The Origins of Optimal Transport

Updated: Jan 24

How transporting piles of sand became an interesting problem



The history of OT starts with a French mathematician and statesman, Gaspard Monge, who is also the inventor of descriptive geometry, and the founder of École Polytechnique. Monge formulated the Optimal Transportation problem for the first time in 1781 out of civil engineering preoccupations.


Monge's solution was however incomplete, and tackled what is now known as a very particular case among Optimal Transport problems. The exact solution remained unknown until 1941, when the Soviet mathematician Leonid Kantorovitch introduced a relaxation method that solved the problem using linear programming.


Widespread applications

Interest for optimal transport was renewed about 30 years ago. Yann Brenier's work in the 90's was followed by Cédric Villani in the 2000's, who wrote two monographs on the topic: Topics in Optimal Transportation, and Optimal Transport: Old and New, contributing thereby to spread knowledge about applications of OT.


Current specialists, in some sort of obsession, are now seeing Optimal Transport everywhere: from meteorology to isoperimetric problems, statistical physics and Sobolev inequalities." (Villani, 2004)

More recently, Optimal Transport has sparked the interest of economists and data scientists.


Optimal Transport is everywhere


On this blog, we post short articles about the intersection between mathematics, economics, and coding, with some degree of focus on Optimal Transport.