**Tadashi Nakayama** was a Japanese mathematician who made important contributions to representation theory.

- Tadashi was brought up in Tokyo where he first attended primary school and then entered the Musasi High School.
- However, perhaps even more of an influence on Nakayama than Takagi was his student Kenjiro Shoda who had studied in Germany with Issai Schur in Berlin and with Emmy Noether in Göttingen.
- In 1934 Nakayama had his first three papers published.
- Nakayama graduated with his Rigakushi (diploma) from Tokyo Imperial University in 1935 and, in the same year, he was appointed as an assistant at Osaka Imperial University (now Osaka University).
- Shoda had been appointed as a professor in the Faculty of Science at Osaka University in 1933 so Nakayama's appointment there allowed them to easily continue their work together.
- Nakayama published the book Local Class Field Theory in the year he was appointed to Osaka.
- Experience abroad was important to leading Japanese mathematicians in this period and Nakayama followed this pattern spending time in the United States having been invited to the Institute for Advance Study at Princeton.
- Before Nakayama left for the United States he had been ill and had contracted tuberculosis.
- Richard Brauer was by this time a professor at Toronto and he invited Nakayama to make two research visits to Toronto during his time in the United States, When he visited Brauer, he become inspired to work on group representations, publishing articles such as Some studies on regular representations, induced representations and modular representations (1938) and A remark on representations of groups (1938).
- While with Brauer, he also met Cecil J Nesbitt, Brauer's first doctoral student in Toronto, and Nakayama and Nesbitt collaborated on the paper Note on symmetric algebras (1938).
- In 1939 Nakayama published the first part of his paper On Frobeniusean Algebras in the Annals of Mathematics.
- Together with Azumaya, Nakayama worked on the representation theory of algebras, particularly Frobenius algebras.
- The first part of the book, written by Nakayama on the structure of rings, is similar to the famous text by Nathan Jacobson.
- Nakayama spent further time on extended research visits.
- Finally we mention that his name is well-known today among algebraists for 'Nakayama's lemma' is named after him.

Born 26 July 1912, Tokyo, Japan. Died 5 June 1964, Nagoya, Japan.

View full biography at MacTutor

Origin Japan

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive