During World War I, he was isolated from European mathematicians and developed his existence theorem in class field theory, building on the work of Heinrich Weber.

As an Invited Speaker, he presented a synopsis of this research in a talk Sur quelques théoremes généraux de la théorie des nombres algébriques[2] at the International Congress of Mathematicians in Strasbourg in 1920.

There he found little recognition of the value of his research, since algebraic number theory was then studied mainly in Germany and German mathematicians were excluded from the Congress.

However, the significance of Takagi's work was first recognized by Emil Artin in 1922, and was again pointed out by Carl Ludwig Siegel, and at the same time by Helmut Hasse, who lectured in Kiel in 1923 on class field theory and presented Takagi's work in a lecture at the meeting of the DMV in 1925 in Danzig and in his Klassenkörperbericht (class field report) in the 1926 annual report of the DMV.

In 1932 he was vice-president of the International Congress of Mathematicians in Zürich and in 1936 was a member of the selection committee for the first Fields Medal.