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Let's say I write a PhD thesis by looking at papers on arxiv. Can I use this as my PhD thesis one I enter into the program?

In other words, can you write a PhD thesis before going to graduate school?

Note. I took a year off and did intensive study. Given that, can I do it?

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closed as too localized by Chandrasekhar, Asaf Karagila, Adrián Barquero, Grumpy Parsnip, Willie Wong Sep 3 '11 at 21:57

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Unless you are one of the 10 most mathematically talented people in the world AND started doing professional math in your early teens, it is completely unrealistic. –  Nicole Sep 3 '11 at 21:15
@Nicole: The point is that I took a year off and learned some graduate math and did intensive study. So is it viable? –  Ross Ton Sep 3 '11 at 21:17
You can peruse my questions and see that I, too, am advanced for my age. But just read some theses. Much of the point of theses is that they are in depth. You need to be familiar with most of the literature on the topic (most of which you will probably not be able to read until years from now) and you have to make sure that you thought about all the ways to think about the phenomena discussed in the thesis. A thesis is meant to be work that takes years to do, and prepares you for independent research. –  Nicole Sep 3 '11 at 21:28
@Nicole: So you are an undergrad student? –  Ross Ton Sep 3 '11 at 21:32

2 Answers 2

No, you can't. There have been a few exceptional undergraduates that I've heard of who wrote papers that could pass as PhD theses somewhere, and they all went to grad school and wrote different (and better) theses as PhD students. Furthermore, your PhD thesis has to be based on work you did at graduate school, normally under the direction of an advisor. You can't get credit for research done elsewhere.

On a positive note, writing a good paper will help you get into graduate school, and will otherwise be beneficial to your development as a mathematician.

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Uh,you certainly can,but I've never heard of anyone,no matter how talented and precocious, doing such a thing. I HAVE heard of individuals who never formally entered a Master's or PHD program, were self taught and produced on their own a work of original research that was so significant, they were immediately awarded a doctorate on the spot and a research position. Karl Weirstruass famously did this, of course-as have several others. I believe there's a prestigious professorship chair at Harvard that's awarded once in a generation for pulling off such a feat.

But I think you can count on your fingers the number of people who have successfully done this. The odds are definitely not with you.I know,I was once arrogant enough to think I could do it. Given my situation, part of me is still hoping I CAN-but I'm far more realistic about its probability of occurring, which converges very near to zero in the limit of the sequence of all my attempts prior to death.

By all means,though-I wish you luck.

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