I was born in 1940 as the second child in a family living in Nagoya, a city with a population of around a million inhabitants. My older sister died of tuberculosis before entering elementary school and so I was an only child until my second sister, who is seven years younger than me, was born after the War. I had a weak constitution and was a thin boy having poor digestion. My parents were worried about my health and repeatedly took me to be examined whenever they heard about doctors with a good reputation. In my infancy, therefore, I did not play with other children of the same age and was raised only among adults, so that I had a very precocious way of speaking. Thanks to this, later at elementary school I could get perfect scores in Japanese examinations designed to test pupils’ ability to use words in practice, for example by constructing short sentences containing specified words. On the other hand I would get almost zero in reading and writing Chinese characters used in Japanese since I had not studied them.
After a new municipal library opened near my elementary school, I went there often and began to read books at random so that I gradually acquired the ability to read between the lines. Why did the author choose to write one way but not another even if they have almost the same meaning? In those days I got into the habit of thinking about the psychology of the book’s author. This habit proved helpful to me later when I became a researcher. When discussing with my friends, I often find myself able to obtain more information from the same papers than they do. Sometimes however, I make an error by reading what is not written in the paper.
When I was in elementary and junior high schools I did not concentrate in class and could not be called a good pupil by any standard. For instance, at the end of my third year at junior high school there was a Japanese class in which the teacher handed out manuscript papers to the pupils to write an essay which was to be inserted in a graduation memorial collection of compositions. My classmates all wrote about their future ambitions; one wanted to become a carpenter following in his father’s footsteps, another hoped to go to university to become a mechanical engineer and so on. But I wrote about the evolution of stars, about which I had been reading in a boys’ magazine at that time. I had not heard the teacher’s explanation that the essay was to be included in the graduation memorial volume.
At that time I had never thought about my future or had any definite goals. I went on to high school with no strong motivation, but simply because my friends did so. The ratio of students who went on to high school then was about 50%. There was a high-achieving girl in my class who had decided not to continue to high school. Although I was not particularly friendly with her, since our seats in the class were well separated, I remember feeling that it was one of life’s absurdities when I heard her tell the teacher that she would not go on to high school.
There is an event engraved in my memory, which I experienced in the period before entering high school but after graduating from junior high school. I purchased the textbooks required for the high school and brought them back home. While I was browsing through the mathematics textbook, I noticed a strange character; the summation symbol Σ. As soon as I read the explanation I understood how to use it. I found that, by using the linearity of the Σ symbol, I could compute the sum of the n-th power of integers, 1n + 2n + … + kn, for any value of n, in principle. I was so excited that I calculated the sum up to rather high powers n, although this took me a long time. Not surprisingly for a boy who had not yet entered high school, I did not have sufficient knowledge to devise a generating function for the sum.
After the war, my parents were engaged in a small business which required them to work together from early in the morning until late in the evening, so that they did not have the time to pay much attention to their children’s study. Taking advantage of this, I played and played without studying. There was also another benefit from the fact that my parents were running their own business from home. They were mainly dealing with sugar as an ingredient for cakes. The ordinary sugar was packed in 30 kg bags of kraft paper like cement bags, and Cuban sugar in 100 kg bags of hemp. They also retailed sugar, subdividing it into 10 kg, 20 kg, and so on, so that the bags were stacked to be discarded. Our parents gave them to us children instead of an allowance. Since they could be sold if they were brought to a suitable place, I had some extra spending money − more than my friends did. I spent almost all my money on books. I still cannot get out of this habit. I buy books in bulk, not selecting them carefully, and read them later when I find them on my bookshelf.
When I was in high school, it had already been ten years since the war had ended and the world was becoming peaceful again. There still remained shortages of cultural materials, however. For example, the supply of new books was still insufficient, so that I had to walk around the area of secondhand bookstores every weekend afternoon with pocket money obtained by selling kraft and hemp bags for sugar. Initially the main genres of the books purchased with this money were detective and mystery stories and novels by Ryunosuke Akutagawa. Later I gradually began buying more mathematics books.
The first book I bought in mathematics was the “Theory of Functions” published as a volume in New Mathematics Series by Baifu-kan, Tokyo. I was very excited to see how a mathematics book was written, since I had seen no books other than school textbooks. I only knew the term “function”, which had already appeared in the high school mathematics textbook. The book gave me a glimpse of the rich world of differentiable functions of complex variable and I felt dizzy as if wandering off into a foreign place, quite different from the world I had previously known.
During my last year of high school, the Soviet Union successfully launched the first artificial satellite, Sputnik I. After this event I began to calculate the orbits of satellites and rockets by using a slide rule and an abacus. From the relative position of the Moon and Earth, I predicted for my friends the day on which the Soviet Union would next launch a rocket. To confirm the validity of the prediction, I always listened to the short-wave broadcasts of Radio Moscow from 11:00 at night. Then I realised that there is an issue with the precision of the time shown by clocks. From my measurements I discovered that my watch had a systematic error of − 8 sec/day and a random error ± 2 sec/day. The problem was the seasonal variation of the systematic error. If the temperature rises, the balance wheel becomes larger and its moment of inertia also gets larger, so that the clock should become slower. The temperature dependence of this deviation was, however, the opposite of estimates. This annoyed me for a few years. I looked for and examined books about clocks whenever I visited big bookshops, but I could not find the answer. About five years later I found the answer at last. The thermal expansion of the balance wheel and change of the moment of inertia were actually compensated by an ingenious mechanical device. I learned a lesson from this experience. I knew that wall clocks have such a temperature correction device since it can be seen. But I didn’t associate it with wristwatches. This taught me to think matters through carefully, taking as many relevant elements into account as possible.
I entered Nagoya University after one year of hard study, motivated by my desire to avoid succeeding my father and becoming a sugar merchant. The first class at the university was mathematical analysis by associate professor H. The first thing he said was: Suppose that there are two arbitrary positive numbers ε and a, then there always exists an integer N such that Nε > a is realised. This is called Archimedes’ axiom. Having declared “I will prove this”, he began the lecture by explaining Dedekind’s cut. What is this! Why isn’t it all right that we calculate a/ε and take N to be the integer part of it plus 1? It was a Culture Shock.
Next was a biology class by professor T. When I took a seat in the front, a sheet of paper was sent to me from behind. It contained some challenges, saying, “Solve the following problems!” There were six mathematics problems written on the paper. I remember that they were problems, which required solving differential equations such as determining the catenary, the form of a suspended chain. In this way the circle of my friends increased and I was also able to meet some good teachers.
At that time at Nagoya University, the campus for freshmen and sophomores was separated from that for juniors and seniors. The campus for the general education course for the students in the first two years of study had previously been a high school in the old system of education and there were several teachers from that system remaining in the Physics Department. When, during discussions with my friends, we encountered problems which we didn’t understand, we used to go to the teachers’ room to ask for help. When these visits became frequent, many teachers began to avoid us since they found us to be troublesome. There was however an exceptional teacher N who coolly answered our questions sitting back in an armchair. He was a young professor just past thirty. When we asked questions, he used to reply in a dignified manner, “I cannot immediately answer questions which are raised so suddenly. Study them yourselves. I will lend you this book if necessary.”
This was the first time that I had met somebody referred to as a researcher. The teachers I had met until my high school days were just teachers, who taught what they knew. But I realised that teachers at the university are also required to do research, discovering novel things. The students who gathered around professor N began to form a relatively fixed group, doing many other things together. The members of this group came from the whole faculty of science, although most were students in the Physics Department. They called themselves the DEPHIO group taking the initials D(Dirac), E(Einstein), P(Pauling), H(Hilbert), I(Ingold), O(Oparin), who were great scientists representing each department. The activities of DEPHIO included, for instance, lodging together in a borrowed country house for ten days during the summer vacation and holding a seminar class at a 2,000 meter high hill of the North Japanese Alps, having carried Dirac’s thick textbook up there. Although these activities were not directly relevant from the viewpoint of doing research, I think they were meaningful in encouraging solidarity among the members of the group and in helping them become researchers together. DEPHIO is no longer active, but the members still keep contact with each another.
At that time, I was mainly discussing mathematics with the group. I also continued to visit second-hand bookshops and found, for instance, books from a series of Mathematics lectures published by the publisher Iwanami before the War. Later I happened once to tell a mathematician that I had studied non-Archimedean valuation using one of those books. He was surprised and said, “I have heard that you are a fan of mathematics, Maskawa-san. But you are even studying such things!”
In our college days, the members of the DEPHIO group discussed together whenever they met. During the year 1960, Japan was politically in chaos since public opinion was split in two as to whether the Japan–U.S. Security Treaty should be concluded or not. The treaty could not be approved in the House of Councillors, but was soon automatically approved because of the dominance rule of the House of Representatives. The prime minister at the time then resigned.
Almost all classes were cancelled during this period because of a student strike. I attended all possible demonstrations, motivated by a young man’s sense of justice. It was inadmissible to me that the clock in the House of Councillors had been stopped to make time to enable the bill to be enacted and to prevent it from being scrapped.
There were no other periods later in my life in which I had as much free time as during those days. Although there were tasks to be performed, like going to demonstrations, distributing bills, collecting signatures and so on, there was also much free time in between. We used some of this time to hold outdoor seminars. Since everybody gathered in the university courtyard, it was easy to organise such seminars with little notice.
When I moved to the Higashiyama Campus as a junior student, I was still hesitating whether to study Mathematics or Physics. Mathematics in Japan at that time still remained under the strong influence of axiomatic Bourbakism. I did not know this definitely, but intuitively felt that this was the case. On the other hand, I felt that Physics was moving forward vigorously and so I submitted an application form for the graduate course in which I wrote that I wish to study theoretical physics. In fact, I had actually not yet decided my intended field of study quite so definitely even at that stage, as illustrated by the following event. When I was walking in the campus of the Faculty of Science at that time, a Professor in the Mathematics Department said to me, “You, Maskawa, will of course take an entrance examination for a Mathematics graduate course, won’t you?” I answered, “No, I have just submitted the application form for a Physics graduate course.” The professor looked upset hearing this totally unexpected answer. Probably, I had been saying until recently that I was planning to go on to the Mathematics graduate course.
In the graduate course of the Physics Department, there were about ten beginning students who intended to major in theory, of which about six wanted to study particle physics. But this over-concentration on particle physics was merely due to their ignorance of the various interesting fields in science which they might tackle. After one year of study in the graduate course they spontaneously scattered, finding the scientific fields which fit their personalities best, like astrophysics and nuclear physics.
The students majoring in theory were not assigned to any specific laboratory for their first year, but worked in turn for three month periods in a number of laboratories: particle physics, condensed matter physics, and so on. Thanks to this system, I had the chance to study condensed matter physics. During this period, in addition to my studies, I began a voluntary circle to study a perceptron with a few friends, since I thought that research of the brain and human consciousness was important but not yet fully understood theoretically. We read papers in that field but, unfortunately, none of us had any knowledge about the anatomy of the cerebrum. None of the members was sufficiently enthusiastic to transfer to the medical department in order to study it, and so the circle died out in course of time. I noticed then that the number of research papers about the perceptron was decreasing significantly. I understood the reason later. Nuclear submarines had become increasingly important strategically because of the Cold War. The perceptron became a subject of military research because of the possibility that it could be used to identify nuclear submarines by sound spectrograms.
In the Physics Department of Nagoya University, the first year students majoring in theoretical physics in the masters course had to attend the seminar on field theory as a compulsory subject for a year. In those days, all the particle physicists throughout the world believed for a variety of reasons that field theory would be replaced sooner or later by a future new theory. This was also the case in Sakata’s laboratory. The curriculum of the field theory course was designed in the 1950s. It began with Dirac’s quantization of fields using the variables of amplitude and phase. The course then continued to Heisenberg–Pauli‘s field theory and Fock space, and through Feynman‘s ingenious theory describing electromagnetic interaction as an action at a distance eliminating the photon picture, ending with Dyson’s renormalisation theory supplemented with Salam‘s paper on b-divergence. This course made me pay attention to field theory, which no one took any notice of in the 1960s. Thanks to this, I got interested in theoretical problems related to weak interactions. When the importance of field theory was later appreciated, the situation had turned full circle and the curriculum of theoretical physics at the graduate school of Nagoya University was again at the forefront of world physics.
I entered the laboratory of Professor Sakata in 1964 and began my research in particle physics. However, my capriciousness did not change after this and I continued to collaborate with physicists in other fields like nuclear physics, condensed matter physics and so on.
Finally I would like to thank Professors Taichiro Kugo and Christopher Sachrajda who kindly translated my Japanese draft into this English form.
This autobiography/biography was written at the time of the award and later published in the book series Les Prix Nobel/ Nobel Lectures/The Nobel Prizes. The information is sometimes updated with an addendum submitted by the Laureate.
Toshihide Maskawa died on 23 July 2021.