Early Years
He was born in Tokyo. He graduated from the University of Tokyo in 1938 with a degree in mathematics and also graduated from the physics department at the University of Tokyo in 1941. During the war years he worked in isolation, but was able to master Hodge theory as it then stood. He obtained his Ph.D. degree from the University of Tokyo in 1949, with a thesis entitled Harmonic fields in Riemannian manifolds. He was involved in cryptographic work from about 1944, at a time of great personal difficulty, while holding an academic post in Tokyo.
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