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We give a negative answer to Ulam's Problem 19 from the Scottish Book asking{\it is a solid of uniform density which will float in water in every positiona sphere?} Assuming that the density of water is $1$, we show that there existsa strictly convex body of revolution $K\subset {\mathbb R^3}$ of uniformdensity $\frac{1}{2}$, which is not a Euclidean ball, yet floats in equilibriumin every orientation. We prove an analogous result in all dimensions $d\ge 3$.

A negative answer to Ulam's Problem 19 from the Scottish Book