Saturday, November 23, 2002
M I N D  G A M E S

The first Samurai

Aditya Rishi

The essential point in algebra does not lie in the nature of the elements (which are not necessarily numbers), but in the way elements are composed.
— Teiji Takagi (1875-1960)

KAZUYA village near Gifu in the 19-century central Japan: Teiji, son of an accountant on a farm in this mountainous region, discovers a secret in the cupboard of his authoritarian father. It is a Samurai sword, weapon of the emperor's chosen soldiers; there is no reason for it to be in the house of an accountant. Teiji reads the words inscribed on the metal: "COURAGE IS IN THE MIND", then, hearing his father's footsteps, quickly, puts the sword back in.

"You didn't go to school today; where have you been all day?" says Takagi Senior to his son. "Mother took me to the temple of Buddha for the first time; I was there all day," says Teiji. "Which prayer did you hear there?" says the old man, with suspicion in the eyes. The child starts reciting the prayers he had heard in the temple; he has memorised all, something that even the head priest can't do. The courage with which he faced his father surprises even Teiji.


Soon, he enters middle school in Gifu in 1886, where mathematics text are not written in Japanese, so, the pupils use English texts to study mathematics. The first books that he reads there are Algebra for Beginners by Todhunter and Geometry by Wilson. His academic brilliance takes him to the Third High School in Kyoto, after three years of which, he enters Tokyo University, the only university in Japan in 1894. Here he learns advanced mathematics more by reading books than from lecture courses that he attended. He learns about algebraic curves from George Salmon's book and he also studies Serret's Algèbre Supérieure. He is among the first ones to read Heinrich Weber's algebra text when it arrives in Japan.

Takagi is told that the department head is angry with him for not attending lectures and he should see him in his office. Head: "I find you to be non-serious and unfit to continue here; what promise can you show me?" "I have published my first paper," says Teiji, handing over a copy to the head. The paper shows a remarkably modern approach to algebra. He is chosen as one of 12 students from Japan to study abroad, where his discovery of a special case of Hilbert Zahlbericht's 12th problem makes him famous. In four years after returning from Germany, he becomes Professor in Tokyo University. His lectures are without prepared papers and rapid, so, students have to listen with great attention, as he does not repeat anything.

"The decimal expression of a natural number 'a' consists of 'n' digits, while that of a^3 consists of 'm' digits. Can n+m be equal to 2001?" he asks his class. No hand goes up; the students are too scared to attempt this seemingly tough problem and earn a bad reputation. From his long briefcase, he takes out the Samurai sword and shows it to a student, who reads the words on it and, instantly, comes up with the answer. Takagi (to the student): "This is the sword of courage, which has been in my family for countless generations and which, now, passes on to the first Samurai of your family... to you." What was the student's answer and why did Takagi give away his family secret and treasure. Write at The Tribune or