MoM Ep14: Gaspard Monge

This podcast episode of Men of Mathematics discusses Gaspard Monge, the inventor of descriptive geometry and founder of the École Polytechnique, whose work significantly shaped technical education.

Key Topics:

• Descriptive Geometry
• École Polytechnique
• Optimal Transport Problem
• French Revolution's Impact on Education
• Monge's relationship with Napoleon

Summary:

Gaspard Monge, born in 1746 in Burgundy to a knife grinder, displayed exceptional mathematical abilities early in life. His talent led him to a military school where he invented a groundbreaking method for designing fortresses. This method, known as descriptive geometry, was classified as a military secret for 15 years due to its strategic value.

Monge's descriptive geometry provided a systematic way to represent three-dimensional objects in two-dimensional drawings using multiple views to capture spatial information precisely. This innovation revolutionized architecture and engineering, replacing immeasurable perspective drawings with a precise language for 3D design. His work evolved from stereotomy, the ancient art of stone cutting, making it mathematical and applicable to various fields. In 1781, Monge introduced the optimal transport problem, concerning the most efficient way to move dirt between piles and holes, which has become fundamental in modern mathematics, machine learning, economics, and meteorology. He also contributed to the study of curved surfaces, influencing Gauss's later work on differential geometry.

During the French Revolution, Monge was instrumental in establishing the École Polytechnique in 1794 to rapidly train engineers. This institution broke from traditional norms by emphasizing rigorous mathematics, meritocracy, practical applications, and the blackboard teaching method. The École Polytechnique produced influential mathematicians and scientists, including Cauchy, Fourier, Poisson, Carnot, Fresnel, and Coriolis, leading to French dominance in mathematics during the early 19th century.

Monge accompanied Napoleon to Egypt and helped found the Institut d'Égypte, contributing to the Description de l'Égypte, which sparked European interest in ancient Egypt. His loyalty to Napoleon would later have consequences. After Napoleon's defeat at Waterloo, the restored monarchy stripped Monge of his honors and expelled him from the Institut de France. His health deteriorated, and upon his death in 1818, the government forbade students from attending his funeral, though many defied the order. Despite the controversies surrounding his later life, Monge's contributions as a creator and teacher profoundly influenced French mathematics and technical education, leaving a lasting legacy in engineering and mathematics worldwide.