Johann Bernoulli (= Jean; 1667–1748) posed the problem of finding the ‘brachistochrone’: the curve between two points along which a body starting from rest at the higher point and freely accelerated by uniform gravity would descend in minimum time to the lower.

Gottfried Wilhelm Leibniz (1646–1716) thought the problem beautiful; so did Guillaume de l’Hospital (1661–1704).

Bernoulli (and others) proved that the brachistochrone was again an inverted cycloid. He thought that the equality of the cycloid, tautochrone, and brachistochrone curve would leave his readers ‘petrified with astonishment’, and thought that it suggested some deep design in nature.

One of Bernoulli's proofs was what he considered a ‘very beautiful’ geometric demonstration that the cycloid was the brachistochrone.

But he did not publish it until 20 years later. Why? Apparently in part due to Leibniz, who had thought it so beautiful and extraordinary that he counselled against publication, with the aim of ‘so frustrating those who are not very grateful and who are accustomed to profiting from the inventions of others’.

**Here, mathematical beauty contributed to the suppression, albeit temporary, of mathematical knowledge.**

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