NTT has established the Institute for Fundamental Mathematics
Advancing the pace of exploration into the unexplored principles of quantum computing

1. Background

With the aim of building a new technological infrastructure that bridges the gap between information and humans, NTT is actively working in various fields, including media processing, knowledge processing, human science and brain science. As a fountain of knowledge to support this work, we are also studying basic information theory, quantum information theory, and quantum cryptography. In order to make our Innovative Optical and Wireless Network (IOWN) concept a practical reality, we will need to solve social issues of increasing complexity and diversity that are now coming to light, such as the processing limits of smart society, the limitations of digital technology, and the limits of human capabilities. The solution to these issues will require a fundamentally different long-term approach, rather than a mere combination of the current state-of-the-art technologies or short-sighted improvements.
　Throughout the ages, mathematics has been a discipline with universal value. It has provided us with mathematical structures that appear in different fields and in completely unexpected contexts, and has demonstrated "unreasonable effectiveness" in the natural sciences ^(*1). The deep exploration and broad application of mathematical theory - which continues to make significant progress even today - may lead to the proposal of new approaches that are fundamentally different from those of the past. Therefore, in order to further strengthen the source of this fountain of knowledge in NTT's research and development, we have established the Institute for Fundamental Mathematics as an organization for researching the fundamental theories of modern mathematics.

2. Outline of the new research center

3. Mission of the Institute for Fundamental Mathematics

The Institute for Fundamental Mathematics will explore diverse and wide-ranging issues in modern mathematics and promote the search for mathematical truth through the development of the necessary language and concepts. Furthermore, by discovering new mathematical problems and cultivating new ground in mathematical nature, we aim to contribute to the solution of problems such as those mentioned below.
　By promoting the construction of a new theoretical foundation to tackle important unsolved challenges in modern mathematics, such as the Riemann hypothesis ^(*3) and Langlands conjectures ^(*4), we will accelerate research geared towards innovations in quantum technology that surpass the capabilities of digital technology, including clarifying the origins of the superior power of quantum computing, which are not yet clearly understood, and devising new cryptosystems that are guaranteed to be unbreakable even by quantum computers.
　Also, regarding the interactions and unexplained behavior of diverse phenomena in life science, neuroscience, social science and the like, we expect to create opportunities for collaboration with researchers in all areas of research while making advances in modern mathematics such as topology/geometry, number theory, group theory/representation theory, functional analysis, differential equations/dynamical systems, probability theory, category theory, graph theory, and game theory. Through the exploration of mathematical formulations and the utilization of modern mathematical methods in each research field, we hope to contribute to endeavors such as the elucidation of unknown diseases and the discovery of new drugs, the prediction of disasters through the fusion of ultra-large-scale simulations and evolutionary AI, and the construction of avatars and robots that can play a substantial role in disaster recovery efforts. We expect to shed light on human behavior mechanisms and the dynamics of the human brain, which is the ultimate multi-body system, and on the mechanisms that give rise to memories, thoughts, and consciousness. We also hope to contribute to the development of theories for the realization of new brain-like computers.
　In the future, we will contribute widely to academia by inviting first-class researchers in basic mathematics from around the world. At the same time, we will train young researchers to approach and solve various issues by applying the latest modern mathematical methods in partnership with other research organizations in various fields.

^(*1)From the title of an article by Eugene Wigner (1902-1995). Wigner was an American physicist, who was born in Hungary and moved to the United States in 1930. In 1963, he was awarded the Nobel Prize in Physics for his work on the structure of atomic nuclei and subatomic particles.

^(*2)Profile of Masato Wakayama: Graduated from Tokyo University of Science in 1978 and completed a doctoral course at Hiroshima University's Graduate School of Science in 1985 (Doctor of Science). Before becoming a Research Principal of NTT Fundamental Mathematics on October 1, 2021, he had held many other academic positions: an associate professor at Tottori University and Kyushu University, a visiting researcher at the Department of Mathematics, Princeton University, Professor, Distinguished Professor in Mathematics, Dean of the Graduate School of Mathematics, Kyushu University, the first Director of the Institute of Mathematics for Industry, Executive Vice President of Kyushu University, and Vice President and Professor of Tokyo University of Science. He is also a Principal Fellow of CRDS (Center for Research and Development Strategy, Japan Science and Technology Agency), and a Professor Emeritus of Kyushu University. He specializes in representation theory and number theory. Recently, he has been pursuing to clarify the mathematical structure of quantum interactions such as asymmetric quantum Rabi models in relation to the problems of the Riemann hypothesis and arithmetic geometry.

^(*3)Riemann hypothesis: A conjecture that the nontrivial zeros of the Riemann zeta function (the points on the complex plane where the value of this function is zero) are confined to complex numbers whose real part is 1/2. The hypothesis was put forward in 1859 by the German mathematician Bernhard Riemann (1826-1866), after whom it is named. It is known to be equivalent to the "ultimate prime number theorem" (i.e., the ultimate enumeration of prime numbers) in the sense that the distribution of prime numbers cannot be expected to be any greater than this. The Riemann hypothesis is reckoned to be one of the most important unsolved problems in number theory.

^(*4)Langlands conjectures: Also known as the Langlands program, this is a very broad collection of conjectures (1967, 1970) proposed by the Canadian mathematician Robert Langlands (1936-) that have only been partially resolved. It is said that solving all of them will lead to a grand unified theory of mathematics, and mathematicians around the world are studying them deeply from various perspectives. These sustained efforts of many mathematicians have greatly facilitated the progress of mathematics so far.