**Hidehiko Yamabe** was a Japanese mathematician who published important results in differential geometry and on group theory, including Hilbert's fifth problem.

- Hidehiko attended elementary school in Ashiya than continued his secondary education close to his home.
- The war was reaching its climax in 1944 when Yamabe entered the University of Tokyo to study mathematics.
- Despite the problems Yamabe published some fine mathematical papers.
- In On an arcwise connected subgroup of a Lie group published in 1950 in the Osaka Mathematical Journal Yamabe gave a direct proof of the theorem that an arcwise connected subgroup of a Lie group is a Lie subgroup.
- Yamabe began to produce partial results in papers such as On some properties of locally compact groups with no small subgroup (1951) written with Morikuni Goto, which shows that in a locally Euclidean group with no small subgroup every point sufficiently near the identity is on a unique one-parameter subgroup.
- Despite the large amount of progress that Yamabe was making to solve Hilbert's Fifth Problem, he was also producing many other papers such as: (with Zuiman Yujobo) On the continuous function defined on a sphere (1950); (with Morikuni Goto) On continuous isomorphisms of topological groups (1950); On an extension of the Helly's theorem (1950); and A condition for an abelian group to be a free abelian group with a finite basis (1951).
- This is undoubtedly Yamabe greatest achievement, although he went on to produce many more very high quality pieces of work.
- In the following year Yamabe published A unique continuation theorem for solutions of a parabolic differential equation written jointly with Seizo Ito.
- Yamabe returned to the United States in July of following year to continue with his position at the University of Minnesota.
- Finally let us note a publication by Yamabe, together with David Pope, A computational approach to the four-color problem which appeared in 1961.
- The Yamabe Memorial Lecture has been held in his honour since 1989 and from 2002 this was replaced by the Yamabe Memorial Symposium.
- The Yamabe Memorial Symposium is an enhancement of this tradition.
- One goal will be to advance areas of mathematics related to the interests of Hidehiko Yamabe, which touched in a substantial and ground-breaking way on several quite different areas of mathematics, all of which may be roughly described as having significant geometric aspects.

Born 22 August 1923, Ashiya, near Osaka, Japan. Died 20 November 1960, Evanston, USA.

View full biography at MacTutor

Origin Japan

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive