How to find alternative proofs?

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  • #1
JasonRox
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How do I go about finding alternative proofs?

I wrote an alternative proof to a theorem including its converse, so I'd like to publish it if it does not yet exist.

So far, I just looked into 10 different textbooks that had the theorem. I don't really know much else to do. So far so good though. :biggrin:

Thanks for the advice.

Note: I'm currently reviewing the proof with my professor. Also, that is so far so good. :biggrin:
 

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  • #2
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I just looked into 10 different textbooks that had the theorem.
If you are at a university and have subscriptions to online journals you should do a literature search.

In physics we have the American Journal of Physics (AJP) as the main outlet for pedagological refinements like improved derivations/proofs etc. , I am sure mathematics has something similar.
 
  • #3
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I just looked into 10 different textbooks that had the theorem.
If you are at a university and have subscriptions to online journals you should do a literature search.

In physics we have the American Journal of Physics (AJP) as the main outlet for pedagological refinements like improved derivations/proofs etc. , I am sure mathematics has something similar.

Most things of this nature are too minor to be published in journals, but they are exactly the sort of things from which the next generation of experts will write original textbooks (for example, any Graph Theory text from Bollobas contains dozens of original problems and proofs).
 
  • #4
JasonRox
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Most things of this nature are too minor to be published in journals, but they are exactly the sort of things from which the next generation of experts will write original textbooks (for example, any Graph Theory text from Bollobas contains dozens of original problems and proofs).
Well my professor said it can be published if no one else has this proof. I proved the converse as well, and I think only one of the textbooks had it. The other 9 did not.

Also, it isn't a small theorem. I saw an alternative proof of the fact that there are infinitely primes and that was published. I don't see why mine wouldn't be.
 
  • #5
JasonRox
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But like you said, I think this proof would be perfect for textbooks though.
 
  • #6
JasonRox
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In physics we have the American Journal of Physics (AJP) as the main outlet for pedagological refinements like improved derivations/proofs etc. , I am sure mathematics has something similar.
I'll ask my professor about this. I'm sure he knows about that journal, so quite possibly he knows that of Mathematics.

Thanks.
 
  • #7
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I can think of about 5 distinct proofs of infinitely many primes. (not even counting the standard suppose finite proofs).

What's your proof? Some alternate proofs are cute because they generalize nicely.
 
  • #8
JasonRox
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I can think of about 5 distinct proofs of infinitely many primes. (not even counting the standard suppose finite proofs).

What's your proof? Some alternate proofs are cute because they generalize nicely.
No need to share online. I'm already sharing it with a professor.
 
  • #9
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But we're interested. At least state what you proved without proving it.
 
  • #10
matt grime
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Well my professor said it can be published if no one else has this proof. I proved the converse as well, and I think only one of the textbooks had it. The other 9 did not.

Also, it isn't a small theorem. I saw an alternative proof of the fact that there are infinitely primes and that was published. I don't see why mine wouldn't be.
It really depends on who referees the paper. If they deem the proof obvious and well known, it won't get a favourable review. If the alternate proof is innovative and offers a new and potentially interesting way of thinking of things that has scope for being extended, then it has a better chance. It also depends on how big the result is. Not to mention where you're trying to get it published. The Annals won't look at it, but something like the AMS magazine might be keen.

In short, there is no simple way to guarantee anything is publishable save for some obvious exceptions - it strongly depends on picking the right place to submit it, getting a favourable review, and writing it well in the first place.

Having a proof of something is no guarantee of being published. And looking in textbooks is no real use. There are usually several ways of proving anything, and books won't have most of them in. Your best bet is to get an expert in the area to pass their opinion. Submitting to a journal is one of doing that.

As someone else has suggested, tell us what the statement is. One other idea is to write it up and put it on the arXiv. That way it is in the public domain and you have an irrefutable time line that allows you to claim ownership of the idea. You can then freely discuss the proof here, or elsewhere, without anyone being able to steal it from you if that is your concern.
 
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  • #11
JasonRox
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It really depends on who referees the paper. If they deem the proof obvious and well known, it won't get a favourable review. If the alternate proof is innovative and offers a new and potentially interesting way of thinking of things that has scope for being extended, then it has a better chance. It also depends on how big the result is. Not to mention where you're trying to get it published. The Annals won't look at it, but something like the AMS magazine might be keen.

As someone else has suggested, tell us what the statement is. One other idea is to write it up and put it on the arXiv. That way it is in the public domain and you have an irrefutable time line that allows you to claim ownership of the idea. You can then freely discuss the proof here, or elsewhere, without anyone being able to steal it from you if that is your concern.
Well, the idea does bring out an innovative on how to look at the theorem. As well as when you look at a visualization of the proof for a simple case, you can see the construction of it really nicely.

I may discuss it with another professor who is an expert in the field, so he can give me more advice on how to go about it. The professor I'm talking to now is someone I trust, so I'll work with him right now. He already said he'd be willing to send it for publication.

He told me took look around if the same proof exists anywhere else, but I'm not sure how to do so. I'll ask him more about that.

As well as I'm including the converse, and out of the 10 textbooks, only one of them talked about it.

The AMS Monthly was the journal I was thinking of. I don't know much about journals, but I knew about that one. I can read some the articles in those. :redface:

Note: I'm not too keen on publishing it on arXiv. I'd probably reserve that as my last resort.
 
  • #12
matt grime
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Note: I'm not too keen on publishing it on arXiv. I'd probably reserve that as my last resort.
Why? It is the place almost everyone else puts everything before they submit it to a journal. And it isn't publication on the arXiv. It is a service to the academic commuinity to place things in freely available format, instead of ridiculously expensive journals. Note that journal publication is no guaranteed indicator that what you write is actually correct, or has been read carefully. I would look poorly on anyone who choose not to place things on the arXiv. Arguably the most important results in mathematics appear there and at the moment nowhere else (Perelmen, and the proof of finite generation of some ring in algebraic geometry - Roy would be able to name it), and the journal system is under close scrutiny as being a poor academic standard. To wit, the mass resignation of the Topology editorial board, and the refusal of many to submit to Elsevier in boycott of their support of arms fairs. Not that the journal idea itself is flawed, you understand (though many would say it is), but that the companies that run the journals do not have acedemia's best interests at heart.
 
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  • #13
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Why? It is the place almost everyone else puts everything before they submit it to a journal. And it isn't publication on the arXiv. It is a service to the academic commuinity to place things in freely available format, instead of ridiculously expensive journals. Note that journal publication is no guaranteed indicator that what you write is actually correct, or has been read carefully. I would look poorly on anyone who choose not to place things on the arXiv. Arguably the most important results in mathematics appear there and at the moment nowhere else (Perelmen, and the proof of finite generation of some ring in algebraic geometry - Roy would be able to name it), and the journal system is under close scrutiny as being a poor academic standard. To wit, the mass resignation of the Topology editorial board, and the refusal of many to submit to Elsevier in boycott of their support of arms fairs. Not that the journal idea itself is flawed, you understand (though many would say it is), but that the companies that run the journals do not have acedemia's best interests at heart.
If that is the case, why not I just wait until I send it in before putting on arXiv?

It's not even fully written yet, so I have nothing to post on arXiv anyways. It could be another a week or two before it's complete.
 
  • #14
matt grime
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Yours is a non-traditional case, admittedly. But the reason to put it on the arXiv in one sense is that appears in the public domain immediately. It can take anywhere up to 2 years for a paper to appear in a journal from submission time (and anything less than 9 months is rare), assuming it is even accepted. I recently had a paper rejected from a journal after 9 months from the initial submission. So don't hold your breath.

The reasons not to bother submitting to journals instantly are long, complex, and very odd - in the UK there is a pressure to submit to journals because of something called the RAE, which assess a department's worth. It is easiest to do well in the RAE if you have 4 journal papers in the 7 years previous to the RAE date (currently Dec 31st 2007). You can submit non-journal papers but they get close scrutiny, but you cannot submit more than 4 papers, period. Thus if you have 3 good papers in journals and 2 good preprints, you submit only 1 of the new preprints to journals, and hold the other one back until after Dec 31st 2007 so that you're more employable later on when departments are recruiting people to try to boost their RAE scores. It's rubbish, really. And it isn't your situation. The point for you is that it puts your result in the public domain, with your name on it quickly. Far more quickly than any journal publication attempt. Also, you put it there, other people notice it, read it and give you feedback, thus potentially saving you from months of waiting for a referees report to comeback. View it as a free peer review/cooling off period when you can sit back for a couple of months after writing before deciding if you really want to submit it to a journal, and to which journal etc. You might suddenly decide after a month that you hate the way you wrote it.

And, moreover, journal format is not necessarily the way you'd naturally write (depends on the journal), so you get freedom to explain exactly what you want and how you prefer to state it (basically, you get to put much more detail in). Of course, this implies, as I hope you realised already, that you don't need to submit the same thing to the arXiv as you do to a journal. Oh, and that's another thing. After you've carefully written it out in lovely LaTeX to your own standards, the journal submission guidelines might require you to completely rewrite it (LMS and elsevier do, communications in algebra, say, is more forgiving) to conform to the house style.
 
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  • #15
JasonRox
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Yours is a non-traditional case, admittedly. But the reason to put it on the arXiv in one sense is that appears in the public domain immediately. It can take anywhere up to 2 years for a paper to appear in a journal from submission time (and anything less than 9 months is rare), assuming it is even accepted. I recently had a paper rejected from a journal after 9 months from the initial submission. So don't hold your breath.

The reasons not to bother submitting to journals instantly are long, complex, and very odd - in the UK there is a pressure to submit to journals because of something called the RAE, which assess a department's worth. It is easiest to do well in the RAE if you have 4 journal papers in the 7 years previous to the RAE date (currently Dec 31st 2007). You can submit non-journal papers but they get close scrutiny, but you cannot submit more than 4 papers, period. Thus if you have good papers in journals and 2 good preprints, you submit only 1 of the new preprints to journals, and hold the other one back until after Dec 31st 2007 so that you're more employable later on when departments are recruiting people to try to boost their RAE scores. It's rubbish, really. And it isn't your situation. The point for you is that it puts your result in the public domain, with your name on it quickly. Far more quickly than any journal publication attempt. Also, you put it there, other people notice it, read it and give you feedback, thus potentially saving you from months of waiting for a referees report to comeback. View it as a free peer review/cooling off period when you can sit back for a couple of months after writing before deciding if you really want to submit it to a journal, and to which journal etc. You might suddenly decide after a month that you hate the way you wrote it.
I will take your advice seriously though. But like I said, I must wait until I'm actually done writing it.

I will also talk to my professor about how long it might take to get it published.
 
  • #16
JasonRox
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And, moreover, journal format is not necessarily the way you'd naturally write (depends on the journal), so you get freedom to explain exactly what you want and how you prefer to state it (basically, you get to put much more detail in). Of course, this implies, as I hope you realised already, that you don't need to submit the same thing to the arXiv as you do to a journal. Oh, and that's another thing. After you've carefully written it out in lovely LaTeX to your own standards, the journal submission guidelines might require you to completely rewrite it (LMS and elsevier do, communications in algebra, say, is more forgiving) to conform to the house style.
I was aware of this, which is why I want to wait until I have the journal in mind so I can have the format done as I write it.

Then I will just post that article on arXiv. If there are things I want to add, then I can just add them.

I'll probably write some stuff for arXiv that I doubt is good enough for publication but worthwhile to know.

Thanks for all the comments and advice, matt.
 
  • #17
matt grime
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I Then I will just post that article on arXiv. If there are things I want to add, then I can just add them.

Thanks for all the comments and advice, matt.
That is frowned upon - the submission then alteration of articles to arXiv. All versions are kept on display as well. Alterations should be made to correct errors, and indicate if the paper has been accepted for publication somewhere. Also some journals do not allow the posting of a submitted article to arXiv. Whereas some positively encourage it (like the Annals). When you put it in journal style you may need use a style file they provide, and that is their IP, which carries some extra restrictions.
 
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  • #18
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That is frowned upon - the submission then alteration of articles to arXiv. All versions are kept on display as well. Alterations should be made to correct errors, and indicate if the paper has been accepted for publication somewhere. Also some journals do not allow the posting of a submitted article to arXiv. Whereas some positively encourage it (like the Annals). When you put it in journal style you may need use a style file they provide, and that is their IP, which carries some extra restrictions.
Oh boy, all these rules. I guess I won't change it at all.

I'll talk to my professor on which way is the best to go about it. I don't want to submit it to arXiv and then get a rejection because I submitted it to arXiv already. That would be a waste of time.
 
  • #19
matt grime
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You cannot be rejected for submitting it to the arXiv. Where on earth did that idea come from? The arXiv is not a journal. It is a free repository for papers, to share knowledge. Everyone pretty much puts things on there now. It does not stop your work being publishable elsewhere.

Putting it on the arXiv is like putting it on your web page, only thousands of people see it, and you get some assurance that you have a time stamp on the work as being yours if you're worried about someone else attempting to appropriate it.
 
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  • #20
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Sorry, I misread what you said.

Also some journals do not allow the posting of a submitted article to arXiv.
If a journal published my work and told me not to put it on arXiv, that won't really bothered me that much. It got published in the end.
 
  • #21
matt grime
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Evidently your aim is to have your name next to something in a journal, whereas mine is to advance the state of mathematics. Sorry for trying to convince you to do something that costs you nothing and would enable others to benefit from your work free of charge instead of having to pay exorbitant rates to some company who has little interest in mathematics.

Being published is not the be all and end all, and anyone who says different is in it for the wrong reasons. The vast majority of papers that appear in journals didn't need to see the light of say, but pressure on research grants dictates otherwise. If you put it only in a journal you arguably have far less exposure than putting it on the arXiv.
 
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  • #22
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Evidently your aim is to have your name next to something in a journal, whereas mine is to advance the state of mathematics. Sorry for trying to convince you to do something that costs you nothing and would enable others to benefit from your work free of charge instead of having to pay exorbitant rates to some company who has little interest in mathematics.
Those are my interests that's what you must understand. I have no experience in this at all. So, I'm a little nervous in throwing my work around. Also, I heard bad things about arXiv, which is why I might seem nervous about it. I read on this very website from other members on how the site is getting infected with crackpots. That's not a very good thing in my book. Which again makes me nervous.

Like I said, I would like to talk to my professor about which way to go about it. I trust him, and I know him personally.

Plus, if I have to pay a dime to get something published, then I certainly won't publish it!
 
  • #23
matt grime
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You don't pay the publisher. But anyone who reads it must pay, or work for someone who pays, a huge fee that doesn't go to any of the mathematicians who work free of charge in the process.

arXiv is not infected with cranks. Just look at what goes on to it. arXiv is also moderated. You have completely the wrong idea about arXiv. Just put it there and be done with it. Putting something on the arXiv has no bad connotations for you at all. It is a vital service to academia.
 
  • #24
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You don't pay the publisher. But anyone who reads it must pay, or work for someone who pays, a huge fee that doesn't go to any of the mathematicians who work free of charge in the process.

arXiv is not infected with cranks. Just look at what goes on to it. arXiv is also moderated. You have completely the wrong idea about arXiv. Just put it there and be done with it. Putting something on the arXiv has no bad connotations for you at all. It is a vital service to academia.
Is this where you publish all your work?

In the end, it's still nice to get something published. I do plan on going to graduate school. It would really help my application.
 
  • #25
matt grime
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It is where everyone I know puts all their work first.

Search it for, say, Atiyah, as an author.... See, full of cranks.... Pick your favourite mathematician and see if they have something there, then tell me it is infected with crackpots.
 
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