At the heart of the ellipse

If Condorcet is known as the great defender of public education, we often forget that he was first and foremost a mathematician. His work in analysis was praised by the Academy of Sciences, even if it must be acknowledged that judgments on his mathematical work were sometimes rather negative. This is undoubtedly largely due to his attempt to found a social mathematics, that is, to apply probabilities to human questions, particularly electoral ones. This stems from a desire to use mathematics to eliminate reasoning errors and prejudices from our actions. It was also from this perspective that he advocated for popular mathematics education just as he opposed the magical thinking surrounding Mesmer's experiments. In the same way, he was politically engaged for women's suffrage and for the abolition of slavery. Condorcet is the author of a rich body of thought where mathematics always serves as a substrate.

With the parabola and the hyperbola, the ellipse is one of the three conic sections. First examined in the context of solving problems requiring tools beyond the straightedge and compass, such as the duplication of the cube, they were later unified by their geometric definition as the intersection of a plane and a cone. The ellipse, which may seem to be merely a flattened circle, exhibits surprising properties, whether concerning the calculation of its perimeter, various construction methods one might devise, or the practical properties allowed by its focal definition, one of which is the proof of heliocentrism.