A new era in the history of mathematics opened when Gauss proved the fundamental theorem of algebra. Abandoning the futile attempts of his predecessors to solve algebraic equations of higher degree by root extraction, he took a step of general significance by proving merely the existence of the roots in question. For the first time it was clearly understood that the primary task in a mathematical problem is to prove the existence of a solution. To find procedures by which the solution can be explicitly obtained is a further question, distinct from that of existence. Since the beginning of the last century this distinction has played a clarifying role contributing greatly to progress in all fields of mathematics.
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