ɪn nˈaɪntiːnhˈʌndɹɪd twˈɛnti nˈaɪn, hiː pɹəpˈoʊzd ðɪ ˈɑːpənhˌaɪm kəndʒˈɛktʃɚɹ ɐbˌaʊt ɹˌɛpɹᵻzˈɛntˈeɪʃənz ʌv nˈʌmbɚz baɪ ɹˈiːəl kwɑːdɹˈæɾɪk fˈɔːɹmz ɪn sˈɛvɹəl vˈɛɹɪəbəlz.
In 1929, he proposed the Oppenheim conjecture about representations of numbers by real quadratic forms in several variables.