Abstract
A general phenomenon, little understood by the public, which often believes that everything has already been discovered, can be observed in the history of mathematics. Frequently, when a question is solved, or partially solved, the question does not die, but gives birth to several new questions to be studied in the future. My only ambition in this paper is to illustrate this phenomenon for three classical problems in real algebraic geometry. I do not claim that the new problems I identify are particularly important or meaningful, or that solving them should deserve millions of dollars [4]. Nor do I claim that the phenomenon I choose to illustrate is the main one to observe in the development of mathematics: topics do die, and new topics do emerge.
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