By Nicolas Bourbaki
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Extra info for Algebre, Chapitre 8: Modules et anneaux semi-simples (Elements de mathematique, Fascicule 23, ASI 1261)
In technique as opposed to symbolism, on the other hand, the cossists made no advance. A student of Leonardo's algebra would have discovered nothing essentially new in any of the later books, and even a reader of al-Khwārizmī would have found much that was still recognizable. The Arab-cossist tradition lasted for eight centuries without extending either its scope or its methods, until eventually it ran into the ground. Fortunately for the future of mathematics, cossist algebra was not A DISCOURSE CONCERNING ALGEBRA 45 the only strand in the story: in mid sixteenth-century Italy something entirely new was under way.
It also demonstrates that 18 A LARGE DISCOURSE CONCERNING ALGEBRA A treatise of algebra contains a considerable amount of material that can be traced to Pell, a surprising and hitherto unsuspected ﬁnding, and one that leads to a completely new understanding of the long relationship between Wallis and Pell. The ﬁnal part of the book is an evaluation of the signiﬁcance and inﬂuence of Wallis's ﬁnest work, his Arithmetica inﬁnitorum, which gave rise directly or indirectly to a great deal of new mathematics, culminating in Newton's brilliant discovery of the general binomial theorem.
In his discussion of the spread of the Hindu-Arabic numerals in particular Wallis drew his conclusions not from earlier authorities but from direct reading of manuscripts and artefacts, and in this respect he can be considered perhaps the ﬁrst modern historian of mathematics. Unfortunately his enthusiasm for historical research did not extend to the rise of algebra in Renaissance Europe, which had little bearing on his English theme, and here I have attempted to redress the inadequacies of his history with my own account of European algebra from the medieval period to the end of the sixteenth century.
Algebre, Chapitre 8: Modules et anneaux semi-simples (Elements de mathematique, Fascicule 23, ASI 1261) by Nicolas Bourbaki