The origin of the Bernoulli numbers: mathematics in Basel and Edo in the early 
eighteenth century

Kitagawa, Tomoko L.

doi:10.1007/s00283-021-10072-y

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The origin of the Bernoulli numbers: mathematics in Basel and Edo in the early eighteenth century

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Kitagawa, Tomoko L.
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Kitagawa, T. L. (2022). The origin of the Bernoulli numbers: mathematics in Basel and Edo in the early eighteenth century. The Mathematical Intelligencer, 44(1), 46-56. doi:10.1007/s00283-021-10072-y.

Cite as: https://hdl.handle.net/21.11116/0000-0009-0692-B

Abstract

The Bernoulli numbers were named after the Swiss mathematician Jacob Bernoulli (1654–1705; Figure 1), whose posthumous book Ars Conjectandi (1713) demonstrated the calculation of sums of integer powers. The same sequences of numbers were also published in the Japanese capital, Edo (today Tokyo), also as a posthumous publication, by Takakazu Seki (?–1708), appearing one year prior to Bernoulli’s book, and so these numbers might just as well have become known as Seki numbers. This paper introduces the parallel development of mathematics in Basel, Switzerland, and Edo, Japan, and highlights the global conditions that allowed for multiple origins of mathematical discoveries.