My favorite phrase: Mathematics is the burning up of life

Q: Why did you choose this phrase?

When the mathematician Kiyoshi Oka was awarded the Order of Culture, Emperor Showa asked him: "How would you describe the study of mathematics?"

Oka's response was: Mathematics is the burning up of life.

Everything about it is cool: what he said, as well as the way and situation in which he said it. I wish that I could leave behind a saying like that. That’s the reason why I chose it as my favorite phrase.

What makes mathematics so wonderful is that it is our lives that make the flame glow.

Q: What kind of research are you doing?

The three main themes of my life are infinity, space, and complexity, and broadly speaking, my research is concerned with the complexity of infinite dimensional space.

Specifically, my current goal is to establish PL Seiberg-Witten theory. As a first step, I am studying the discretization of Dirac operators by drawing on ideas from lattice gauge theory. This must sound like a bunch of arcane words.

Simply put, I use tools like differentiation and integration as tools to investigate absurdly twisted figures. However, mathematics has a “reality that is ruined when it is simplified” (cited from Masaya Chiba’s book, Gendai Shiso Nyumon) and I want to respect that reality.

In my early 30s, I spent a lot of time trying to figure out whether infinity minus infinity divided by infinity equals infinity. 

Q: How did you get into this research?

I can pinpoint the exact date and time when I knew I wanted to do research in mathematics: midnight on January 1, 1998.

It was the New Year and my third year of junior high school was almost over.

On New Year's Eve, my friend and I were waiting in a long line on the first floor of the Landmark Tower in Minato Mirai, Yokohama, to watch the year’s first sunrise from the top of the tower. At first, we were excited to be out in the middle of the night and talked about many things, but gradually we ran out of things to talk about, so I sat on the floor and read a book. 

The book was an introduction to modern mathematics that I randomly picked out in the library. In that book, I came across Cantor's diagonal argument, a proof that demonstrates that infinity has an infinite hierarchy. It was a groundbreaking discovery that showed mathematics could encompass the infinite. 

I remember being so excited by Cantor's argument that I rattled on about it to my friend without pausing for breath. I felt something profound—something beyond the brilliance of what Cantor had demonstrated.

Then, the New Year arrived and all the ships in the Port of Yokohama blew their whistles. That's the moment when I decided to do research in mathematics.

Q: When do you find that research is interesting or rewarding?

I think a common answer to this question is something like "the moment when I discover something for the first time that no one else knows," but I do not feel that way at all.

For me, research has always been hard and I have never found it enjoyable or fun.

However, lest there be any misunderstanding, I would like to emphasize that finding something hard is not the same as disliking it.

I have never felt that I don't like research. I do research simply because there is something I really want to know. It doesn't matter if it is a completely new area of research or if it is a field that somebody else has already explored.

In the past, I was able to find answers to my questions just by studying.

But now no one knows the answers to my questions, and so my research is a way of finding those answers.

Would you ever ask a practicing monk, "When do you find penance enjoyable?"

When we wander alone like a rhinoceros, we can glimpse the edge of human intelligence. It is a grueling journey, yet it glows with the burning of life.

Q: Do you have any advice on how to study for people who feel they aren’t good at math and don't know how to improve?

The first thing I would like to say is that mathematics is outrageously difficult.

I've been studying it for a long time, but there are still a lot of things I don't understand when I read papers and textbooks.

So, one piece of advice is: "Don't lose heart, let's keep working!"

Having said that, the difficulty of math is something that is cruel and seems to push people away.

So sometimes you may not even know what you are striving for. In such cases, I would suggest transcribing both the problems and solutions described in a standard math workbook over and over again and taking your time to analyze them, keeping in mind the following: 

- Are there any terms you don't understand?

- Where is the condition given in the problem used in the solution?

- Have you seen any similar problems before?

- What are the similarities and differences between the answers to those similar problems and to the current problem? 

It is important to fully analyze both the problems and the solutions. It takes quite a lot of time, but there is no royal road to learning.

Q: Do you have any stories that you can only share with us now?

A few days before the deadline of my master's thesis, I was hospitalized with swollen tonsils. Thankfully, my academic advisor took care of the submission of my thesis and all the paperwork, including the procedure for the JSPS’s Research Fellowship for Young Scientists.

My ray of hope was that I had completed my thesis and had sent it to my academic advisor. 

I remember desperately communicating with him on a flip phone while I was in a daze with a high fever.

I owe him a lot of gratitude, and this memory is where I feel most indebted to him.

Not knowing what might come your way is just part of submitting a master's thesis. 

Q: How do you spend your days off? What do you do to recharge yourself?

Actually, what I want to do most in life is research in mathematics, and fortunately I get to do that as my job. So I don't really feel the need to distinguish my weekdays from my days off.  

That said, it's not realistic to do research 24 hours a day, 365 days a year. 

In my case, sometime in the evening, I suddenly lose concentration. Suddenly I can't think of anything, as if I've used up all my energy for the day. When this happens, I drink beer and sake or wine, eat something delicious, and watch a comedy show to charge up my energy for the next day.

Q: What are your goals and ambitions for the future?

I will continue to study and research, so that at the end of my life I can be at my wisest.

Dr. Matsuo’s website:

https://www.math.nagoya-u.ac.jp/~shinichiroh/index_en.html