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I am trying to learn proof based math on my own and once I construct a proof, I often have a gut feeling that it's not airtight.

What is the best way of asking such questions?

My findings till now:

  • This question's answer in Meta points out that reading other people's long and formal proofs is pretty boring and annoying (which I agree with). But, it's not always possible to write an airtight proof even if I feel I know the subject.
  • Some posts state that one should include it as a part of the answer and others state that I should answer my own question and leave the body only to the question.
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    $\begingroup$ Does your gut give you any indication of what part of the proof might not be airtight? That is, how precise can you make your gut feeling? $\endgroup$ – Rahul Jul 7 '12 at 8:44
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    $\begingroup$ @RahulNarain. Yeah I could narrow it down. I mean, my goal would be to point the readers at a particular portion of the proof where I'm not sure. The last thing I'd want is someone to waste time going through a huge formal proof. $\endgroup$ – Inquest Jul 7 '12 at 8:59
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    $\begingroup$ @Inquest Just ask them, you'll learn what is the best way to do so eventually. $\endgroup$ – Pedro Tamaroff Jul 17 '12 at 17:43
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A question as to whether a certain self-made proof is correct or not has two drawbacks:

  1. The question is usually extremely localized; it is not that likely that somebody else will come up with exactly the same proof and wants to know whether the proof is correct. Somebody else might want a proof, but the proof is likely not to be the most canonical, for otherwise the poster would be more confident.

  2. While such questions usually have rather clear answers, it seems odd to post something like "Yes." or "Yes, if you change $\delta$ in line 2 from $\epsilon/3$ to $\epsilon/4$.", so the question is likely to be answered in the comments. That's certainly how I and many others answer such questions, but it leads to the question not having a formal answer.

On the other hand, such questions show the research effort we demand in the clearest manner, so I would not want to discourage them. A format that avoids these problems is asking the question as a regular question (maybe with a remark that one is mainly interested in whether ones own proof works) and the attempted proof as a regular answer. I would suggest that the questioner accepts the answer that seems to be best to her. A slight problem is that an attempted proof is more likely to be wrong and therefore to attract downvotes. So I would suggest posting the answer in community wiki mode, but that is ultimately the decision of the OP.

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    $\begingroup$ Another potential problem is that if the OP is primarily interested in the community's analysis of their own proof, it is less likely to get the community's attention, and thereby serve its purpose, if it's in an answer rather than in the original question. $\endgroup$ – Ben Blum-Smith Apr 15 '13 at 18:01
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The best way to ask check-my-proof questions is not to simply ask users to check your proof. In what follows I've been strongly influenced by Raphael's answer on meta.cs.SE, and somewhat echo Qiaochu Yuan's answer to a previous meta.math.SE question.


Questions of the form

I have to prove that if ${D_{M,K}}$ is a universal factor, then $\Psi \le-1$. Here's my attempted proof.

We begin by considering a simple special case. Of course, $\tilde{\mathbf{{c}}} > \sqrt{2}$. Therefore if $d$ is not equivalent to $R$ then $N$ is greater than ${\mathfrak{{l}}^{(\mathfrak{{p}})}}$. Next, if $\mathbf{{x}}$ is less than $\Phi$ then $x < P$. Because $e \cong \overline{{\mathbf{{w}}^{(\zeta)}}}$ if $k$ is larger than $\mathcal{{D}}$ then $| \pi' | > \emptyset$. By Thompson's Theorem, if the Riemann hypothesis holds then $\bar{\lambda} \subset 1$. On the other hand, if $\mathscr{{E}}''$ is co-essentially Archimedes and local then $b < \hat{y}$. Hence if $K''$ is singular and real then every uncountable, Frobenius, non-universally quasi-intrinsic function is $X$-Hausdorff and connected. On the other hand, if $\bar{\kappa}$ is distinct from $K$ then $$H'' \left( \mathbf{{x}}, \dots, \Gamma \right) > \limsup_{K \to e} \int_{2}^{\infty} \tanh \left( e i \right) \,d {\mathcal{{M}}^{(Y)}}.$$

QED.

Is this correct? Any suggestions to improve? Thanks!

are often bad in part because in the cases that it turns out that the proof is correct, we are left with either a

Yes, it looks good to me.

answer, or perhaps we start nitpicking minor (and essentially non-mathematical) deatils (e.g., "there should be a comma between '$e \cong \overline{{\mathbf{{w}}^{(\zeta)}}}$' and 'if' in the fifth sentence.") Neither of these leave us with good answers.

Also, such questions aren't really focused, and it is uncertain what the user's specific mathematical question is (or if they even have one).

Note, too, that we generally dislike questions asking us to verify "proofs" of long-standing open problems, or which purport to disprove standard theorems. Why should such questions be treated differently?

Compare the above with the following question:

I have to prove that if ${D_{M,K}}$ is a universal factor, then $\Psi \le-1$. Here's my attempted proof.

We begin by considering a simple special case. Of course, $\tilde{\mathbf{{c}}} > \sqrt{2}$. Therefore if $d$ is not equivalent to $R$ then $N$ is greater than ${\mathfrak{{l}}^{(\mathfrak{{p}})}}$. Next, if $\mathbf{{x}}$ is less than $\Phi$ then $x < P$. Because $e \cong \overline{{\mathbf{{w}}^{(\zeta)}}}$, if $k$ is larger than $\mathcal{{D}}$ then $| \pi' | > \emptyset$. By Thompson's Theorem, if the Riemann hypothesis holds then $\bar{\lambda} \subset 1$. On the other hand, if $\mathscr{{E}}''$ is co-essentially Archimedes and local then $b < \hat{y}$. Hence if $K''$ is singular and real then every uncountable, Frobenius, non-universally quasi-intrinsic function is $X$-Hausdorff and connected. On the other hand, if $\bar{\kappa}$ is distinct from $K$ then $$H'' \left( \mathbf{{x}}, \dots, \Gamma \right) > \limsup_{K \to e} \int_{2}^{\infty} \tanh \left( e i \right) \,d {\mathcal{{M}}^{(Y)}}.$$

QED.

I am uncertain about my use of Thompson's Theorem. Is it applicable in this case? Thanks!

Sure, a very poor (and essentially not-an-answer) answer can still be "Yes," but even better is

Yes. Recall that to use Thompson's Theorem we need.... Since....

Similarly, in the "No" case answers should include an explanation about why it is not applicable.

But beyond that we have a specific mathematical question: the applicability of a certain theorem in a certain case. Even better, many of our veteran users should be able to pare down the attempted proof to its essential elements to leave a concise, specific and searchable question. (Yeah, this is more work for us, but it improves the site.)


tl;dr

From Raphael's meta.cs.SE answer:

If a questioner wants their work checked, they should be able to pinpoint their doubt and [provide] a question that allows meaty answers either way (i.e. for "yes" and "no" answers).

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    $\begingroup$ Gibberish theorem and proof kindly provided by Mathgen. $\endgroup$ – user642796 May 23 '15 at 5:58
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    $\begingroup$ The gibberish is so good that initially I believed it was advanced math. $\endgroup$ – Santropedro Jan 19 '17 at 16:14

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