This article is devoted to explaining the role of Takebe Katahiro, who inherited a tradition and opened a new trend in wasan, or Japanese mathematics. We discuss his role as a wasan mathematician by comparing his mathematics research with that of his mentor, Seki Takakazu, to explain the achievements with which he surpassed his mentor. We also investigate several wasan texts written after his Tetsu-jutsu Sankei to show the trend he started. Finally, we take Takebe Katahiro’s commentary to his predecessors’ works in the Tetsu-jutsu Sankei as an example of Takebe Katahiro’s modesty, and explain the reason for the high prestige and status he had among those who are proficient in mathematics and for elevation of the academic status of mathematics in the Edo period.