Old mathematical challenges: Precedents to the millennium problems


Abstract


The Millennium Problems set out by the Clay Mathematics Institute became a stimulus for mathematical research. The aim of this article is to highlight some previous challenges that were also a stimulus to finding proof for some interesting results. With this pretext, we present three moments in the history of mathematics that were important for the development of new lines of research. We briefly analyse the Tartaglia challenge, which brought about the discovery of a formula for third degree equations; Johan Bernoulli’s problem of the curve of fastest descent, which originated the calculus of variations; and the incidence of the problems posed by David Hilbert in 1900, focusing on the first problem in the list: the continuum hypothesis.


Keywords


cubic equation; Cardano–Tartaglia formula; brachistochrone; Hilbert’s problems; continuum hypothesis

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References


Boyer, C. B. (1989). A history of mathematics. New York: John Wiley & Sons, Inc.

Dunham, W. (1990). Journey through genius. New York: John Wiley & Sons, Inc.

Hilbert, D. (1902). Mathematical problems. Bulletin of the American Mathe­matical Society, 8, 437–479. doi: 10.1090/S0002-9904-1902-00923-3

Kline, M. (1972). Mathematical thought from ancient to modern times. New York: Oxford University Press.


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Texts in the journal are –unless otherwise indicated– published under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

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Creative Commons License
Texts in the journal are –unless otherwise indicated– published under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

____________________________________________________________________________________________________________________