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Yitang's PhD is in a completely different field of math: algebraic geometry. Number theory is his hobby.

This is a very inspiring story!

"Completely different" is a bit of an exaggeration. Some number theorists are really algebraic geometers.

But yes, there are people who switch away from their thesis areas. Barry Mazur, if the story is correct, wrote an awesomely short thesis on topology. But he's famous as a number theorist.

The old saw is that when you finish your PhD you will either be sick to death of the subject and do something quite different, or still interested and spend most of your career on the same subject. It does seem to be quite binary in practice.

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