# What needs math?

I probably do not understand the forum https://mathoverflow.net/questions

Have noticed that if someone asks how to solve any equation - then this post with a question quickly removed. Okay. Suppose this question is easy, but often no one knows how to solve any equation.

Often do not understand and do not know the method of calculation and the post is still removed.

Or alternatively write a triviality, but it is perceived well. When the task of generalizing and trying in General to solve post again removed.

I understand that modern mathematics doesn't like the formula, but not to the same degree. If we write the solution of the equation, then it will be removed for sure.

Can explain to me why such hostility?

• May I ask what is your professional relation to mathematics? Working mathematicians have a strong intuition about what is research level mathematics and what is best left for MSE. If mathematics happens to be to you more of a hobby than a profession, I can understand well that you disagree with many other users about what is interesting. (The question in the title is quite different from the one at the end of the body, so the title could be improved.) – Joonas Ilmavirta Jan 26 '15 at 18:55
• Let me add that I am only a professional in some areas of mathematics. I do have genuine questions about other areas as well, but I tend to take them to MSE because I'm quite sure that they would meet with hostility (= rapid downvotes and closure) here. I'm far from understanding what makes many questions at MO interesting or what some of the questions or answers even mean, but I don't let that bother me since I know I'm a layman in those areas and MO is mainly not for the laypeople. – Joonas Ilmavirta Jan 26 '15 at 19:02

Since the question is nonspecific, I can only guess that what instigated your complaint here is the response to a recent answer you gave: https://mathoverflow.net/a/194916/2926 I have temporarily undeleted the post so that others can see what is going on here, and I have placed a lock on the question so that no further voting can take place while we discuss this. (However, this action is as I say temporary: the action of the community members who voted for deletion should not be reversed without strong arguments.)

I agree with the commenters who say they do not see how your post answers the question as asked. The problem statement asks whether one can prove a statement of the form $\forall n \; \text{(under some conditions)}\; \exists D \in \mathbb{Z}[x] \ldots$. Giving an example (in a comment) about a special case $n = 2$ does not constitute a proof, and the body of the answer doesn't give a proof either: it seems only to give a (well-known) method for generating a set of solutions. But to give a proper answer, you have to give an argument which applies to all $n$, covering all the (infinitely many) cases.

It's my observation that many of the answers you give at MO do not go into such proofs at all, but rather exhibit sets of solutions to Diophantine problems in parametric form, which may or may not be the complete solution sets. Just to pluck one such example, there's this thread: Does the Diophantine equation $(x^2+ay^2)(u^2+bv^2) = p^2+cq^2$ admit a complete solution? Generally your posts seem to involve a series of algebraic or symbolic manipulations whose correctness is perhaps best tested using software which handles symbolic algebra, but in all the examples I've looked at, I've not seen a proof from you which is guaranteed to handle all possibilities. Meanwhile, the formulations of the questions make it clear that that's what is wanted and expected. Thus, your posts are often considered to be unsatisfactory according to the mathematical standards here. This is frustrating both to you and to others.

Joonas has asked about your professional relation to mathematics. Certainly your answers give (me, anyway) the strong impression of someone who is not a professional but someone who likes Diophantine equations or number theory as something of a hobby. Obviously there is nothing wrong with that, but the standards of proof at MathOverflow are very high, and it seems to be the opinion of many that such answers do not meet the standard.

Edit: The lock I placed has apparently been removed. To the best of my knowledge, only diamond moderators can remove a lock, but I can't tell who. Anyway, I'm going to redelete the answer, to return matters to where they stood earlier.

• It might be added that partial answers are welcome when appropriate, and many on MathOverflow who post such answers understand this by including text like "This is not a complete answer, but may be useful." If the original poster does not understand what is desired, even despite helpful comments directed to help them understand, then this forum may be the wrong one for the poster and such answers. Gerhard "Partially Answering With Helpful Comments" Paseman, 2015.01.26 – Gerhard Paseman Jan 26 '15 at 22:14
• I still don't understand. In the topic You mentioned the author wrote the sets of polynomials without conclusion and evidence and that no one removes. My attempt to discuss the solution of systems of nonlinear equations - I was erased. mathoverflow.net/questions/146768/… I'm trying to sort out these issues that are in front of you never had. Are you interested in the completeness of the solutions. I am interested in methods of calculation. The formula can either be or not. Bad formula does not happen. – individ Jan 27 '15 at 5:11
• individ, in the post that you linked to, are you saying the community response to the question is inconsistent with the response to your posts, or is it the answer? I think the answer is great: it places the question in a clean conceptual framework where the method of solution (parametrizing a conic via stereographic projection) has been known for centuries. The question itself is not to my own taste because it's very busy or too detailed to be easily readable, but at least someone latched onto the key component and explained what was really going on. – Todd Trimble Jan 27 '15 at 13:17
• @ToddTrimble Who told You that used this method of calculation? I on the contrary was told that you can only use one method of calculation. In the case of using other methods of calculating the answers will be deleted. Here in this topic mathoverflow.net/questions/173541/… When led as an example, formula solving quadratic forms. To see some of you there math.stackexchange.com/questions/738446/… math.stackexchange.com/questions/794510/… – individ Jan 28 '15 at 6:40
• individ, I can barely understand your English, but it sounds like you are too angry to be able to understand the points that people are making. (For example, your post at the Hilbert's 10th problem was wildly off-topic.) I think there is little point now in my trying to help you see. I gently suggest that you take a break from MO for a while. (Or, you can continue down this path of mutual frustration. It's your choice.) – Todd Trimble Jan 28 '15 at 14:38

Here is another typical example. This proves that fights with me. Because of the method of solution.

Integer polynomials taking square values

Ask for exactly the formula for solving the equation. I wrote a formula linking this equation with equation Pell. I wrote the formula in General. You can substitute any of the coefficients. These formulas look quite simple.

For these equations we use the standard approach.

For a private quadratic form: $$Y^2=aX^2+bX+1$$

Using solutions of Pell's equation: $$p^2-as^2=1$$

Solutions can be expressed through them is quite simple.

$$Y=p^2+bps+as^2$$ $$X=2ps+bs^2$$

$p,s$ - these numbers can have any sign. Finding solutions of equations Pell - standard procedure.

Most interesting is that all the examples which lead shows the relationship of this equation with Equation Pell. What is the point to write thousands of sequences ? If there's one formula that describes them all.

Bring as an example the numbers, and it is good. When I write a formula - it require to remove!