I'm pretty sure Dmitri Pavlov is not a moderator. But in a sense everyone has some kind of moderation role on MO.

I think the objection is you haven't made a precise mathematical question. I think you've asked a very suggestive question which is quite nice in a way, but the intention for MO is for it to be about precise mathematical questions that have specific answers. As has been pointed out in the comments and answers, in near any interpretation of your question we're a long way from having any kind of formal justification of the periodic table from QM. Similarly, well-known open problems are not encouraged on MO.

You've mentioned a system of postulates for QM, but you have not given a precise definition of what the "periodic table" is. For example, which version of the periodic table? Do you allow for any atoms that aren't in some version, and what formal language do you use for this? Do you have a formal definition of an atom, and what is it? for example, in your formal language, what is the definition of uranium?

Ryan, I do not give definitions, because any system of definitions will satisfy me. Why can't the reader write: "in this system of definitions a version of Mendeleev table is proved, see... ", or ".. is not proved...", or "the problem is that atoms are not defined yet, that's why the Mendeleev table is not yet justified..."? And I indeed need a reference, you told before that the problem is open, where did you read this?

Tom, can you explain simply (just for future), why was this concrete question closed? The moderators (I call them so, because as far as I understand they closed my question, although I do not know who of them is actually a moderator) wrote initially that this is a physical question, a chemical question, a senseless question, a non-mathematical question, and I tried to explain that this is not true, finally they told me that I can ask people to explain this here. So I ask people here.

Ryan: If what you write -- "choose the definitions so that everything is tautologically true" -- was published somewhere with the title like "Justification of the Mendeleev table", that would be an example for me as well. I would not blame a reader who gave me such a reference. I did not understand, "nailing down a framework" is also my duty, when I ask something here?

I really don't understand the controversy with the original question. Perhaps it is not a mathematics question, but it certainly is a sensible mathematical physics question. The periodic table, by which one means the existence of atoms with certain properties which for the purposes of this discussion are not essential to recapitulate, is an empirical fact. Atoms exist and they do indeed exhibit the properties ascribed to them in the periodic table. This is beyond dispute. Furthermore, the simplest atom (hydrogen) is pretty well understood theoretically. Indeed we teach this to undergraduates: a typical undergraduate course in quantum mechanics includes a derivation of the spectrum of bound states in the hydrogen atom and there is a reasonable agreement with experiment. Later in a more advanced course, one learns how to incorporate relativistic corrections, solves the Dirac equation and gets even better agreement with experiment. Since (relativistic) quantum mechanics is so successful with the hydrogen atom it is a sensible question to ask how it fares with more complicated atoms. That is how I understood the original question. It seems not at all controversial and frankly, I'm a little taken aback by the hostility with which it has been met. I think all this talk about which formal system,... to be pretty spurious and if anything shows a certain lack of magnanimity when it comes to interpreting the question. Terry Tao seemed to have read the question in the way that it was intended and I don't think one can do better than his answer. It is a difficult problem under current investigation, but the sheer complexity of multielectron atoms makes progress difficult. For what it's worth, I think the question should be reopened and Tao's answer accepted.

Jose, the question specifically raises the issue of formal axioms for quantum mechanics. So I don't think it's silly to think that's the mode it was intended to be in. If you want to interpret it as an undergraduate/grad level QM topic, isn't the question on the wrong forum? I mean, wouldn't it be fair game to ask for surveys of any physics, engineering or chemistry argument that involves some mathematics -- what makes this topic specially suited for MO?

I feel like we're in a situation where contributors want to answer a different question than the one asked. Moreover, it's hard for me to imagine what I described as being unfair when there's still such freedom of interpretation regarding just what the actual question is. Perhaps people should ask the questions they want to ask, rather than reinterpreting questions to fit what they want?

I think there's a sense in which what he's saying is true. He's likely referring to the work of people like Pauling in the late 20's and early 30's. Of course, "comprehensively" is an over-statement, presumably this is in the standard physics undergraduate jargon for "a talented person seeing Pauling's set-up, with some sweat and years of work could work this out..." the idea being there's something of a framework, an edifice to work with.

There's of course still lots of physical chemistry to be done.

I agree the diversity of the number of reactions is strange. IMO it's a sign the question is clearly not focused enough. Everyone has their own take on what it's supposed to mean. So the question should really be re-written, taking one of these more focused directions, and possible ways of misinterpreting it.

@Ryan: There is a sense in which quantum mechanics "fully, quantitatively and comprehensively" explains chemistry, biochemistry and biology? A useful sense?? Come on.

@Pete: you see this kind of behaviour often enough in physics. The assertion that "X explains Y" does not mean they've actually done the explaining, let alone testing the explanation, it's an assertion that "I believe you can explain everything in Y given X as a starting point and enough creativity and time". The statement is to be taken like a meta-physical law, in that it has been tested in many different ways so it seems to be true, at least often enough for people to think it's true. :)

Instead of looking at this question, let's think about a much more well known one - Hilbert's Sixth Problem, which says "Axiomatize all of physics."

A lot of water has gone under the bridge in mathematics, physics, and philosophy since 1900. Nowadays, I think a lot of mathematicians, physicists, and philosophers, if not blinded by the prestige of Hilbert, would say that the question is (very sophisticated!) nonsense and the mere asking of such a question shows such monumental (and subtle!) philosophical confusion about what mathematics and physics are that one doesn't quite know where to begin to untangle this confusion.

One major problem with Hilbert's problem, and with this question, is that it is phrased in a way that makes very little sense outside of a philosophical framework which is both Platonist and Pythagorean - one which takes it as at least plausible that the world is metaphysically mathematical, where mathematics actually is the structure of the world. (I should backtrack - it also makes sense in a philosophical framework which is very strictly Kantian Idealist - in which mathematics actually is the structure any rational being imposes on experience.) Nowadays, to a large extent because of quantum mechanics, many of us think of mathematics as merely a source of models which approximate experimental results, not as the stuff the world is made of, but merely as a tool that we can use to organize our descriptions and predictions about what we observe, and many of us think of theoretical physics as choosing among (and helping the development of) mathematical models for this purpose, not as finding the correct description of the world.

Because Hilbert was Hilbert, people have taken the trouble to try to interpret the Sixth Problem in a way that makes sense (roughly "Axiomatize various particular physical theories," which actually might be what Hilbert really meant anyway), but unfortunately for the this questioner, the questioner doesn't have Hilbert's standing.

I agree that there is an interesting question hidden here, but I protest at the actual wording: "I wonder if there is a mathematical proof of the Mendeleev table?" Perhaps someone suitably brave can edit that. I am loath to engage the poster, in light of the rather acrimonious string of comments stuck to the question.

Here's one possibility: "Do we have the mathematical means to give a sufficiently precise description of the chemical properties of elements from quantum-mechanical first principles, such that the Mendeleev table becomes a natural organizational scheme?" This seems to avoid the sticky business of proving a table. Maybe one should add a note that we might as well make the simplifying assumption that the nucleus is just a very small ball of charge with comparatively large mass and small magnetic moment.

+1 Gerry

More seriously, I think Scott's reformulation is about as good as it can get.

"@Pete: this is Motl we're talking about. Life's too short..."

He *is* the only one who answered, the answer has been upvoted and is consistent with the remarks on TP.SE. So one can presume that no other physics poster there thinks that the answer needs improving.

Thanks to all for the response, and excuse me for the delay.

Special thanks to José, who gave a quotation of Feynman. José's interpretation indeed would have been a good question, but I must confess, it is not what I wanted to ask. I had in mind the axiomatization of quantum mechanics, so Ryan understood me correctly, although I do not share his idea that "the question is clearly not focused enough". I do not see a way to focus it more clearly, than it is already focused. (I would not protest againts Scott's reformulation, but I am sure this would not solve the problem of "acrimonious string of comments ".) Ryan says that I could cut my question into a sequence of more specific questions, but I do not see how this could be done. I must say also, that I do not agree with Andreas Blass: I think that questions like "what is the definition of atom?" must be legal at least in the situation where questioner sees mentioning of atoms in mathematical texts. Anyway, if there are no objections, I will edit my original post, quote there Feynman (with reference to José) and give reference to Scott, Andreas and Alexander.

I started this thread in Meta (and put it to this category -- Etiquette), because people's reaction to my original post reflects a problem which I find to be very important and urgent - the problem of interdisciplinary communication.

The problem is the following. When somebody (let's call him A) asks a specialist (we call him B) a question concerning his discipline, then there are only three possibilities for A to count on a reasonable answer:

1) A can try to formulate his question in the language of B's discipline, and B will give an answer in this special language (so this is the situation, when both A and B actually are specialists in this field),

2) A can count on their common language, the langauge, that unites A and B (I would call this situation "polite specialist", since it does'n require from B any efforts, he should just recall some words which he had been taught, but maybe did not use them for a some time),

3) B can try to understand A's language, then translate his question into the language of his discipline, find an answer, and retranslate it again into the language that A understands (this can be called a situation of "a generous specialist", since this line of behavior can require some efforts from B).

I claim that the modern scientific society moves step-by-step to the top of this list (remark: I am speaking about communication, not about the situation of business, where A pays B money, or A and B are in some other mutually beneficial relations, like partnership, friendship, etc.). In my life the situations 2 and 3 occured only when I was a student in USSR. This does not mean that I am a supporter of the communist idea, but the unpleasant truth is that when we lived under communism, the idea of solidarity between mathematicians was much more popular than now. I could telephone any mathematician in the USSR, no matter who he was and where he lived, and he willingly was answering my questions. After the fall of the iron curtain almost all these mathematicians emigrated, and what is pity, almost all of them do not reply when you try to contact them.

I deduce from this (and from my own expirience of communication with western mathematicians) that the situation in the West is even worse. My experiment at theoreticalphysics.stackexchange shows that you can't count on generocity of specialists (situation 3). My post here in MO shows that even counting on politeness of colleagues (situation 2), of whom everyone undoubtedly had been taught the language you try to use (everyone of us knows what axiomatic system is, isn't it?) -- is too idealistic. Of course, I am extremely grateful to those three persons who managed to give their answer before my question had been closed, Terry Tao, Denis Serre and Physicist (and after reopening it to Jeff Harvey, who added his opinion) -- but I hope, you understand, that my impression of what I saw here would have been much more pleasant if I had not been mocked at two websites before coming to Meta.

I so far stayed out of this discussion as the subject of the question is/was quite far removed from things I have a meaningful amount of knowledge about, however since now this is taking a very genaral turn some remarks:

Sergei Akbarov, you suggest that:

1. Before closing a question, a moderator should verify that the questioner indeed does'not understand what he wants.

I would say it is also, or even more, important to make sure that others can understand what the questioner wants. For a highly ill-formed question the questioner can still know very precisley what she or he wants, but nevertheless it could be completely incomprehensible for anybody but the questioner. In such a case to me the only useful course of action is to ask the questioner to rephrased, make more precise,... what she or he wants to ask, and posibly close the question in between (with the idea that it is then reopened once clarified). Look, it seems to me some people simply at first (mis)understood your question as one being not about mathematics but rather physics/chemistry, so off-topic here (and I can assure you from observation that for example Greg Kuperberg is a very helpful and tolerant person on this site, so to me it is really a given that he simply could/did not understand what you want, or what he thought you wanted was not on-topic). Then you explained that, no, it is actually more mathematical then they understood it, then it was not quite clear to some what was meant precisely. Then some more explanation happened, until some people agreed that it is now precise enough to be understandable. While the main purpose of the site is to allow people to ask question and get answers, another purpose is also to allow others to learn something by reading what is written; so one really also needs to make sure it is somewhat easy to understand what is meant.

Regarding your question, I would say that at least to me the problem was/would have been [I did not interact with it in any way] with 'proof the Mendeleev table'. What should this mean? What even is the Mendeleev table? In some sense I assume you do not refer to some specific original historical document from the 19th century but what nowadays goes by this name, but these tables are not unique and change over time. So, what exactly? And, what is 'a proof'?

You yourself and others later gave meaningful interpretations of this, and still others anticipated (guessed?) the intent correctly. But, I think it is at least not completely unfounded to say that a question for a 'proof of the Mendeleev table' is not a precise question, as 'Mendeleev table' is not defined and neither is 'proof' and there is sufficient room for reasonable interpretation. (What if there were something that worked until atomic number 42, is this then a 'proof' of 'the Medeleev table'?)

In this sense in my opinion your question in it original form simply does not meet your point 2., as 'proof the Medeleev table' is not sufficiently precise, and can mean quite different things to different people (as experimentally verified).

(cont.)

Dear Sergei,

1) It is true that mathematics nowadays, especially in the United States, runs by the principles of Geselleschaft and not Gemeinschaft, but it is such a large enterprise that there is no choice.

2) To me, in the 21st century, naive realism, naive Platonism, and naive Pythagorianism are all signs of crankdom. For me, the way your question was phrased set off this alarm.

Sergei,

a triple of observations:

• your question was really an outlier in the context of MO. Surely you can see that questions involving proving anything regarding the real physical worlds and, much less, the periodic table, do not exactly abound. I suggest that you not base your opinion of the site based on your experience regarding such a question, for it is really not representative of anything. In my humble opinion, your question was off-topic—this is no obstacle to certain great users of ours who have the amazing capability of turning off-topic and/or blatantly bad questions into what they might have been in optimal conditions and answer them all in one big swoop.

• your comments regarding politeness and generosity of the community simply startle me. One of the most amazing things of MO is the immense display of generosity and politeness it offers! I have been reading through the site for a long time now with steady frequency and I still marvel, every day, at the energy, good will and good manners that most of its active participants put into it.

• the site is run more or less in a communitarian way. Any user gets voting powers, long-term users get closing powers, even longer-term users get deletion powers. The moderators are are very, very small set of users (three or four?) who only in rare cases get involved in those matters.

It's a made-up word, referring to <a href="http://en.wikipedia.org/wiki/Crank_%28person%29">crank</a>.

@Todd Trimble: thank you very much.

@Alexander Woo: following your reasoning, naive questions, like "what time is it?", must also be a sign of crankdom, since only a person who never heard about Big Bang can ask them.

@Todd Trimble:

"I entered a vote to close"

I agree.

@akbarov:

I mainly referred to the FAQs for 'procedural' things, e.g., who is a moderator who is not, how the site is run in genral. Explained somewhat to the end, and in the point on the reputation points. This is not really relevant to the question, but possibly to some of your inferences on the MO-community in general.

Something else that is in the FAQs that could have been helpful, is this:

What if I don't get a good answer? In order to get good answers, you have to put some effort into the question. Edit your question to provide status and progress updates.

For example somebody mentioned of having overlooked your clarification regarding your question given in a comment.

Specifically you said in a comment this:

The Mendeleev table claims, for example, that the first electronic orbit can have only 2 electrons, the second - 8, the third - again 8, the fourth - 18, and so on.

Which I find quite helpful in understanding what you are after. So, once you noticed there is some confusion what you are asking for you could have added things like this in the question. Now, not doing this, is certainly not breaking some rule. All I am trying to say is that I think some people really found it difficult to figure out what you are asking for, and perhaps you could have helped them a bit more, and by doing so accelarated the process of arriving at a version that more people appreciate/understand.

I think the question in principle is good for MO, it is just that it took some time to collectively figure out what it was.

Finally, and a bit unrelated, I am not sure how you can say that you agree with me that MO is better than Russia, as I said nothing on Russia. (And would not as I have not detailed knowledge.)

@Todd Trimble: perhaps it's me who did not understand something. "I entered a vote to close" - does it mean that you would like this discussion to be closed? If yes, I have no objections.

@quid: "how you can say that you agree with me that MO is better than Russia" -- I had in mind that in comparison with what happens in Russia, what happens here looks better. So I agreed with you when you wrote that "you can appeal, and the appeal was even successful".

@grp: I don't agree with what you write:

"Should mathematicians be robots? I don't know, but that has nothing to do with what is considered appropriate for MathOverflow."

But I agree that the further discussion will be a waste of time. I think everybody here made his point, and I do not believe that something essentially new can be added. However, if somebody wants to tell me something more, he is welcome -- I'll willingly answer by e-mail, or continue here, it's up to you.