Monge and Optimal Transport

Etienne Ghys

Etienne Ghys (from

Mathematicians are ignorant of their history. They know the names of the greats but generally can repeat only one or two (erroneous) stories about them. For example, if asked for a mathematical story from the French Revolution, then many would plump for a story about Galois, shot at dawn. However, there were many other revolutionary mathematicians. One such is Monge. His name is familiar to differential geometers through Monge form and to analysts of PDEs through the Monge-Ampere equation.

Information about him is scant in English. All the important books are in French and so my attempts to study his life in more depth have been thwarted by my lack of fluency. I think I first became interested in him when I was a student. I read a book (the name escapes me) which stated that he had studied the concept of the optimal transport of soil when constructing fortifications. The fact that caught my imagination was that the answer was constrained by the observation that the paths of two particles should not cross. At the time I came up with a counter-example but that was because I didn’t really understand the parameters of the problem.

I was greatly interested then when I heard that one of this year’s Hardy Lectures would be about Monge and the optimal transport problem. I was greatly disappointed when I discovered that it clashed with previous commitments. When I was at the conference in Liverpool to celebrate the birthdays of Bill Bruce and Terry Wall Andrew Ranicki told me that the lecture had been recorded.

And I’m glad it was, it’s a great talk. It’s given by Etienne Ghys. He takes in the cutting of stones, including how Monge designed a never used plan for the ceiling of a new parliament and shows the reasoning that led up to the Monge-Ampere equation. A bit of familiarity with developable surfaces and envelopes is perhaps necessary but most of the talk is accessible.

Here it is.

EMS_130_Ghys by Carmen_Rovi

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