How to find alternative proofs?

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Discussion Overview

The discussion centers on the process of finding alternative proofs for mathematical theorems, including considerations for publication. Participants explore various methods for verifying the originality of proofs and the potential for publishing them in academic journals.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks advice on how to find alternative proofs and mentions reviewing their proof with a professor.
  • Another suggests conducting a literature search through online journals, particularly highlighting the American Journal of Physics as a resource for pedagogical refinements.
  • Some participants note that many proofs may be too minor for publication, yet they contribute to the development of future textbooks.
  • Concerns are raised about the criteria for publication, including the need for the proof to be innovative and not widely known.
  • One participant expresses uncertainty about how to verify if their proof has been published elsewhere and considers consulting another expert for guidance.
  • There is a discussion about the merits of using arXiv for preliminary sharing of proofs, with differing opinions on its importance and necessity.
  • Some participants express interest in the specifics of the proof being discussed, suggesting that sharing details could be beneficial.

Areas of Agreement / Disagreement

Participants express a range of views on the publication process, the significance of originality in proofs, and the utility of arXiv. There is no clear consensus on the best approach to take regarding publication or the necessity of using arXiv.

Contextual Notes

Limitations include the potential for varying definitions of what constitutes a significant or publishable proof, as well as the subjective nature of peer review in academic publishing.

  • #31
Gib Z said:
I've been looking on arVix and see some papers I am dying to dead, but when i Press the pdf link next to the papers name, nothing works. I WANT "A matrix generalization of Euler identity e^(ix) = cosx + i sinx" by Gianluca Argentini!

Are you being patient enough? When you hit the pdf link, it doesn't link to a pdf. It links to a little script that latexs the plain text file and sends you the result. This may take a minute.
 
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  • #32
Ahh I don't know know where it would send them to >.< I think i fixed it though, it just doesn't download but I can save the page and it works. Thanks, this site is awesome!
 
  • #33
matt grime said:
In my opinion, yes. But that is my opinion. And possibly that of Terry Tao too since he is one of the moderators.

Arxiv is a recent(ish) thing. For instance, Artin has 'only' published 4 papers in the last 12 years according to mathscinet. A similar thing occurs for Wiles - if people aren't writing things then they aren't posting them. And they might not share my view of the benefit of the arXiv. But plenty of younger people do.

Terry/Terence Tao has 129 hits on the arxiv. Does that convince you of anything?

But it would really bother if my professors aren't participating in this.

Like you said, everyone should.
 
  • #34
JasonRox said:
But it would really bother if my professors aren't participating in this.

Why? Bother you to the point of you not putting things there? If it's good enough for Fields' Medallists...

How many papers have your professors written in the last 5 years? Who are they - search for their output on mathscinet (assuming your university subscribes, which it almost certainly does), then decide if it is so amazing that they haven't put anything on the arXiv.

If you're at UWO, then Christensen and Jardine put things on the arXIv.

Perhaps the people you are thinking of put their work on other preprint servers - there are plenty of them, arXiv is one of the more famous and general ones.
 
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  • #35
matt grime said:
Why? Bother you to the point of you not putting things there? If it's good enough for Fields' Medallists...

Oh, my soul, will you leave the poor guy alone already?

If he doesn't want to put anything up on arXiv, then he doesn't want to
*and* he doesn't have to explain why he doesn't want to.

I don't put my papers there, nor (from what I can tell) does Mathwonk. Nor do a lot of other people.
 
  • #36
Absolutely. Jason is entirely free to do as he wishes. However, if he says 'I'm not going to do it because my professor doesn't, and I'm worried that it mean I can't get it in a journal if I do', then I'm going to correct the misapprehension of the second part. And point out that saying 'I won't do it because X doesn't' means I'm free to say 'but person Y does, so that's just a good a reason for putting it there as not putting it there'. If you have a good reason for not putting it there, fine, but don't use the 'oh he doesn't so I won't routine'; it's as weak as my 'but he does so should you' come back.

There are reasons for using it, and I'm sure you have reasons for not using too. Feel free to offer a different opinion. At least that way Jason can hear both sides of the argument for its use or non-use.
 
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  • #37
matt grime said:
Why? Bother you to the point of you not putting things there? If it's good enough for Fields' Medallists...

I meant it in a why aren't they helping the academics kind of way and not in a I-won't-put-it-on-because-my-professor-doesn't kind of way.

The only reason why I can see them not publishing on arXiv is maybe because of journals they publish in, like you said, or because of funding issues, which I know nothing about and I know nothing about whether or not funding would prevent publication on arXiv. I can't think of any other reason.

I already decided that it would be the best thing to do.
 
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  • #38
Your repeated refusal to tell us at least the statement you have proved gives me a tiny feeling that you really haven't done anything at all, and are just posting this thread to sound smart.

That would explain why you aren't putting it on arVix, because then we should be able to see it. We wouldn't find it, you would be in a tricky spot.

So either tell us the statement, or we shall think you are pulling our legs.
 
  • #39
Jason hasn't phyhsically been able to put it on the arXiv because, as he makes clear at several points, he hasn't written it up in LaTeX, irrespective of whether or not he wishes to use the service.
 
  • #40
Well either way, not telling us the statement is suspicious.
 
  • #41
matt grime said:
Jason hasn't phyhsically been able to put it on the arXiv because, as he makes clear at several points, he hasn't written it up in LaTeX, irrespective of whether or not he wishes to use the service.

I'm using the service. I don't think I can wait that too long for it to get published. Another plus, like you said, is the fact that it can be in any format. As long as it's nice and clean, I can post it on there.
 
  • #42
Gib Z said:
Your repeated refusal to tell us at least the statement you have proved gives me a tiny feeling that you really haven't done anything at all, and are just posting this thread to sound smart.

That would explain why you aren't putting it on arVix, because then we should be able to see it. We wouldn't find it, you would be in a tricky spot.

So either tell us the statement, or we shall think you are pulling our legs.

I wrote an alternative proof to Tychonoff's Theorem.
 
  • #45
Good luck!

I personally await reading it. :smile:
 
  • #46
Hmm. Definitely a possibility to be interesting, even if the proof doesn't hold water.

Do you use the AoC directly?
 
  • #47
ZioX said:
Hmm. Definitely a possibility to be interesting, even if the proof doesn't hold water.

Do you use the AoC directly?

Well, I don't use it directly.

At first it seemed like I had a gap in my proof that I couldn't overcome, but I wrote up a Lemma up for it now to patch it up.

It seems really solid right now though. I'll probably see my professor tomorrow to talk about it.
 
  • #48
You should keep in mind that Tychonoff is equivalent to AoC in ZF set theory (IIRC).
 
  • #49
morphism said:
You should keep in mind that Tychonoff is equivalent to AoC in ZF set theory (IIRC).

I am aware of that, but I haven't read into though. I do know this though, but it's not of my interest right now.

My proof does involve the Axiom of Choice though. Now that I think about how the set is being constructed, I'm certainly using the Axiom of Choice although you're choosing anything technically.

You'd have to wait and see. Hopefully I get things down and good soon so I can start writing it in LaTeX. I will put it on arXiv. I can't stand waiting around for responses.
 

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