My grades are average and I want to study mathematics in top institutions like cambridge, princeton etc. If I am able to publish a paper in mathematics in high impact journals, then will it be possible to pursue a research career from best universities?
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2If it is ground breaking enough you may even be promoted instantly to professor. See Liu Lu and the Seetapun conjecture. – yoyostein Feb 27 '16 at 14:54
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7Not to be discouraging, but even though the answer to the question is yes (assuming you made a significant intellectual contribution to the paper and didn't simply help a faculty coauthor in routine ways), doing this is several orders of magnitude more difficult than getting good grades in undergrad. – Feb 27 '16 at 15:30