Navier: Blow-up and Collapse, Volume 50, Number 1

I n the 1820s Claude Louis Marie Henri Navier1 was a professor at the École des Ponts et Chaussées in Paris, which was the Grande École that trained engineers in nineteenthcentury France. At the same time as publishing his famous fluid equations (now known as the Navier-Stokes equations), he designed the first monumental suspension bridge to be built in Paris over the Seine. His bridge developed a crack just before it was to open, and political battles resulted in the removal of the bridge. Accusations were made that Navier was “too much of a theoretical mathematician” and not “practical” like the British bridge builders such as Brunel or Stevenson. This debate was a version of a more general dispute between the French and British approaches to mathematics, physics, and engineering. The different national approaches to science were in fact also reflected by the way Navier (in 1822) and Stokes (in 1845) derived their eponymous equations. The word “blow-up” of the solutions for the Navier-Stokes equations is familiar to at least a subset of mathematicians, most of whom probably do not know of Navier’s bridge. In 1824–6, however, Navier was best known for a two-volume treatise on bridges [13] and the impressive design for the Pont des Invalides over the Seine (Figure 1). The controversy that followed the collapse of this bridge received wide coverage in the French press of the time, had repercussions for the Parisian world of finance, and was detrimental to Navier’s reputation.