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I'm now retired and would like to learn about number theory purely for my own enjoyment. I have a knowledge of pure mathematics that I would guess is up to about first year undergraduate level but I'm very rusty on it.

I want to ask a question about which route(s) to take in order to further my progress. I have some ideas already about how to proceed. For example, I could take the historical route via the ancients through Fermat or I could ignore history altogether and just focus on those aspects of number theory that are most relevant today, e.g. complex analysis and group theory etc.

Question

I'm not asking for an answer here to the above - my query on Meta is whether my question can be formulated in a way that is suitable for Stack Exchange or whether I should seek a different forum.

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    $\begingroup$ Not really an answer to your question, but an encouragement. It's good to see ancients such as myself with comparatively limited knowledge of math discovering the benefits of SE, because mathematics truly is a social enterprise. I say 'comparatively' because the path I took in life is non-academic. Someone I know referred to me as a 'genius.' But here I can benefit from the experience of other SE members. I love having a forum where I can bounce my ideas off of people. All the best to you in your endeavours! $\endgroup$ – Adam Hrankowski Sep 8 '15 at 12:36
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    $\begingroup$ I think that before you can ask what route to take to further your progress, you had better figure out just what kind of progress you want to make, and then present that in your question. Do you want to prove the Riemann Hypothesis? Do you want to be able to understand the proof of Baker's Theorem? Do you want to have fun learning all kinds of neat and beautiful facts? There will be no way to answer your question, if you don't tell people what you want to do. $\endgroup$ – Gerry Myerson Sep 8 '15 at 12:39
  • $\begingroup$ @AdamHrankowski - Thanks for your comment - it implies that this may be the right forum. I'll have a look at some of your questions. $\endgroup$ – chasly from UK Sep 8 '15 at 12:43
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    $\begingroup$ @GerryMyerson - Thanks. That's exactly the right comment for me at the moment. As you say I need to define my goal before I look for a route. I'll give some serious thought to this. $\endgroup$ – chasly from UK Sep 8 '15 at 12:45
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    $\begingroup$ @GerryMyerson - The Riemann Hypothesis? I answered that months ago. I haven't posted it, because I didn't know how to put my result in the form of a question. :D $\endgroup$ – Adam Hrankowski Sep 8 '15 at 12:48
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    $\begingroup$ @AdamHrankowski - You should add it to the list here! ;-) empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/RHproofs.htm $\endgroup$ – chasly from UK Sep 8 '15 at 12:58
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    $\begingroup$ If you are close to a university, I would also make a visit to their library and brouse through their mathematics stacks. I have found that most university librarians are very pleasant and helpful. $\endgroup$ – steven gregory Sep 12 '15 at 22:10
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    $\begingroup$ @chaslyfromUK, try Chatstackexchange and try making friends there. Make a chat for number theory discussions and try your discussion there. I am sure you will find people interested in number theory. $\endgroup$ – Aditya Agarwal Sep 21 '15 at 11:18
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I would say that this type of question is "seeking personal advice" and not on topic for this site. However, that doesn't mean it's a bad question, it is just not the kind of thing that is appropriate here. You might get good responses on www.physicsforums.com

To answer your question, just start learning. Don't be paralyzed be trying to learn the "right" way. Just find a decent number theory book, and start working through it. I suggest that you do ample problem solving. Math is learned through problems. I also recommend that you review high school algebra. Even if you know it, you probably don't know it as well as you could.

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