I'm curious if it is common or quite rare for mathematicians to change their area of expertise, whether it be after their PHD or mid-career, how radical this change might be, whether it's often for reasons of evolving tastes or rather conforming to the type of research done at their institution, and any other thoughts anyone has on how mathematicians stake out the fields they will be producing research in, thanks =].
Do mathematicians Switch Fields of Expertise?
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6The great mathematicians usually seem to be involved in many fields. I can't say much about great mathematicians today, but I looked up Terry Tao a few days ago and his research interests are extremely varied it seems. – 2011-10-23
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4If I remember correctly, Grothendieck didn't get into algebraic geometry until fairly late (it wasn't his thesis). Another example: Quillen studied partial differential differential equations in graduate school and went on to become a leading homotopy theorist. – 2011-10-23
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3There are a couple of relevant MO posts [here](http://mathoverflow.net/questions/69937/changing-field-of-study-post-phd) and [here](http://mathoverflow.net/questions/12684/switching-research-fields), and I like Gower's concise answer in the second link (recommended in a comment in the first link). Adam's answer below is in the same vein. – 2011-10-23
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2To supplement Akhil's comment: many people are aware that Grothendieck did not begin in algebraic geometry, many people seem unaware of the fact that he made fundamental contributions to the field he began in--- the theory of topological linear spaces, and specifically Banach spaces (Albrecht Pietsch's *History of Banach spaces and linear operators* is a good reference, although for Banach space enthusiasts only). There are people in this area who say things like "if I remember correctly, Grothendieck went on to do things besides Banach space theory," and aren't kidding. – 2011-10-23
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0Wow, excellent comments everyone, very informative, thanks – 2011-10-31