Takakazu Seki Kowa
1642 - 1708

Seki Kowa came to be known as “the arithmetical sage.” What do you think this means? A sage in this sense doesn’t refer to the spice that belongs to the mint family, but instead refers to one who is wise and perceptive. Seki was considered “the arithmetical sage” because he was very knowledgeable skillful in mathematics and was highly respected because of his wisdom.

Seki Kowa was born into a warrior, or samurai, family in March 1642, in Japan. At an early age he was adopted by a noble family and assumed the family name Seki. At an early age, about nine years old, Seki was introduced to math by a servant. From then on, Seki studied math and became self educated, now considered a prodigy. Seki collected math books from the Chinese and Japanese cultures and eventually became recognized as an expert in mathematics. This recognition led to many students for Seki to instruct.

Contributions by Seki are difficult to identify due to the secrecy that surrounded rival schools in Japan. Seki was also held to the Samurai Code that demanded modesty. There is plenty of evidence that he made major discoveries in calculus and is considered to be the founder of Japanese mathematics.

In 1674, Seki wrote Hatsubi Sampo in which he provided solutions for math problems that had been posed four years earlier. The solutions are known for being carefully analyzed and for the thoroughness of the answers.

The year of 1683, Seki was busy exploring the realms of mathematics, studying determinants and magic squares. He developed a theory of determinants that predated work by the 18th century German mathematician, Gottfried Leibniz. Seki also studied magic squares and the work by a Chinese gentleman, Yank Hui, on the same topic. Seki is credited with bringing the idea to Japan, even though there is evidence that magic squares were discovered as early as 2000 BC.

The actual date is unclear, however, Seki Kowa is also credited with discovering Bernoulli numbers before Jacob Bernoulli. He studied equations using both positive and negative numbers, however he did not have any notion of complex numbers.

Toward the end of his mathematically prosperous life, being a descendant of the samurai class, he qualified to serve as an examiner of accounts to Lord of Koshu. The Lord of Koshu became heir to the Shogun, and in 1704, Seki was given a position of honor as master of ceremonies in the Shogun’s household.

Seki’s rich life came to an end in October of 1708 in Japan. His tombstone is carved with the most fitting phrase: “The Arithmetical Sage.”

Contributed by Cynthia Schmidt


  1. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Seki.html
  2. http://britannica.com/
  3. http://www.roma.unisa,edu,au/07305/magicsq.htm

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