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Mathematical physics has the
power to describe the universe.

Daisuke Takahashi
Professor
Q. One of the research projects of Dr. Takahasi is the new mathematics that connects analog and digital. For example, I suppose that the old LP records that picked up sounds with a needle and the CD that we now have are creating a completely different world.

Analog and digital are not the presumption. With the LP record and CD, for example, music is the target of both devices. Music is the presumption, and there are analog and digital devices as methods to mathematically express the music. Let us suppose that we apply analog to science. I am talking about the world in which the differentiation and integration discovered by Newton and other scientists in the field of physics and chemistry are used to create formulas to obtain a solution. For example, continuous phenomena like a smooth wave traveling across the surface of water can be expressed with a differential equation using fluid dynamics. Digital equations can also express phenomena like waves on the surface of water. Yet, we lack tools to analyze it. I believe that the digital world also has such mathematics. I am therefore studying it by naming it digital calculus.

A new mathematics that is both analog and digital

Analog processes can be automatically transferred to digital processes if certain mathematically correct procedures are implemented. I came to reach such a conclusion. This simply means that the method of expression is different for the same target. Also, there are mathematics and targets that are both analog and digital. This is what I am trying to create.

Q. What happens when such mathematics is created?

Analog mathematics is advancing like physics, and there are many noteworthy achievements. If we can translate analog mathematics into digital mathematics, we can transfer the entire and enormous achievements of analog mathematics to digital mathematics. For example, traffic jams look like continuous changes in waves when seen from a distance. If an analog equation of fluid can be replaced by a digital equation, mathematics can be applied to the world in which scattering objects like cars are the main actor. Then we can forecast what happens next for individual and separate cars like waves passing each other.

Q By the way, what does applied mathematics mean to you?

I am originally from a field related to physics in an engineering department. My graduate thesis was to take out rod‐like macromolecules from E. coli and create crystals. Surprisingly beautiful crystals can be created when a piece of bread was placed in a large flask to culture E. coli, and then it was centrifuged. Phase transition is a phenomenon in which separate crystals become perfectly aligned when the crystals reach a certain concentration. I studied crystals using this mechanism. Phase transitions like this are expressed only using a mathematical formula based on the laws of physics and chemistry. I can then forecast at which concentration the phase transition will occur. I then realized the necessity of studying mathematics as well. I then transferred to a laboratory called Dynamics Class studying fluid and studied logical mathematical physics. I studied computer simulations in this laboratory. I was translating the principle of the numerical calculations of fluids into computer programs. Writing programs helped me better understand the original differential equation of fluids. This was about the time when I became more interested in science like I was awakened. Physics, mathematics, and computers started to spin around in my mind. I realized that mathematical physics had the power to describe the universe.

It is important to become passionate about something while young.

Q. Give a message to students who are applying for this department and high school students who will become leaders of the next generation

The Department of Mathematics is for you if you want to pursue the logical world, and applied mathematics is for you if you want to apply the knowledge to something. Mathematics is the process of exploring the universe using logic. We can also say that it is the process of creating the universe. Fortunately, the School of Fundamental Science and Engineering offers one entrance exam, and students can explore a variety of fields in the school during the first year. I encourage students to examine different fields well before selecting their specialties. I think it is important for young people to become passionate about something, which can be study or sports or anything. I always tell students in my laboratory, “You must find one specialty. With the specialty, you will lead others by showing them your passion towards it.”