Economic theory is a mathematically rich field in which there are opportunities for the formal analysis of singularities and catastrophes. This article looks at the historical context of singularities through the work of two eminent Frenchmen around the late 1960s and 1970s. René Thom (1923-2002) was an acclaimed mathematician having received the Fields Medal in 1958, whereas Gérard Debreu (1921-2004) would receive the Nobel Prize in economics in 1983. Both were highly influential within their f...