It is often said that the big mathematical advances and discoveries are made in early careers, and that mathematicians can burn out or fade away. We have prob-ably all heard this and wondered a little. It is true that early career mathematicians are unencumbered by the weight of the past and thus more curiosity driven and more radical in approaching big problems. In maths this seems especially possible since, unlike other sciences, one does not need to develop experimental skill, teams, equipment, or domain seniority and influence in order to attack big questions. One can attempt anything with a pencil, paper and some learning. A quick Google search produces a number of very useful articles on this very matter that provide contrary evidence: stories of mathematicians who remained radical and at the cutting edge over long careers.
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