Publishing mathematics

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?

Solution 1:

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.