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8 - Euler and analysis: case studies and historiographical perspectives

Published online by Cambridge University Press:  19 July 2021

Niccolò Guicciardini
Affiliation:
Università degli Studi di Milano
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Summary

Two parts of analysis to which Leonhard Euler contributed in the 1740s and 1750s are the calculus of variations and the theory of infinite series. Certain concepts from these subjects occupy a fundamental place in modern analysis, but do not appear in the work of either Euler or his contemporaries. In the case of variational calculus there is the concept of the invariance of the variational equations; in the case of infinite series there is the concept of summability. However, some modern mathematicians have suggested that early forms of these concepts are implicitly present in Euler’s writings. We examine Euler’s work in calculus of variations and infinite series and reflect on this work in relation to modern theories.

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Anachronisms in the History of Mathematics
Essays on the Historical Interpretation of Mathematical Texts
, pp. 223 - 250
Publisher: Cambridge University Press
Print publication year: 2021

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