... it did not really matter, since I was not a quick boy. On the contrary, when I was a child, say, four ... , I was called 'bonchan', which means a boy who is very slow in responding, very inadequate. I think I am very much the same now, ha! ha! Anyway, I turned thirteen right after entering middle school. In December of that year, Japan entered the war against the allied forces: U.S., UK, Holland, and China.

After Pearl Harbor, the British fleet was destroyed in the Far East, Singapore was occupied, and so on. Things looked favorable for Japan. But soon after, a year or so later, things started changing. This was the beginning of my hard experiences. My regular courses in middle school lasted for only two years, and the rest of my school life was total chaos. The war in the Pacific ended on May 15, 1945. The first atomic bomb was dropped on August 6, 1945, after which the USSR declared war on Japan in order to secure the Kurilsk and Sachalin islands. At that time I was fifteen. Being a teenager, I had to work in factories. From 1943 to 1945, I had to carry coal. Very hard work ... bad food ... In late 1944, the systematic bombings of civilian targets by the U.S. started, after the fall of Micronesia, which then served as a base. In early 1945, Tokyo was a target. The first attack on Tokyo was on March 10, 1945, and some 80,000 were killed that night, but my family was spared. This was a short respite, since a month later there was a second attack and another broad area of Tokyo was burned down, including our house. I narrowly escaped the fire. We lost everything, but the family was safe. Due to the smoke, I partially lost my eyesight for a couple of weeks. Who cares about such details, anyway? Well, Japan had been rough on some people elsewhere, like the occupation army in China, and now it was hard for Japan. It was hard for many. ... the government decided to move the schools to the countryside - they were practically closed, anyway. We could not find a place or job outside Tokyo. In a way, our family collapsed. We did not have any relatives in the countryside we could stay with, and we had no house. Pupils with family or friends in the countryside were supposed to go there, and those without such advantages had to join a party led by a schoolteacher. My father was a lawyer, but in 1941 or 1942 he fell ill and could not work as such anymore. Still, he thought that he could provide for his family. But then there was a sharp devaluation of the yen, by a factor of 100 (a yen was nearly the equivalent to a dollar before the war). Soon, the money my father had left from his work was down to practically nothing. We could not live on that anymore, and we nearly starved.

I worked out hyperfunction series and outlined the theory for several variables - though the complete theory was finished later, since it required a generalization of cohomology theory.

... an exposition of the elements of a theory of hyperfunctions (analytic distributions), motivated by the classical work of Luigi Fantappiè on analytic functionals and of Laurent Schwartz on the theory of distributions, and by a relatively recent article by Gottfried Köthe putting together these viewpoints.... The generalization of the concept of function is carried out by using the cohomology theory with coefficients in sheaves.

It seemed to me that even André Weil did not like my way of putting things in terms of cohomology very much. In fact, I learned that he was very much against cohomology. I got the idea that hyperfunctions were not taken very seriously, and since I was sort of a little boy (though I was 32!) I just wanted to show the usefulness of my ideas. My general program, which I had expanded at the colloquium talk of 1960, was just a very formal kind of general nonsense. I then wanted to give some concrete example of it in the analysis of differential equations. But my knowledge of that field was very poor. I'm not a reader of big books and specialized papers. I live for practical examples and, just as now, I was very slow in developing my deeper thoughts.

The basic structure of the paper hinges on my talk at the Katata conference, but the manuscript was completely prepared by Kawai and Kashiwara. Let us say I presented the whole story, but did not prove every detail. For example, concerning the notion of microdifferential operators, I worked out some cohomological constructions, but then Kawai and Kashiwara gave a better, more direct presentation .... Kawai and Kashiwara must have taken a lot of effort to complete every detail.

This is the first one of a series of papers on holonomic quantum fields. In this series we deal with these objects: (1) Deformation theory for linear differential equations (Riemann-Hilbert problem and its generalization to higher dimensions), (2) Quantum fields with critical strength (2-dimensional Ising model, etc.) and (3) Theory of Clifford group.

... for his creation of the theory of hyperfunctions. Professor Sato has been the driving force behind a world-leading group of researchers in algebraic analysis. His work in theoretical physics has increased our understanding of the divergences of quantum theory.

Sato's theory of hyperfunctions allows much freer calculations than does classical calculus. A function may not have a derivative which is a function, but it does have a derivative which is a hyperfunction. Every function is regarded as a sum of limit values of holomorphic functions, which means that one uses the fact that immediately outside the real numbers there are complex numbers - this is said to reflect the old idea that phenomena in the real world are limits of complex (imaginary, fictitious!) events that lie very close to but are still outside our reach. A rich theory for differential equations has been the result. The theory of hyperfunctions is competing with the so-called theory of distributions and often gives analogous results, but along a different path. In some sense the two theories are equivalent, but there are important differences in mode of attack. One theory is best known in Europe and the Americas, the other in Japan. Sato is deeply interested in and motivated by problems in theoretical physics. His important contributions concern Feynman integrals and integrable systems.

Mikio Sato's vision of "algebraic analysis" and mathematical physics initiated several fundamental branches of mathematics. He created the theory of hyperfunctions and invented microlocal analysis, which allowed for a description of the structure of singularities of (hyper)functions on cotangent bundles. Hyperfunctions, together with integral Fourier operators, have become a major tool in linear partial differential equations. Along with his students, Sato developed holonomic quantum field theory, providing a far-reaching extension of the mathematical formalism underlying the two-dimensional Ising model, and introduced along the way the famous tau functions. Sato provided a unified geometric description of soliton equations in the context of tau functions and infinitedimensional Grassmann manifolds. This was extended by his followers to other classes of equations, including self-dual Yang-Mills and Einstein equations. Sato has generously shared his ideas with young mathematicians and has created a flourishing school of algebraic analysis in Japan.

Looking back, forty years later, we realize that Sato's approach to mathematics is not so different from that of Grothendieck, that Sato did have the incredible temerity to treat analysis as algebraic geometry, and that he was also able to build the algebraic and geometric tools adapted to his problems. His influence on mathematics is, and will remain, considerable.