Thanks to his exceptional intuition and his ability to see deeply into the heart of a question, Luzin frequently predicted mathematical facts whose proof turned out to be possible only after many years and required the creation of completely new mathematical methods.
Salamat sa kanyang katangi-tangi kawatasan at ng kanyang kakayahan na makita ang taimtim sa puso ng isang katanungan, Luzin madalas hinulaang katotohanan na may matematiko patunay yari sa magiging posible lamang pagkatapos ng maraming taon at kinakailangan ang paglikha ng ganap na bagong pamamaraan matematika.