INTRODUCTIO N The task of the educator is to make the child's spirit pass again where its forefathers have gone, moving rapidly through certain stages but suppressing none of them. In this regard, the history of science must be our guide. —Henri Poincare In the course of the years 1770 and 1771 Joseph Louis Lagrange, mathematician to the court of Friedrich der Grosse of Prussia, read to the Royal Academy of Sciences and Arts a lengthy memoir entitled: "Reflexions sur la Resolution Algebrique des Equations" (thoughts on the algebraic solution of equations). This memoir did not solve any impor- tant problem. It did not explode like a bombshell over the mathematical community of Europe. But it contained an idea. It planted a seed. Many shells would be fired over Europe and America in the ensuing decades. A new nation, based on a new idea of government, would be founded in America, an old dynasty would come to a bloody end in France, and Europe would be convulsed by 25 years of wars and repeated popular insurrections. New forms of government and industry were being born in violence. Meanwhile the seed planted by Lagrange continued to germinate in the minds of mathematicians in Italy, Germany, France, and Norway. Some were staunch royalists some were radical populists. All were assisting at the birth of a new mathematics. Finally 1
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