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Collaborate! And, if you dare, enter into a long term relationship. The vast majority of mathematicians I know do most of their work alone and, when they collaborate, the relationships are often short term temporary ones. But it can be extraordinarily fruitful to commit to a long term collaboration. I recommend it highly.

EDIT: Inserted "I know" after "vast majority of mathematicians" to account for Ben's comment, which I have no reason to doubt.

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Collaborate! And, if you dare, enter into a long term relationship. The vast majority of mathematicians do most of their work alone and, when they collaborate, the relationships are often short term temporary ones. But it can be extraordinarily fruitful to commit to a long term collaboration. I recommend it highly.