Seki was born into a samurai warrior family, the second son of Nagaakira Utiyama, but was adopted as a young boy by another noble family, the Seki Gorozayemon.
He was a self-educated child prodigy in mathematics from the age of nine. He studied determinants and Bernoulli numbers, and was the first in Japan to write on magic squares. He also studied Diophantine equations and the calculus. In some areas his work predates that of Europeans now credited with priority (e.g., Bernoulli numbers). He was also a renowned teacher and the examiner of accounts to the Lord of Koshu.
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