I can't be the only person here who has fond memories of the problems in Vinogradov's Elements of Number Theory. (For people who have not read it - the text itself is just a concise basic number theory book; most of the substance is in the problems.) At the same time, much of what is good about them became clear to me only later. Vinogradov does not give citations or credits (not even to himself!), let alone any sort of historical overview for why the ideas he introduces in the problem sets are important. Standard names for the theorems the student is asked to prove are also completely missing.

Wouldn't it be a good idea to craft a commentary on Vinogradov's problems? Has anything of the sort been already done?

(Incidentally, something learned there recently made its way to http://polymathprojects.files.wordpress.com/2010/07/polymath1.pdf)

  • Surely, it'll be a nice idea. But how can we Mathoverflow-ers help? – Anweshi Jul 13 '10 at 19:47
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    Um, by raising our hands? By pointing out whether there's any discussion of Vinogradov's book in the literature? (I'm not aware of any.) By mentioning some of our favorite topics covered in Vinogradov's problems? – H A Helfgott Jul 13 '10 at 20:45
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    Yes - the solutions we have - it's everything else that's missing! – H A Helfgott Jul 13 '10 at 22:13
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    So.. you are essentially asking for other people who have worked through the book, and have interesting comments to contribute? In other words, you are looking for contributors to build a commentary? – Anweshi Jul 14 '10 at 11:21
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    @ H A Helfgott. I do not want to be impolite. But I must point out that in spite of the five upvotes and four favoritings so far, you haven't asked any question here. You just stated your wish that a commentary for Vinogradov's book be made. – Anweshi Jul 15 '10 at 15:49

Harald says:

My basic question is how to go about this.


  1. If you want to have an intensive discussion with someone over this, through the internet: For communication that may happen burst-by-burst, leading to something definite later, google wave is an idea.

  2. For a collaborative effort allowing anyone to contribute: Since you might perhaps want anyone to be able to contribute, starting a wiki is a good option. There are many sites allowing you to create wikis for free. Adding latex support also will be quite easy. If you want a ready-made place listing tricks, methods and their usage, maybe you can create a few pages at Tim Gowers' site "tricki" for various excerpts from Vinogradov's book.

  • I suppose the most important implicit question really is: Who wants to be a part of this? – H A Helfgott Jul 17 '10 at 11:09
  • @Harald. I do not know who will want to be a part. There is one way to find out: Create a wiki and then invite people to contribute(perhaps by editing this question and announcing the start of the wiki). You can also inform others by writing lists such as NMBRTHRY. – Anweshi Jul 17 '10 at 11:24

To answer a remark above: yes, I think it would be a very good idea to get together group of interested people to build a commentary. What non-interested people (or people who haven't read and will not read Vinogradov) can do is suggest what current technical tools would be most appropriate for such a collaborative project. I have no idea about that myself.

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