Dear fellow mathematicians,
I am an undergraduate at US with a huge interest in the topology and analytic number theory. I am curious if outstanding publication(s) as undergraduate could help when applying for top 10 graduate programs in mathematics. I have been doing research with faculties on my own original idea of applying the algebraic topology and set theory to Goldbach Conjecture, and we strongly believe we made a huge advance toward solving GC. In fact, we are convinced that our theorems could be extended to prove Goldbach Conjecture. If I am able to publish or even put arxiv papers about Goldbach Conjecture or even solving it completely, will it help when applying for the best programs in mathematics?
Honestly, this undergraduate research on Goldbach Conjecture is my last hope as my GPA is not good and I have not taken many graduate classes. My mentors are well-known in their field, with one being incredibly famous.
Is it also true that majority of students accepted in top programs already published some meaningful papers?
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