Is it useful to the community to post questions without having had formal training in mathematics?

As someone who is interested in how numbers behave, but with no formal experience or vocabulary, I recently posted a couple of questions and gained quite a bit of knowledge and insight from the discussion.
They were both closed after a day, then reopened. So my contributions lay somewhere between being useful and not useful. I am wondering if I should refrain from posting questions until I get more some formal training, or should I plough on and put more effort into the meaning of my questions and how I formulate them. I don't mind losing reputation points, but at the same time, they are a reflection of how useful my presence is to the community.
Did I take the plunge too early?

• I checked your questions (all three). The two which have been closed need some more details from your end. Please understand that the closing is in no way related to your experience / maturity in mathematics. You should try to address the concerns regarding details and clarity and hope that the questions get reopened. Aug 12 at 11:53
• In my experience, this is best place for novices (much better than you can hope from a conventional source like teachers, professors), but you need to follow the rules sincerely. Aug 12 at 11:55
• Aug 12 at 11:57
• I think what you should do before posting any question to math.stackexchange is to do a thorough search of the site to see whether a question very close to yours has already been asked and answered on the site. The site has been in operation for over ten years now, and pretty much every possible precalculus question has been asked and answered several times over. Use the efforts that others have already put in to learn the answers to your questions. Aug 12 at 13:54
• @GerryMyerson I do try. The problem with not having the correct vocabulary is pretty dire, because I can't formulate searches properly, and understanding the answers is often laborious when I do find similar questions. Aug 12 at 14:24
• A very good post that might assist you when asking question, is the math.meta post How to ask a good question. The suggestions don't require sophisticated knowledge to utilize. It provides tips on ways you can add context and improve your odds that the question will be well received. Good luck! Aug 12 at 21:32
• Closely related (by same OP): Should I delete my questions? Aug 14 at 17:21
• I would recommend caution in deleting Questions just because there is (so far) no Answer. Your efforts to hone and clarify a Question, provided it is of genuine interest to you, may benefit others in the long run (the dictum being, if you have this problem, so might others who lack the time or skill to articulate it). Aug 14 at 18:07
• @hardmath Here is one. math.stackexchange.com/questions/4222894/… I was thnking of reformulating it to "is an x-dimensional space with all units being $i$ isomorphous to an x-dimensional space with all units being $1$?" Firstly, I am not sure it is what I actually meant, and secondly I think the answer is probably yes. If it is it seems like it might be a bit of an idiotic question. Should I just reopen it, and leave it as it is? Aug 14 at 18:33
• I've never seen "isomorphous" in math or, indeed, anywhere. "isomorphic" is common in math, but only when specified (or clear from context) whether one is talking about isomorphic as groups, or isomorphic as vector spaces, or isomorphic as fields, or isomorphic as topological spaces.... Adding "all units being $i$" doesn't help, as the word "units" has several meanings in mathematics, none of them being compatible with talk of "x-dimensional space". If you post a question like that, you had better know exactly what you are asking, and how to get your meaning across. Aug 15 at 3:21
• @GerryMyerson My mistake, but apparently "isomorphous" exists in crystallography. My question is probably too basic. CalvinKhor said "If you work only with the imaginary line,(...) there is nothing that distinguishes them [imaginary numbers] from the real numbers." The babble about isomorphic is trying to generalise this to any number of dimensions, none of which have a real part. With no formal training, I am rather similar to a child learning to speak by testing words and learning their exact definition through corrections by adults, thankyou kindly for the pointers and your time. Aug 15 at 7:18
• OK. I think Calvin was saying that a line is a line, whether you choose to mark it off in units called $1$ or $i$ or $17$ or $\sqrt2$ or $\pi$ or .... But there's a lot more to mathematics than lines, and there's even a lot more to lines than just marking off distances on them. Aug 15 at 10:25
• Even I have not had any formal training, except more basic high school courses. So as long as you are willing to learn and write good posts, you totally can be a part of the community without formal training. Aug 20 at 1:50
• @GerryMyerson "A line is a line" by Calvin did help me clear up some confusion. I think when the fog clears I will end up realising that where I see some vague property of primes where they are somehow "born" on a 1D numberline, and cannot spontaneously pop out of a 2D grid made up of integers (except where one coordinate is $1$), it is simply a synonym for "they only have two factors, and one of them is $1$". Aug 23 at 15:50

As regards to the question in your title : yes, yes, yes. A big yes. It is very useful to post questions despite having no formal training in mathematics.

Having said that, it seems that many of your questions are being closed for a lack of clarity. For example, you tried to define a variable, clarify the meaning of "building" and at least one one place mentioned that you were searching for clarity on some of the terms that you used and were integral to your question.

So we realize that the question is unclear : that's what is sort of stopping you in your tracks. The reason why it's unclear, as far as I see it, is because of the usage of words which are open to interpretation, in place of a clearer setting.

Now, here's the catch : for the kind of questions you ask, I actually believe that you don't really require formal math training. For example, I think you've asked about some questions on $$i$$, and prime numbers. These are topics that are introduced in school, and not necessarily from a formal viewpoint. (Inasmuch as I hate the treatment of $$i$$ in school because it's almost an out-of-the-blue introduction).

The people you meet here are, on average, college level students who will have understood these concepts at a higher level. Hence, any vague wording will be scrutinised. After all, nobody wants to answer a question that you haven't asked, and they'd rather know and help you to ask your question before answering it. Having said that, I believe that if you have an upper-secondary textbook (Grade 9, I believe) in mathematics which is well written, then you will be able to get far more clarity on the kind of questions that you want to ask about $$i$$, and on the definitions of prime numbers (which may also be there in a grade 7 or 8 textbook.) These texts contain clear enough expositions on what prime numbers and $$i$$ are.

Since I'm recommending that you stay on site and not take a complete step away and study before coming back, here are some tips that can help you firm up your intuition vis-a-vis these concepts.I also see you as an experiential learner, and therefore Kolb's model would say this : Experiment, Experience, Observe , and Conceptualize (and repeat for a new concept). You need to find ways to do each of these things for concepts that you learn, and naturally with higher mathematics this is more difficult, so I understand your conundrum. Having said that :

• Draw diagrams : Plenty of them. A picture speaks a 1000 words, and also explains exactly what is going on, provided it's well-labeled.

• Use examples : If someone wants to understand any kind of pattern, the first thing they need is plenty of examples to work with. So when you are asking questions that try to discuss a particular phenomena, make sure you have examples illustrative of that phenomena.

• Read and link heavily : I've suggested a very rough type-of-reference, but you will find many online references, including videos, slideshows, PDFs etc. that will be able to place your question into a better framework than you are able to. Reading allows you to borrow the frameworks of other resources, and linking allows you to let the readers of your question know about these frameworks.

• Discuss : Questions on math.se don't start out on hold, which means that a lack of clarity must be spotted by users, discussed on the question and only then can action be taken. In all this time, an answer can come up, the one that came up in one of your questions was a bit off, for example. You (have the reputation for this, don't worry, and) can use chatrooms like the Mathematics chatroom (or visit various chatrooms and see which one you find comfortable) and find people that will help you clarify your question and prepare it for asking on MSE (or who knows, answer it!)

Of course, there are other constraints that we would place on an MSE question other than being clear, but keeping that aside this would address what seems to be the wrecker-in-chief for your questions.

Of course a formal mathematical training would help, but I cannot help but feel that experiential learning is what it is : it's a slow process, but also a complete process in that the learning is imbibed well and understood from multiple points of view. So I would say : choose carefully your resources for study, and find those that best suit you. (I'd say videos, slideshows and math learnt from physical activities would be great for you rather than walls of text).

I do not think you have taken the plunge too early, I just believe that if you follow the four bullet points I've set out above, then you and your questions will benefit massively from these. Experiential learners are very rare in mathematics, therefore I would say keep going, and I know that you will grow into a good contributor!

Side note : This is a note on searching. Discussions in chatrooms on math.se will help you find questions on site linked to yours, of which as Gerry says there are plenty.

So part of your "list of references" is math.se itself, and while resources such as Google and/or the standard search engines may not be of much use for your questions (given the "absence of keywords", which is something that search engines use very well), it is important to know that reading will give you a list of "keywords" that you will hope capture your situation well, and will reflect in searches. Thus, finding material will be easier to do once you have discussed sufficiently.

Finally, this is the How to ask a good question page, something that you can always look at if you would like to improve your question.

• @TheresaLisbon I realise that thanking everyone is not useful, but your answer took a good deal of time and thought, and pointed me to many important issues. I feel that deserves gratitude. Thankyou. Aug 14 at 7:48
• @ToMath I would like to thank you for airing your concerns on the meta platform once again, and I wish you a good time on the site! Aug 14 at 7:57
• @TheresaLisbon The lack of clarity appears to me to be due to my almost total grasp of mathematical vocabulary. It may be uncommon to be an "experiential learner", so perhaps a useful standpoint, but unless I obtain some basis in the shared vocabulary, my questions will always seem vague. There is little to be gained in finding new words for existing concepts which are already described by well-defined mathematical terms. Is there a ressource which ressembles a dictionary of mathematical symbols where I could rapidly find their context and meaning? Aug 14 at 7:59
• Sorry, I just realised I could search for "mathematical symbols". Silly me! (en-gb). Duh! (en-us). en.wikipedia.org/wiki/Glossary_of_mathematical_symbols Aug 14 at 8:13
• Yes, that's a good place @ToMathto be searching for math related terminology. Let me know if you need assistance in asking further questions in the future. Aug 16 at 6:16
• @ToMath: I just read through everything here and my recommendation is, for now at least, to avoid getting caught up in "gee whiz" and avant-garde sounding math that you encounter, and instead tread carefully and thoughtfully over school level mathematics for a while, much of which leads naturally into the more interesting-sounding esoteric stuff that you'll then be in a much better position to self-study/investigate. With this in mind, I strongly encourage you to get copies of the following, many of which can probably be found in public libraries or small college libraries, (continued) Aug 18 at 17:40
• or can be obtained by interlibrary loan using public libraries (at least in the U.S.). I've listed them in my recommended reading order. Realm of Numbers by Isaac Asimov (1959); Realm of Algebra by Isaac Asimov (1961); Mathematics for the General Reader by Edward Charles Titchmarsh (1959, 1981 Dover reprint); Recreations in Mathematics (continued) Aug 18 at 17:56
• by H. E. Licks [pseudonym for Mansfield Merriman] (1917; this is more for casual browsing than cover-to-cover reading); Mathematics and the Imagination by Edward Kasner and James Roy Newman (1940; 2001 Dover reprint); Mathematics for the Million by Lancelot Thomas Hogben (first published in 1936, several editions and a huge number of printings since then; a bit long, but after a bit of background you can easily skip around and look at the chapters that most interest you). Aug 18 at 17:56
• @ToMath: This list of books, which I plan on expanding and giving more details about at some future time, might also be of use. Aug 18 at 18:01
• @DaveL.Renfro Thanks for your brilliant resources, I hope OP will benefit from these. Aug 19 at 22:24