ðə ɡɹˈeɪdiənt θˈiəɹəm ˈɔːlsoʊ hɐz ɐn ˈɪntɹɛstɪŋ kˈɑːnvɜːs: ˌɛni pˈæθˌɪndᵻpˈɛndənt vˈɛktɚ fˈiːld kæn biː ɛkspɹˈɛst æz ðə ɡɹˈeɪdiənt əvə skˈeɪlɚ fˈiːld.
The gradient theorem also has an interesting converse: any path-independent vector field can be expressed as the gradient of a scalar field.