One might, perhaps, be more willing to help educate you, if you showed more willingness to be educated. If you cannot tell the difference between constructive criticism and "making fun" then I suggest you find somewhere else to pursue your interests. He that hath ears to hear, let him hear.

I don't think that anyone on this site knows the answer to your question, and indeed it is quite possible that no number theorists at all know the answer. That is the reason that there is no answer forthcoming.

Regards,

Matthew Emerton

Something else: when I visited that question yesterday I saw two comments of you on Franz Lemmermeyer's answer there. Now, they are gone.

Please recall that you have been sent an email by the moderators which, amongst other things, said: "and so I would ask that you do not post again on the site". As such, the moderators will delete anything your account posts on the site. Please try math.stackexchange.com.

yours sincerely, Scott Morrison

Again, I take Andrew Stacey's stance (from another thread)and recommend tolerance.

If you truly wish to take my stance here then the recommended course of action is actually tolerance of sigfpe's attitude even though one might think it bizarre and an over-reaction. The tolerance that I commend is not that which says, "Let's agree to disagree" or "Everyone's point of view is equally valid" but rather than which says, "I think that X is right, you think that Y is right. I shall act in accordance with my views, but knowing that you think otherwise I shall do my best to act in such a way that I do not cause unnecessary offence.". Thus, to take the matter in hand, if I am offended by something then I do not hide that fact, but my reaction to it is tempered by the fact that I realise that not everyone else will be similarly offended.

If you decide to take him up on his offer for you to email him, or should you email anyone else for that matter, not only should you make an effort to use correct grammar, capitalization, and punctuation to the best of your ability (1). You should probably also avoid carrying on at length about what your personal philosophy of mathematics is, and you should also avoid going into your personal circumstances at great length. (Some brief description may be okay. Long descriptions are not -- they will almost undoubtedly backfire.)

Your task at hand in contacting a mathematician (or talented student -- we are all students in some sense) should be how to more effectively understand modern mathematics. It would be unwise to go into the deficiencies of the Indian educational system -- even if you have a point there. Just stick to the task at hand. And don't offer effusive thanks ("touching your feet"); that too will probably backfire, as it sounds too effusive too western ears, and possibly sounds insincere. You can say, "I really appreciate your help; thank you very much", and most mathematicians will be pleased to hear they were helpful in some way.

As an American mathematician, I tend to the democratic feeling that we are all in mathematics together, and most of us enjoy sharing knowledge with each other when we can. People like me tend not to think of themselves as demigods who deserve to have their feet touched with reverence -- in fact, most people from the culture I am familiar with are rather uncomfortable around such notions. We are just human beings. I advise you to keep "touching your feet" to yourself, and not make others uncomfortable.

(1) Of course, the international language of science is "broken English" -- a lot of allowances are made for less than perfect mastery from non-native speakers. But one should try to do one's best anyway. People appreciate care and thoughtfulness in presentation.

P.S. When emailing professors, as with posting on mathematics fora, I think you'll get a better response if you capitalize and use proper grammar, though I understand you only apparently recently learned how to use a computer.

As a person of a similar age who also participates on this forum, let me try to offer you some advice.

First, I recommend following the many suggestions offered you by Todd Trimble, Gerry Myerson, and others who have commented on your threads. Even if your goal in mathematics is purely recreational (i.e. you seek to appreciate the field for its own sake, but have no thoughts of a potential career in it), to understand any aspect of modern mathematics requires a great deal of training, and working mathematicians have undergone this. You have opined that everyone needs to start somewhere: this is precisely what you should do. If you have not already done so, reading books such as Ireland-Rosen (and to name a few more, Serre's "A Course in Arithmetic," Rudin's books on analysis, etc.) is a prerequisite to understanding fancier things. Note that there is much interesting mathematics outside of number theory. This is what mathematicians did when they were youngsters.

Second, I recommend that you change your handle to something religiously neutral, and that you not use the phrase "touch one's feet." Most mathematicians (at least in my experience) are quite happy to answer questions, and don't consider it a waste of their time. In some (extremely nebulous) sense, it is their job. A simple "thank you" will be much better received.

Finally, I recommend finding an expert to talk to, who will be able to offer more detailed advice. If it is not possible to do that in person, at least an email exchange. Like you (and probably most people on this thread), I too tried to learn mathematics by myself for a while, but it is very hard to do, and talking to other people helps you understand what is important.

If you want advice (and I'm not sure you do), it would be to first master things more within reach. Are you able to solve all the exercises in a book like the one by Ireland-Rosen?

I am not saying that you will never solve a grand problem like a Millenium Problem (which by the way is probably the hardest way yet devised to earn a million US dollars), but you have to start from a much more realistic level first. It would be a very good idea to ask for advice from a professor face-to-face, and devise a program of systematic study. Unfortunately MO cannot take the place of that. It really can't.

The behavior Alex describes bothers me though. MO is supposed to be a professional environment, and as a general rule it's inappropriate to bring religion or politics into professional settings.

I would like to add that this is a situation that makes SE's uniform "no sigs" policy make a lot of sense.

Well, the gracious suggestion made by Pete Clark has been acted upon. David Speyer posted a beautifully formulated question and got some excellent responses, so at least something positive came out of the experiment. But I have to agree that as far as tg is concerned, nothing seems to have changed. It is 'nice' that tg thanks these efforts (profusely), but aside from that he has no meaningful response, and there is no indication that I can see that he has learned anything from them.

Therefore I see no real counterargument against the latest thoughts of Will Jagy and Alex Bartel. This experiment has run its course, I'd say. It's sad, of course, but continuing down this path was bound to lead to disappointment anyway. Sometimes disappointment is the best teacher. I wish tg future growth and success.

Trust God hasn't engaged in any proselytization beyond his or her name.

That's not true. He wrote in a comment addressed to me at some point (when I objected that I didn't want to be blessed by anyone) that if god doesn't bless me, then my life will be hell, etc. This comment is now deleted.

Taking the nick Trust God and signing mathematical questions with "may god bless you" is, to me, comparable to calling oneself Joseph Stalin and signing the posts with "may the proletariat of the world unite against the evils of capitalism". Actually, I see hardly any difference at all.

Anyway, seeing as this site is supposed to be a place where professional mathematicians have pleasant mathematical conversations, a user who keeps alluding to god, babbles jargon he doesn't understand, shouts, writes in his profile that he wants to have nothing to do with us snobs, who purposefully try to obscure our ideas, etc. has already been cut too much slack, in my opinion. I am with Will Jagy. I will flag his posts as spam until their quality shoots up by several orders of magnitude. Given his history (and the fact that I wouldn't want to have this person around in our common room, of which MO is supposed to be a virtual analogue), he will have to ask much better questions than an average user, before I stop perceiving of them as spam.

And if I were to tell you that 'sigfpe' represents an otherwise unutterable derogation which bothers me every time I see it, would you change your handle?

If a sizable group of people felt this way, yes, I'd change it. It'd be the polite thing to do.

But I can see I likely hold the minority view here so I'll follow your recommendation for tolerance (which I am, of course, already doing).

But you know, if no one else wants to do it....Anyway, I agree that reading Franz Lemmermeyer's paper first is basically a prerequisite: it embarrasses me to admit that I have not yet done so.

I hope it's reasonable to add a request (possibly already understood by now) that whoever asks such a reformulated question acknowledge Iyengar/trust god's posts in some way as having led to this. This in order to assure him that no one is trying to undercut him or 'steal' from him, and also perhaps to boost his morale a little. I just hope that wouldn't backfire in some way.

In principle, this can be a reasonable question even if A is well-known to be open, as an intuition/big-picture question.

Agreed.

It also seems clear by now that Iyengar has burned through too much goodwill to get answers to his questions: he is now asking minor variations of the same question over and over again and not getting anywhere. But as a practicing number theorist let me say that his questions are not nonsense: they are in fact not so far away from good questions that an inquisitive student of the field would do well to ask. Part of the problem seems to be that he asks for a lot without putting in a lot. E.g. sometimes he simply asks things that we just don't know the answers to, e.g. from his latest post:

1)is there any similar interpretation of the Tamagawa numbers in the case of elliptic curves ,by using the Gauss genus theory to relate it to the Class group,as done in the case of pell-conics

Logically speaking this is pretty fuzzy: what is the "Gauss genus theory" of elliptic curves? If anything, it should be the Shafarevich-Tate group. What is the "class group" of an elliptic curve? Most working number theorists would say that the closest analogue we know is again the Shafarevich-Tate group. So can we relate the Shafarevich-Tate group to itself? Well, yes, but obviously this is not a fruitful question.

Nevertheless there's something here: for instance, Cristian Gonzalez-Aviles gave a very stimulating lecture series at UGA a couple of years ago on, broadly speaking, this circle of issues. When I mentioned the conventional wisdom in the above paragraph -- i.e. that Sha is basically the class group in the elliptic curve context -- he gave me a big smile and shot back, "By the end of this talk I hope to convince you that that's not true." (What he convinced me of by the end of the talk was that there was a lot of complicated, interesting mathematics there and his guess was probably better than mine.) I would love to hear someone explain some of the analogies here -- e.g. between Sha of tori and Sha of elliptic curves -- and give some account of why the beautiful theories in the case of linear algebraic groups hit a wall with elliptic curves. In fact, an old friend of mine once expressed the desire to inquire of John Tate exactly when he saw that the theory that he was developing wasn't going to work in the elliptic curve case in the beautiful way that it did for GL_1 in his thesis and what he learned from it. (I don't know if he ever got up the nerve...)

[2] and is the up to now a good cohomological definition of the Tate-shaferevich group of elliptic curves ,and references will be useful,

Again, this needs sharpening. I could say that the Shafarevich-Tate group is defined cohomologically, and ask exactly what is not good about the current definition. But if I were in the mood to be more sympathetic, I might admit that the fact that it's so incredibly hard to show the finiteness of this group -- whose finiteness is the key to everything: more and more it is the case that if we assume the finiteness of Sha we can go on to prove our big theorems, but without that we are absolutely stuck -- and that this is indeed some evidence that our cohomological definition is not "good".

So I like the idea that someone else could ask a question along the lines of what Iyengar has been repeatedly asking, and experts could take a good crack at answering it once and for all. (Or until the field advances, of course.) I know I would learn something from this, and it would remove the bad taste in a lot of people's mouths right now that someone is repeatedly asking deep mathematical questions (or, at least, questions about deep mathematics!) and garnering little more than downvotes, closures and comment wars. I think it would be a fun exercise for some enormously respected not-quite-insider -- e.g. Terry Tao -- to perturb Iyengar's questions into a question that the real experts in the field are willing to answer. If they like, they could play the game of changing as few words as possible: a complete overhaul would not be necessary.

Any takers?

It is sad, although it's not clear to me how passionate he is about mathematics. I can't imagine what we're seeing is at all enjoyable for him, and it's hard to conceive of someone being passionate about mathematics who isn't deriving any enjoyment from it, big or small.

Yet, while there was some small positive reaction to this (I am thinking of the one reference request for somewhat introductory material), by and large these suggestion get ignored or misinterpreted. So, it seems to me to repeat them (in increasingly direct or snarky or even rude form) does no good. Although, yes, it is difficult to not say something as response to certain of his statements.

Perhaps, a strategy could be to ignore him for a while; not completely, but in the sense that if one has nothing specifically mathematical to say on his questions, say nothing (and also do not vote to close).

Of course, it could happen that the site gets flooded by ever more of his questions, and one would have to rethink this startegy. But, and this is my hope, perhaps he will after a while either arrive at the conclusion that this community is unable to answer his questions and leave us alone (which would be a solution of the problem) or in a calmer mood really rethink his approach and eventually arrive at a more reasonable one (which would also be a solution of the problem, and indeed a better one).

Finally, I find the situation quite unfortunate without really knowing a good solution, because afterall a 19 year old that is so passionate about mathematics is in some sense great; if only he would/could direct his energy and enthusiasm into a more reasonable direction.

p.s. This discussion assumes 'trust god' is real; I already entertained they idea this is somebody trolling. If so, the ignoring seems also reasonable.

I can't tell how much sense or nonsense there is behind these questions. Even to a complete outsider like myself, it's clear that there is at least some sloppiness in trust god's latest question; for example, instead of a product of Tamagawa numbers being related to class groups, he has a single Tamagawa number $c_p$, and even later he refers to 'the' Tamagawa number $c_{p}'$ of an elliptic curve. The fact this goes unnoticed or uncorrected for quite a few hours after he posted his question could lead one to believe he's just playing around with words without real understanding.

But I leave to the experts to decide -- quite apart from the history or what sort of person trust god appears to be -- whether there is a germ of an interesting question there. That's what I'd really like to hear!

@Zev: thanks. Obviously it's still not a great discussion, but I guess there's no need for deletion at this point (trust god removed some of his comments as well, which will prompt me to remove mine and simply leave a pointer to this discussion instead). IMO, trust god may forfeit his right to ask questions if he continues with the implicit insults.

As to your proposal to ban trust god / prevent questions from him about BSD, I'm not sure. Thinking only in terms of the end result, I think it would be best, but in some sense I feel like trustgod has a "right" to continue asking questions that outweighs that action.

As I wrote in a comment, this reflects very poorly on MO, and I feel some action might be warranted. For example, this particular question should perhaps be locked and deleted by Math Overflow.

Since trust god seems to be unable to post a question about Birch and Swinnerton-Dyer that avoids the fate of being downvoted and closed, I also wonder whether it makes sense to have him (I suppose not 'her') continue to post on this topic. Part of the problem seems to be the sheer history of these posts (which are all on the same topic, having to do with interpretations of Tamagawa numbers). It seems to me that there might be the germ of a reasonable question if it came from someone else and were properly reformulated in correct mathematical English, and it could lead to a more enlightening response.

But in the case of trust god, this seems to be an impossibility, and so the question is whether it might be more compassionate in the long run to undertake an action such as barring more questions of this type from trust god, or bar him from MO altogether, rather than subject him and everyone else to these tiresome and predictable outcomes.