It happened to me sometimes that I could not immediately grasp [the lecture's] content, but I could always reconstruct it by taking enough time in reviewing my notes and it was the greatest pleasure to do this in the evening of the day I heard the lecture.In his second year of study Iyanaga took further courses by Takagi which developed group theory, representation theory, Galois theory, and algebraic number theory. Although it was this latter topic which would eventually attract Iyanaga, at this stage of his undergraduate career he was attracted to differential equations. He studied this topic in T Yosiye's course and became interested in conditions under which dy/dx = f (x, y) has a unique solution. Yosiye :-
... encouraged the student to do original work and exempted him from undergoing an examination to obtain credit if he presented a good paper. Iyanaga posed the question of finding some intuitive or geometrical reasons why ... conditions assure the uniqueness of solution.Iyanaga's paper was so good that Yosiye had it published in the Japanese Journal of Mathematics. Surprisingly Iyanaga wrote a second paper while in his second undergraduate year. This came about through talking to the Departmental Assistant T Shimizu who discussed with him questions about power series. They wrote a joint paper which was published in the Proceedings of the Imperial Academy of Tokyo. Both Iyanaga's two papers appeared in print in 1928.
In his third undergraduate year Iyanaga was allowed to take part in Takagi's seminar on class field theory. He studied Takagi's famous 1920 paper on extensions of algebraic number fields and also a paper by Hasse written in 1926 to give more details of Takagi's results. A question by Takagi led Iyanaga to prove a result which further led to his first paper on class field theory (and his third published paper while he was an undergraduate). Graduating in 1929, Iyanaga remained at Tokyo University where he worked under Takagi for his doctorate. It was an exciting time with increasing mathematical activity in algebra. For example K Shoda, who was a student of Takagi, had studied with Schur in Berlin and with Emmy Noether in Göttingen, and returned to Japan around the time that Iyanaga began his graduate studies.
Most of the graduate students from Tokyo went to study in Germany but Iyanaga decided to go to France as well as Germany. He obtained a scholarship from the French government in 1931 and in that year he went to Hamburg where he studied with Artin. He writes :-
I was very lucky to follow Artin's course on class field theory together with Chevalley.The International Congress of Mathematicians was held in Zürich in 1932. Takagi came over to Europe for this Congress (he was vice-President) and met up with Iyanaga who had gone from Hamburg to Zürich for the Congress. He writes:-
I met Takagi in Zürich and accompanied him when he visited Hamburg, Berlin, and Paris.Iyanaga went to Paris in 1932 where he met up with Chevalley whom he had got to know well while in Hamburg. He also met Henri Cartan, Dieudonné and André Weil, and he finally returned to Tokyo in 1934. He was appointed as Assistant Professor in 1934 and began his teaching career. He helped Takagi with his calculus course in 1935-36, the last time Takagi gave it before he retired. Iyanaga writes :-
I published no research papers in the period 1935-39. I realise now that I was idle in doing research in these years because of the pressure of teaching and other business to which I was not accustomed.In fact Iyanaga did, for various reasons, little original research from this time on. Perhaps his last important idea which he published in his own field was prompted by an invitation to submit a paper to a collection being assembled to honour Furtwängler. Iyanaga managed to solve a question of Artin on generalising the principal ideal theorem and this was published in 1939. He wrote :-
I received from Professor Furtwängler a letter thanking me for my contribution, which I cherished but lost together with my house which burned in a bombardment in the Spring of 1945.He did publish a number of papers, however, which arose through the various courses such as algebraic topology, functional analysis, and geometry, which he taught. Iyanaga was promoted to Professor at Tokyo University in 1942 but by this time Japan had entered World War II. He wrote:-
... towards the end of the War, Tokyo and other Japanese cities were often bombarded and we had to find refuge in the countryside. Everyone was mobilised in one way or another for the War. And just after the War, the whole country was in distress, but on the other hand freed from military oppression, we began to make efforts to rebuild our science and culture in a better form. This kept us busy. I was particularly busy in editing textbooks from primary and secondary schools ... I continued to give courses and organise seminars, in which I used to discuss class field theory with my younger friends.Iyanaga joined the Science Council of Japan in 1947. He was invited by Stone to join the International Mathematical Union and in 1952 he became a member of the Executive Committee. In this role he helped organise the 1954 International Congress of Mathematicians in Amsterdam, which he attended. As a member of the Science Council of Japan he was the main organiser of an International Symposium on Algebraic Number Theory held in Japan in 1955.
Iyanaga spent the year 1961-62 in Chicago :-
In 1962 I received an invitation from the University of Chicago to join its Department of Mathematics for 1961-62. ... I was most happy to accept this invitation which gave me a chance to escape from administrative work which was making one busier every day. I met there Stone, Mac Lane, Schilling, Albert, Suzuki, and other old friends.In 1965 Iyanaga became Dean of the faculty of Science at Tokyo University. He held this post until he retired in 1967. However this was not the end of his career for he was visiting Professor at Nancy in France during 1967-68 and then Professor at Gakushuim University for 10 years from 1967 to 1977.
One important role which Iyanaga had that we have not yet mentioned was that of President of the International Commission on Mathematical Instruction from 1957 to 1978.
Iyanaga received honours such as being awarded the Rising Sun from Japan in 1976, being elected a member of the Japan Academy in 1978, and receiving the Order of Legion d'Honneur from France in 1980.
Article by: J J O'Connor and E F Robertson