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How or where does one express work they've done to others?

What does it mean formally to 'publish' mathematical work you've done?

How do you know if your work is any good?

Or if someone has already addressed or came up with the same idea as you? Is there a certain age required to show your work?

Do you need a formal education or degree in mathematics to share your work with others?

Also I'm about 17, and I'm going to be trying to apply for colleges soon, I don't have very many extracurricular activities, or awards or anything. And I know some art schools accept portfolios of art work people have done, can you submit research or work you've done to a technical college as part of your admission application?

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People publish things in a vast number of places. Journals, newsletters, magazines, websites, blogs, bulletin boards, etc. Typically, publishing academic work involves either submitting a paper to a journal, writing up lecture notes and putting them online, publishing a book, or writing an article that gets circulated among others. 'Good' work is subjective, but how others react to your work tests the value of your work to others. Age is not really relevant to publishing material. You do not need a formal education or degree, but one may need some connections to people to get published. – anon Nov 25 '12 at 8:14
For example, recommendations come in handy and if you have any resume / name recognition for a potential publisher to think about it would benefit you. (Honestly, it is unlikely you have any need to worry about any of these sorts of issues for many years to come!) And surely you can talk about whatever you've done with yourself and your time on an admission application to a technical college. – anon Nov 25 '12 at 8:16
How do you know if your work is worth publishing, or if someone has published somthing similar before? – Ethan Nov 25 '12 at 8:19
To tell if someone has published something similar before, you go scavenging through publications in the subject area for similar material, as well as ask around to see if anyone else has seen anything similar. Even then you might not succeed: there is no perfect method to finding information. Whether something is worth publishing is slightly subjective, and depends drastically on what sort of venue you wish to publish in. (For instance, on a blog, you should just do whatever you want, as opposed to say in a serious journal or a local newsletter.) – anon Nov 25 '12 at 8:22
I love this question. The posters here really shed a light on publishing and put it into a more reasonable and realistic perspective. Great job, members of Math.SE. – 000 Dec 30 '12 at 4:21
up vote 3 down vote accepted

You can publish your work on the arXiv; this is sufficiently formal. To know if your work is any good you need feedback, but you should not expect any feedback as a direct result of publishing. To know if your work is original you will have to do research. There is no age requirement. There is no formal education requirement but to communicate effectively you will need to have equivalent skills. Including a mathematical paper with a college application is unorthodox but would probably be well-received if your work is any good.

Also, you may be interested in the ongoing controversy regarding publishing standards in mathematics and the sciences.

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Can you tell me if my work is any good, its not very long, I could send some of it to you? – Ethan Nov 25 '12 at 8:21
You can send it to my email address in my profile and I will have a look. – Dan Brumleve Nov 25 '12 at 8:24
I take a long time typing in math tex, if I just take pictures of the work (its only two sheets of paper, and there are no proofs) and send it to you sometime tomorrow would you be able to get back to me? Thanks alot also – Ethan Nov 25 '12 at 8:38
Sure, I would tell you what I think about it. – Dan Brumleve Nov 25 '12 at 8:39
However, you'd need endorsement for a first arXiv publication. – Hagen von Eitzen Nov 25 '12 at 10:49

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