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原始链接: https://news.ycombinator.com/item?id=40044901

该用户表达了他们希望出版 Ramanujan 的数学著作，并将其与 Linux 等自由开源软件 (FOSS) 进行比较。他们提到了拉马诺金独特的笔迹，并欣赏陶哲轩等专家的潜在见解。用户在拉马努金的作品中找到灵感，特别是回想起通过梦或神圣干预而变得可以理解的困难数学的例子。他们推荐布鲁斯·伯恩特 (Bruse Berndt) 和 G.H.哈迪 (G.H.Hardy) 讨论拉马努金工作的书籍。该用户还承认在理解高等数学方面存在一些挑战，并对他们之前的言论造成的任何混乱表示歉意。他们分享通过梦想和直觉解决问题的个人经验。尽管对西方无神论提出批评，但该用户强调了在科学追求中相信世界的合理性和可理解性的重要性，并将其比作泛神论的观点。用户最后讨论了系统管理员的完美性，他们将其与斯宾诺莎的上帝概念联系起来。该用户表示，围绕智力本质、发现过程以及信仰在数学中的作用的讨论仍然是有趣的话题。

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

Yeah, when I read "more than one hundred pages written [...] in Ramanujan's distinctive handwriting" in the Wikipedia article, I was thinking "almost indecipherable scrawl", but this borders on calligraphy...

This sounds exactly like the thing I’ve kind of wanted—a compilation/overview of Ramanujan’s work, ideally with commentary. I’ll have to take a closer look at this. What I’d really like is something akin to Yves Hellegouarch’s Invitation to the Mathematics of Fermat-Wiles which seems to be not only out of print, but rather rare now (it’s listed on Amazon at over 400 bucks although that could be algorithmic madness among the sellers).

I think Bruce Berndt's Number Theory in the Spirit of Ramanujan (2006) may be along the lines of what you're looking for, and also possibly G. H. Hardy's Ramanujan: Twelve Lectures on subjects Suggested by His Life and Work (originally 1940, but republished 1991/1999 by AMS with further commentary by Berndt). I'm not qualified to say for sure, as they get too hard for me pretty fast. :) [Some of Ramanujan's easier papers I was able to read (very slowly) for quite a few pages though, such as the one on highly composite numbers.]

> 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

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 think the parent commenter was using the word 'equation' in its colloquial sense to refer to any mathematical expression or statement, despite their statement containing a 'not equals to' symbol, rather than actually equating them (which would have an equals sign).

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.

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)

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).

> 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

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 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?

I had a similar experience while in college, although not as dramatic! While studying CS I was working on problems every night late into the night. I came a across a issue I could not figure out, and went to sleep frustrated. That night I had a dream where a very specific solution was told to me(a voice with text) and it was in a way I had never thought of. I tried it out the next day when I woke up and it worked. It always freaked me out as I don't know how that solution was given to me, my assumption is maybe the subconscious is more powerful than we thought in terms of reasoning.

Its a bit of a psychedelic experience. If someone was on LSD and seeing stuff i would compare it an emotional experience. Of course it goes deeper but just explaining the reasoning behind the word emotion

“Western atheism” doesn’t lack depth, it’s more that the people actively arguing with others that call themselves atheists tend to lack knowledge of their own position. Dawkins, Hitchens, etc. are notoriously uninformed on the topic of religion.

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.

Till you have spent time with a text from one of the "eastern schools of thought" you might naively see them as "religion".

The problems is that they are more nuanced and complex than that. Hinduism, buhddism, Taoism are all lifestyles, thought processes, philosophys, self help, educational, informational... They dont fit in the neat little bucket that western thinking wants to put things in. This is one of those things that you wont find a satisfactory explanation for and needs to be experienced, consumed, lived rather than taught in a rote manner.

I highly recommend that you start with something like Sidhartha by Herman Hesse, and maybe the Tao of Pooh as just a primer on how different these things are. Getting past the surface of hinduism is going to be a battle that would require not only some reading but engaging with actual hindus (who are almost always happy to share).

>And yours are the words of a contemptous, snarky Internet troll.

Mildly contemptuous and somewhat snarky, I definitely can be, intentionally, in some justified contexts, such as in the context of replying to your original comment, which was intellectually unsound, vague and vapid (using your own word against you). Weasel words, like I said elswhere in this subthread. (And don't pretend that your words to me are not contemptuous either. Can't handle tit for tat, or an eye for an eye?)

A troll I am not, although I don't expect you to agree with that. Opinions, bro, opinions. Mine is as good as yours. You don't get to lay down the standard for what is right or wrong, even though it might be a wet dream of yours.

>You might find Reddit a better place for your edginess.

He he, I left Reddit a long time ago, so as to come here and trouble passive-aggressive people like you (just kidding).

>It's not welcome here.

Neither is your kind of crap talk. In fact, I'd hazard a bet, that my kind is more welcome, among the HN cognoscenti (a.k.a. the sane ones), who exist, although they are probably much fewer in number than the hive mind or echo chamber crowd here. Normal distribution and all that, y'know.

Can't help it, bro. :)

We grow up on a diet spiced, on almost a daily basis, with some combination of cumin, coriander, clove, cinnamon, cardamom, ginger, turmeric, pepper, onion, garlic, fenugreek, mustard, sesame, fennel - and many [1] other spices less or not known to the West or via "curry" (!) restaurants and YouTube cooks.

[1] For example, have you ever heard of mango ginger, karonda, mahani, green pepper, black cumin, white vs. black sesame, or long pepper, to name just a few of those, off the top of my head?

Betcha not, mostly ...

And we relish all( )spice (pun intended).

You are confusing using emotion to reach God with emotion being God.

And of course there is "such a thing." You even described what it refers to, a definition which is sufficient for the purposes of this thread.

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.

I would suggest that the answer to that is "yes" in that the Spinozan God is... for lack of a better word the Universe.

(Kaizō in 1923 https://books.google.com/books?id=vLm4oojTPnkC&pg=PA262#v=on... )

> Scientific research can reduce superstition by encouraging people to think and view things in terms of cause and effect. Certain it is that a conviction, akin to religious feeling, of the rationality and intelligibility of the world lies behind all scientific work of a higher order.

> This firm belief, a belief bound up with a deep feeling, in a superior mind that reveals itself in the world of experience, represents my conception of God. In common parlance this may be described as "pantheistic" (Spinoza).

https://www.gutenberg.org/files/3800/3800-h/3800-h.htm

(Ethics was one of the hardest reads I had back in modern philosophy class)

And while it is a gross simplification of Ethics, from news://rec.humor.funny ( https://everything2.com/title/Existence+of+the+System+Admini... )

    1. The System Administrator is defined as the most perfect user possible.
    2. The property of necessary existence means that anything which possesses it must necessarily exist.
    3. If existence is better than non-existence (see the ontological proof), then necessary existence is better still.
    4. Any perfect user must possess the property of necessary existence.
    5. Therefore the System Administrator must necessarily exist.

    However:

    6. Being perfect, the System Administrator cannot make mistakes, delete the wrong account, trash the root directory, mess up a tape load, etc.
    7. Being perfect, the System Administrator can not be capable of goal-directed action, because such action would imply that the network is somehow less than perfect in its current state.
    8. Therefore, the System Administrator is really more of a force of nature within the system.
    9. Arguably, then the System Administrator *is* the system itself.

    Counter-argument:

    1. None, since the System Administrator has been defined to the point where it is a totally useless concept, there's no point in arguing.

    At least this resolves one of the major issues: the Spinozist argument proves that *if* the System Administrator does exist, it cannot be intelligent.

---

The God of Spinoza and Einstein is the magnificence of the universe as it reveals itself to us. The universe is real as is its majesty.

> 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

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.

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

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?

This is a really unnecessarily rude way to call out a minor grammar quibble. The sentence was perfectly understandable. Also, whether you like it or not, it is quite common English (at least in the US) these days to use they/them as third person singular. Perhaps we are slowly losing the distinction between singular and plural the same way we lost it for second person. Language changes.

GP is obviously using "them" to refer to the formulas. I understand how it could be confusing; on first pass I too looked back for the first word "them" could be referencing - but GP tricks us by writing out "god" again later in the sentence! Since we know Ramanujan is male and "god" is used again, the only valid noun "them" could be referencing is "formulas".

Since Ramanujan is dead, I assumed that he had no interest in arguing with the man and was instead talking about anyone with such inspiration.

As an English grammar stickler, of course thou should have said "Why art thou" since the use of "you" in the singular is simply grammatical hooliganism and has no place in polite society.

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).

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.

"we don't know anything about his math generation process" My man just look at the notebooks. He did not use formal proofs but he was very organized and most of his equations had quite a logical buildup from equations that he wrote before. And even the ones that came out of nowhere are obviously worthy discoveries.

I see that. But you're making it sound like you know that for sure. Do you see that there's a middle ground? I.e. "I had a dream where it seemed that God was describing to me these new theorems"?

> By his own admission he saw visions of math/theorem god, which is a BS claim since god doesn't exist

Shit reasoning like this from atheists like you is why I cringe to admit I'm an atheist when people ask me about my religious beliefs. It is entirely conceivable that he saw visions of math, produced by his own subconscious, and attributed these visions to a god. It would not be terribly dissimilar from any artist who attributes their creative visions to a muse. Do you accuse any such artist of plagiarism too?

Lacking formal training does not equate cannot understand something. As far as copying something goes, there should have been an equivalent mathematician nearby from whom he can copy, right? Who is it?

As an atheist myself, I do not believe in god and I do not believe Ramanujam got it from god. However, it does not change the fact Ramanujan thought he got it from god because he could not necessarily explain how he made those intuitive leaps.

The results of his collaboration with Hardy (the approximations for the partition function and the circle method) make it clear he knew well what he was doing. Nobody was doing anything similar at the time.

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

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

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