ðə kˈɑːnvɜːs stˈeɪtmənt ʌvðə ɡɹˈeɪdiənt θˈiəɹəm ˈɔːlsoʊ hɐz ɐ pˈaʊɚfəl dʒˌɛnɚɹəlᵻzˈeɪʃən ɪn tˈɜːmz ʌv dˌɪfɚɹˈɛnʃəl fˈɔːɹmz ˌɔn mˈænɪfˌoʊldz.
The converse statement of the gradient theorem also has a powerful generalization in terms of differential forms on manifolds.