 Takeuti’s work on his conjecture instead focused on partial results. A major breakthrough that galvanized research in proof theory, especially ordinal-theoretic investigations, was made by him in 1967. In Takeuti 1967 he gave a consistency proof for \(\Pi^1_1\)-comprehension and thereby for the first time obtained an ordinal analysis of an impredicative theory. For this Takeuti vastly extended Gentzen’s method of assigning ordinals (ordinal diagrams, to be precise) to purported derivations of the empty sequent. It is worth quoting Takeuti’s own assessment of his achievements.