Young mathematicians



In my opinion, young professional mathematicians are often evaluated based on three things as follows.

  • How high potential they have,
  • How many and good works they have made,
  • How deeply they understand things in mathematics.

The problem is that these three things can be false things. If they want to, they can cheat on them all. For example, potentials can be false because their supervisor has a great power and they only say so. Works are, too, because there is no guarantee that they wrote their papers by themselves. Understanding of math cannot be checked unless they have a paper examination. There is too many mathematicians who don’t understand basics of math well.


In my understanding, in the Graduate School of Mathematical Sciences, the University of Tokyo (Todai-Suri, for short), master thesis and doctor thesis are not so different in quality. The difference between them is how to make them. Normally, students in Todai-Suri write their master thesis with suggestion or help by their supervisor. But they write their doctor thesis by their own, except some (or many?) people. Finishing writhing doctor thesis by their own, from finding what problem they should solve to making their work be accepted by a journal, will mean that they have become a scholar. That’s why they obtain their Ph.D. degree.

The most important thing in the doctor course in Todai-Suri is that students go there to become a scholar, say, improve their ability in math to the extent of being a scholar alone. When they get Ph.D., they will be able to work alone in the future. Of course, collaboration is also very good, but professional mathematics will often mean works by a mathematician alone.

About Yamashita-san

I read Yamashita-san’s master thesis and listened to her talk on video. Unfortunately, I don’t understand it completely (of course). Therefore I cannot evaluate how great her work is. But I can definitely say that her work is almost never affected by her supervisor Prof. Kawahigashi. His interests are operator algebra and mathematical physics. But her paper seems to be related to almost nothing of those. Perhaps it’s true that in Todai-Suri, Prof. Furuta is the best professor who can understand her master thesis.

That means that she wrote her master thesis almost all by her own. I guess that, she no longer needs her supervisor at the moment. So she should have got her Ph.D. degree by the reason above. But in Todai-Suri students spend at least one year at the doctor course to obtain it. That’s a rule. Thus Prof. Kawahigashi decided that make her to be an assistant professor in RIMS, before her getting Ph.D. degree, I guess.

Of course, this abnormal treatment cannot be done even by Prof. Kawahigashi’s power. I think that Prof. Furuta should be involved, and at least one professor at RIMS.


Let’s return to the first topic of this article. For her, what are lacked? The answer is her next works. She has to prove that her master thesis is not just a lucky thing. She has to make two or three works by her own by the time she is an assistant professor, for example, in 5 years. There ware almost the same persons who got their profession in RIMS at very young age; Prof. Shinichi Mochizuki and Prof. Kei Irie. They are succeeded in math very well. That’s well known.

I hope that she will make good works in math in the future in a quiet place in Kyoto. In addition, I want people to stop making noise about talented, cult of genius. It won’t be good for her. If you talk about her, you need at least read her paper and watch her video. People who don’t, yet say she is a talented genius of something like that, are nothing but embarrassing.

I want to add one thing. To make good works in math, youth is not a critical thing. Continuing making effort in math takes a lot of time. Spending much time in math won’t mean they are never good mathematicians. It’s very normal. Remember three things I argued first. Not to make a lie in these things is critical.