is even available online: http://ramanujan.sirinudi.org
Unfortunately the actual notebook links on that site appear broken
Just enter a page number; it works fine. Or if you wish, here are the direct links:
http://ramanujan.sirinudi.org/Volumes/01/01.pdf
http://ramanujan.sirinudi.org/Volumes/02/02.pdf
http://ramanujan.sirinudi.org/Volumes/03/03.pdf
http://ramanujan.sirinudi.org/Volumes/04/04.pdf
Ramanujan's total known/preserved output today is 37 published papers and these four notebooks; all of it is available on the site. The notebooks have been transcribed and published in several volumes with explanation (as mentioned above); those are the only thing not included on this site (and arguably, not "by" Ramanujan).
The page number selector appears to link to working PDFs.
> If published someone like Terrence Tao could write formal proofs for them like he and his team did some improvements for the work by Yitang Zhang.
From the second paragraph:
> George Andrews and Bruce C. Berndt (2005, 2009, 2012, 2013, 2018) have published several books in which they give proofs for Ramanujan's formulas included in the notebook
FOSS != piracy
And, frankly, I find it pretty upsetting that you seem to negate that equation.
He's been dead for 104 years, where's the piracy?
Sorry for nitpicking, but just trying to clarify what seems like a double negative - do you mean "to affirm that equation", i.e. that the author claims they are equal?
I guess you're right, negating an inequality is likely the same as affirming an equality? I am not a native speaker.
I expect future AI models to be like Ramanujan. Has tremendous intuition but can't accurately explain it's reasoning for arriving at a solution.
It seems like a misconception that Ramanujan could not explain his reasoning.
He did not write it down on his notebooks (and before going to England he mostly lacked the language of formal proofs to do it), but for the most part the equations are arranged in a logical order, and when meeting with Hardy he had no trouble explaining where each equation came from (though a lot of his reasoning was too unrigorous for Hardy's liking).
Perhaps this will be true, for the types of insights that also require tremendous intuition for people to see. One difference is that it will be possible to examine the full state of the AI which lead to the insight, and perhaps learn from it.
(edit: rewrote to flow a bit better)
I’m an atheist, but when Ramanujan claims to derive all of their formulas from god, I ask how we can make it easier for them to listen to god, rather than feel the urge to argue against them.
I feel like his statements on god are very similar to this one:
> Simon P. Norton, an expert on the properties of the monster group, is quoted as saying, "I can explain what Monstrous Moonshine is in one sentence, it is the voice of God."
Solid.
Pun intended.
I feel like this comment and comments by western atheists make me think that the west has this idea of judeo-christian god that they just bring into any conversation without thinking deeply. For ramanujan god is more like an emotion.
> I feel like this comment and comments by western atheists make me think that the west has this idea of judeo-christian god that they just bring into any conversation without thinking deeply. For ramanujan god is more like an emotion.
From https://en.wikipedia.org/wiki/Srinivasa_Ramanujan#Personalit...
> While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing.
That doesn't seem like an emotion at all. It's a very visual, concrete image. It's closer to the "western atheists" view of god that just an abstract feeling of some sort you were describing, wouldn't you agree?
Atheism is an accepted school of thought in Hinduism [1]
Indian philosophy is diverse and vast. See the comparison of these philosophies [2]
[1] https://en.wikipedia.org/wiki/Charvaka
[2] https://en.wikipedia.org/wiki/Indian_philosophy#Comparison_o...
I was with you right up until the word "emotion." Although "Hinduism" is vast and covers quite a few disparate beliefs and philosophies, none of them (to my knowledge) even approximately equate God with an emotion. Even bliss (ananda) is only one aspect.
I don't claim to know the particular religion of his village and/or lineage, but I understand his God to be something closer to the Consciousness that (supposedly) gives rise to all of reality.
I'll never figured out whether Einstein thought that the god as described by Spinoza is a real thing? Since there's so many misattributed quotes of him which frames him as talking about the judeo-Christian god as most people know by modern standards.
Also, there have been other early religions like Gnosticism in the west, which also falls into this category. Point is, even western religion has way more nuances.
> For ramanujan god is more like an emotion.
for most jewish, christian, and muslim mystics and some theologians, as well.
the 'new atheist' conception of what "all christians" think about when they think about god is, well, not very representative.
Yeah, Hinduism has enough room for non-believers too. I’m not religious at all, so when someone asks me if I’m keeping a fast for such and such occasion, or celebrating some festival, I simply tell them that I don’t believe in these things and I’m usually left alone.
Although this aspect of Hinduism seems to be changing and becoming a bit more hardline
Then you need to understand it from a theoretical perspective first. Firstly, when people use the word "god" they honestly ought to define what they refer to by using that word, and what the abilities of that god are supposed to be.
If we're in a physical universe with energy, then it's been explained that a creator-like god can be argued to have 'created' the principle of existence, itself, on which all other things then evolved with energy. So then, what is that principle, stated concretely? Modern physics has already found out almost everything about it.
What is left of an entity if it becomes capable (at least beyond some meaningful threshold) of functionally discarding / disobeying the influence of untruth?
Is someone (in properly controlled circumstances) going to be more or less perceptive of 'what is' when they are more truthful?
Goddess also, actually.
https://en.m.wikipedia.org/wiki/Srinivasa_Ramanujan
Check section "Personality and spiritual life".
I have a personal theory about human intuition.
It feels like answers come "from outer space" or "from God" but it's really just a highly optimized and efficient part of the brain for a very specific function. For that narrow function your brain has an effective IQ of something like 2000. As our brains have a much lower average IQ, we don't have the context to understand how we found the answer so we experience it and describe it as intuition.
If our entire brain operated at an IQ of 2000, we wouldn't experience it as intuition or a flash of genius, we would just say "I figured it out".
What I have read about Ramanujan sounds like he had some form of high functioning savant syndrome. https://en.wikipedia.org/wiki/Savant_syndrome
Its been a while since I read about it but there is some theorizing on the split halves of the brain and the corpus callosum that connects the two halves.
One theory is that the connection between the two halves is a recent evolution and that people used to and some still do perceive the other half of their brain as a separate entity that communicates with them. Possibly being due to the corpus callosum not being the same in everyone. The greater theory being that this is basically the root of all religion.
If you look the origin of the word genius I think there is a good parallel as thinking that your own genius is an external spiritual entity whispering you solutions
If you meet him, and he thought discussing god was interesting, would you then do it? If he wanted to discuss your faith in god, would you do it then?
Discussing is always interesting but I would probably interpret it as him not being able to explain his own abilities like some people just "see" good chess moves or just "know" that there are actually 48 matches on that floor
> However, Wilson died in 1935 and Watson seems to have lost interest in the project in the late 1930s.[3] After Watson's death in 1965, J. M. Whittaker examined Watson's papers (which were in disarray, due to be incinerated in a few days) and found Ramanujan's notebook
Not expecting too many comments here. These formulas are complicated and it took a single person in the later 20th century to re-derive a good chunk of them.
If you are talking about Bruce Berndt, Bruce did not rederive Ramanujan's results alone; he has a big network of collaborators and students who have worked with him, and of course many independent researchers have derived some of his formulas. His books contain all the relevant attributions and history (I talked with him extensively and got some of his classes when I was a phd student in UIUC).
yes that is him. Same for Peter Borwein
can we please stop spending more ink on this hack?
What's hacky about Ramanujan?
So we dont know anything about his math/theorem generation process. By his own admission he saw visions of math/theorem god, which is a BS claim since god doesn't exist. So "god whispered theorems in my sleep" is just a proxy for "I coped it from someone". Many of his so called theorems are false (by Hardy's own admission). Lot of progress in math depends on the "process", not just the end result. But he shares nothing about the process.
explain yourself
I almost feel like there is a random ramanujan posting generator. Every day it runs on a cron job, and with some probably something about him is posted. Much like the dunning krueger effect. Some topics arise with such consistent regularity. Almost makes you wonder what the reasoning is
Because he’s a fascinating and mysterious character on top of being the most brilliant mathematician since Euler.
From https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu... it looks likethere are like 5 or 6 post per year.
One quarter thought out software project, mild overthinking conspiracy theory, and a non sequitur misspelled reference to Dunning-Kruger. This is like a parody of a Hacker News comment