The mathematician who rejected a fortune to define the limits of calculus

Ideas & Philosophy · Published 3 October 2026 Swipe more like this →

In short: Simon Lhuilier was a Swiss scholar who famously turned down a massive inheritance to pursue mathematics. His dedication led him to formalize the concept of limits, introducing the notation we still use today. Beyond analysis, he shaped early topology and probability, leaving an indelible mark on modern mathematical foundations.

Born in Geneva in 1750 to a Huguenot family that had fled France, Simon Lhuilier demonstrated early academic brilliance. Despite a lucrative offer from a wealthy relative contingent on a career in the church, Lhuilier chose the path of mathematics. He studied under Louis Bertrand and Georges-Louis Le Sage, eventually securing a tutoring position in Poland. There, he spent eleven years at the palace of Prince Adam Kazimierz Czartoryski, where he balanced his duties as a tutor with prolific mathematical research.

Lhuilier gained international recognition in 1786 when he won a prestigious competition hosted by the Berlin Academy. The challenge sought a rigorous foundation for differential calculus, and Lhuilier’s submission, Exposition élémentaire des principes des calculs supérieurs, provided a remarkably modern treatment of limits. He was the first to introduce the notation 'lim' and allowed for two-sided limits, concepts that remain standard in undergraduate calculus today. Although Joseph Lagrange, the lead judge, was reportedly underwhelmed by the submissions, Lhuilier’s work established a vital framework for future analysis.

Returning to Geneva in 1795, Lhuilier held a chair of mathematics until his retirement in 1823. His contributions extended well beyond calculus; he made significant strides in topology by refining Euler’s polyhedra formula and correcting the solution to the famous Königsberg bridge problem. He also authored influential articles on probability and published comprehensive algebra texts for his students. Despite his rigorous academic output, Lhuilier was known for his whimsical side, occasionally composing ballads about mathematical constants and geometric theorems.

Lhuilier’s legacy is anchored in his ability to synthesize complex ideas into clear, pedagogical forms. His work influenced later mathematicians like Augustin-Louis Cauchy and Charles-François Sturm, the latter being his most famous pupil. By the time of his death in 1840, Lhuilier had been elected to several prestigious institutions, including the Royal Society of London, cementing his status as a pivotal figure in the evolution of European mathematical thought.

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