

Since 2021, the Bourse de commerce in Paris has been open to the public, showcasing contemporary art from the Pinault Collection. Its superbly renovated interior offers mathematicians an opportunity to explore… stereographic projections!



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We tend to think of mathematics as a perfectly neutral science. Yet, like any human construct, its uses can prove more political than they appear. That is how an age-old geometry problem found its way into diplomatic debates in recent months.

Since antiquity, navigators have sought to find their position at sea, first developing instruments and then maps before the practice was standardized in the 19th century. This practical and strategic use of mathematics endured for centuries before other tools superseded it.

The best-known maps are based on the famous Mercator projection, named after its Flemish creator, who worked in the early Renaissance. Yet this projection relies on mathematical concepts developed well after the scholar’s death! So how could he have constructed his world map?

During the 19th century, the search for quantities invariant under a particular group of transformations became the main focus of the various branches of geometry. The cross-ratio, a fundamental invariant of projective geometry, also appears in non-Euclidean geometries and their models.
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