Klein on Ancient Mathematics and Its Algebraization Process
Jacob Klein's work on the history of mathematical thought has been neglected by his contemporaries for various reasons,but its value is in-creasingly apparent today.He attempted to activate ancient sedimentary mathematical experience through an intentional analysis of the"actual history"of mathematics.He ingeniously combined phenomenological methods with Case studies and described the process of algebraization promoted by mathemati-cians such as Vieta,Descartes,Stevin,and Wallis from the perspectives of two types of"intentional conversion".He reduced Vieta's idea of logistice speciosa,which based on the theory of proportionality,and Descartes'concept of"symbolic abstraction"to the essence of algebra.He characterized in detail the conceptual history of symbolic mathematics and provided a historical proof of thought for its development,which provided a new perspective for us to understand the essence of algebra and modernity.Unlike previous Whig history studies or the idealized scientific picture of cosmopolitanism,Klein's study highlights the originality,specificity and completeness of the intrinsic elements of ancient Greek mathematics.
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