## Opinion

### Culture and Education

#### Although There Are No Nobel Prizes for Mathematics or Computer Science.

Etsuro Moriya

Professor, Faculty of Education and Integrated Arts and Sciences, Waseda University

##### 1. Mathematics and the Mass Media Effect

In mid-September, an article about mathematics caused a stir in newspapers all across Japan. It stated that Professor Shinichi Mochizuki of Kyoto University may have been the first to solve a difficult mathematical problem known as the "ABC Conjecture." This challenge was proposed in 1985 by European mathematicians, and concerns the prime factors of three relatively prime positive integers A, B, and C, for which A + B = C, and A<B. It is believed that from this conjecture, many existing known theorems can be derived and other, as-yet unsolved conjectures can be settled. For example, it is said that "Fermat's Conjecture (Fermat's Last Theorem)," one of the most difficult problems in number theory (theories concerning integers), which remained unsolved for approximately 360 years until 1995, can be proven in one stroke by using the ABC Conjecture. I personally am not a number theory specialist, and because understanding the ABC Conjecture requires knowledge of algebra (number theory) equivalent to the second year in a university mathematics department, I am unable to explain it to the general public properly and in simple terms, but anyone with an interest in it may refer to the various descriptions that can be found on the Internet.

Professor Mochizuki's theses webpage

Such cases of mathematics-related articles appearing in newspapers are quite rare, and limited only to those instances like this one where unresolved enigmas have finally been(or appear to be) solved. Furthermore, even if the public reads these articles, the great majority of people with no interest in mathematics, or more specifically the large percentage who believe themselves to be weak in mathematical skills, would probably find themselves completely at a loss to understand them. Many articles discussing Nobel Prizes (such as the October 8th commentary on Professor Shinya Yamanaka of Kyoto University winning the Nobel Prize for Physiology or Medicine, for his work on iPS cells) are quite detailed and understandable to a certain extent even if read by non-professionals - but for mathematics, this is not so in nearly all instances. For example, even if mathematicians were to read the newspaper article about Professor Mochizuki's work, they would not be able to gain a clear, proper understanding of what the ABC Conjecture actually is.

However, I believe that there is nothing wrong with this. Even if people do not fully understand these topics, or if precisely because they do not understand them (?), they focus their interest toward Professor Mochizuki's background rather than the mathematical content itself, there is the possibility that just the appearance in newspapers of an article stating that a young Japanese mathematician has (apparently) solved a famously-difficult problem might spur many people, particularly young people, to acquire an interest in mathematics - and if as a result, a second- or third-generation Professor Mochizuki might appear from among those young people, then that would be a source of great joy for mathematicians and mathematics teachers alike. Recently, math problems have often even been featured on television variety programs and quiz shows, and I welcome them as well in the same respect.

##### 2. Education to Cultivate Mathematics Lovers

Of course, education and developing awareness are not matters to be left in the hands of the mass media alone. Educating young people in such a way as to attract their interest is one of the important duties placed upon teachers. I belong to the Waseda University School of Education, which uses a system known as "self-recommendation entrance examinations." This is an entrance examination system where one must make an appeal by describing one's own prominent achievements, but during such interviews, if mathematics candidates are asked to explain the reason for their fondness of mathematics, many will reply "Because my homeroom teachers in junior and senior high school taught me how interesting math is." This answer reveals that the love of mathematics is fostered when students meet teachers who conduct classes not merely focusing on "remembering" formulas and theorems and "learning how" to solve routine problems, but who instead teach the joy of "discovering" the grand truths of mathematics (i.e. theorems) hidden everywhere, no matter how simple they may be, beginning with concrete objects immediately within view and extending to abstract concepts that can only be imagined, and provide valuable support in developing a "sense of appreciation" for these beautiful truths. To give a more easily-understandable example, anyone would feel excited if they could discover a dinosaur fossil, but without acquiring a sense of appreciation for knowing what exactly dinosaur fossils are, and what value they have, this discovery itself would be impossible. There may be many other methods to do this, but in any case, conducting education that can guide students to further know the joy of mathematics is a responsibility given to mathematics instructors like myself.

##### 3. The "Nobel Prizes" for Mathematics and Computer Science

On the other hand, it is a fact that there are some mathematical truths that only geniuses are capable of discovering. Have you ever heard of the Fields prize or the Turing Award? Though it is widely known that there is no actual Nobel Prize for mathematics, the Fields prize is often described as the Nobel Prize of the mathematics world. It was created in 1936 according to a proposal by Canadian mathematician J. C. Fields (John Charles Fields), and is presented at the International Congress of Mathematicians held once every four years, to a young mathematician not more than 40 years of age who has made striking accomplishments. To date, three Japanese mathematicians have received this honor. Similarly, although there is no Nobel Prize for computer science, its equivalent in this field is the Turing Award. Established in 1966, this award is granted once a year to an individual who has carried out innovative achievements in the computer science field. Its title references the British mathematician A. M. Turing (Alan Mathison Turing), also known as one of the fathers of computer science. This year marked the 100th anniversary of Turing's birth, with lectures and events relating to him held at various international conferences in computer science fields. Google even attracted widespread attention by changing its logo on his birthdate of June 23rd, to represent a "Turing machine." (On special dates, Google changes its worldwide logo to one that reflects the occasion.) A Turing machine is a mathematical device introduced by Turing, to mathematically define the concept of "algorithms" which describe computational procedures.

Turing, undoubtedly, was a genius. Japan, too, is of course home to many other geniuses such as Professor Mochizuki, but sadly, no Japanese mathematician or computer scientist has yet received the Turing Award. To all young people reading this: won't you strive to be the first Japanese Turing Award recipient, or Japan's fourth recipient of the Fields prize? (Having lofty goals is important!) To all teachers: please discover and develop the talent hidden in those around you. I will be looking forward to the day when the name of a Japanese mathematician or computer scientist emblazons the front page of my daily newspaper!

#### Etsuro Moriya

Professor, Faculty of Education and Integrated Arts and Sciences, Waseda University (Department of Mathematics, School of Education), Director of The Mathematical Olympiad Foundation of Japan, Former President of the Japanese Committee for the International Olympiad in Informatics.

[Career Summary]

1970: graduated from Department of Mathematics, Faculty of Science and Engineering, Waseda University. Became research associate at The University of Electro-Communications; and assistant professor, associate professor, and professor at Tokyo Woman's Christian University. From 1995: professor on the School of Education at Waseda University.

[Areas of Specialization]

Applied mathematics, theoretical computer science. Primarily conducting research on the topics of complexity theory, formal language and automaton theory, algorithm theory, etc.