The phrase is a translation of the German “man muss immer umkehren”, associated with Jacobi’s approach to difficult mathematical problems. The advice is to turn a problem around: instead of asking how to reach a result directly, examine the reverse question, the opposite case or the conditions under which the result fails.

Jacobi used inversion in his own work, most visibly in the theory of elliptic functions, which arose from inverting elliptic integrals. Problems that were intractable in one direction became manageable when the relationship was reversed.

The saying has since travelled well beyond mathematics. It is often quoted in business and decision-making circles, notably by the investor Charlie Munger, who advised working out what would guarantee failure and then avoiding it. The wording is a later English condensation rather than a documented quotation, and the attribution to Jacobi is traditional rather than firmly sourced.

In original language (German)

“Man muss immer umkehren.”