NTT Institute for Fundamental Mathematics was established as a research center for mathematics with the objective of becoming one of the best research institutions of the world. Mathematical research serves as a "fountain of knowledge" for human beings, supporting the scientific technologies in our modern society. A mathematical theorem, once proven, continues to be true and supports our activities forever. The famous theorem by Pythagoras was discovered thousands of years ago, but it remains one of the most important results in mathematical sciences. The research in fundamental mathematics is thus essential for the sustainable development of our society in the future.

Concepts and languages created for mathematics can drastically transform the entirety of science. For example, Évariste Galois introduced the notion of "group", which is a mathematical formulation of symmetry, for the study of solutions of algebraic equations. Now, the theory of groups is an indispensable concept in modern mathematical sciences. It is an astounding fact that symmetry appearing in so many different forms in the various natural sciences can be represented by a single concept of "group". This shows that an abstract idea in mathematics can have an irreversible impact on the entire scientific research and the power to "connect" seemingly different research fields by uncovering common structures hidden among the various sciences.

The influence of mathematical findings may be unpredictable even to the person who discovers it. Indeed, Galois discovered the concept of group through the profound insight that there is a deep relationship between substitution of solutions of algebraic equations and the existence of formulae for roots. Galois might not have imagined that his discovery would go far beyond pure algebra and become an essential element in natural sciences. There are many other examples of this kind. Number theory, which investigates the properties of integers and rational numbers, was once considered as "the most useless mathematics" due to the lack of known practical applications despite the beauty of its results. However, it is now used widely in the field of information security. Topology, which arose as an abstract study of space, has opened up entirely new fields of application, including the topological insulator and topological data analysis. Furthermore, number theory and topology merged into algebraic and arithmetic geometry, leading to spectacular mathematical achievements such as the solution of Fermat's conjecture. In recent years, they are applied in diverse fields including post-quantum cryptography, cosmology, particle physics and string theory. Moreover, mathematical logic, quantum information, and operator algebras are being used to create new research subjects via the theory of computation and computational complexity, accompanied by the rapid improvement of the performance of computers.

It is a remarkable fact that truly innovative mathematics that lead to completely new applications are often created out of the pure curiosity of mathematicians. This shows that unpredictable value is hidden precisely in explorations based on intellectual curiosity. Curiosity is an invisible, but great ability of mankind to make new discoveries and to develop new technologies. We, NTT Institute for Fundamental Mathematics, will lead the exploration of the frontiers of human knowledge as a world-class research center for mathematics that finds routes between different fields and uncovers unknown truths, with intellectual curiosity as our compass and sail.

- In the above logo on the left, the zeta function is hidden. The zeta function and its variants appear in many areas of mathematical sciences, and connect different research fields. This logo represents the power of fundamental mathematics to merge different fields into new one.

- Another logo on the right represents our spirit and will to reveal mathematical truths following our intellectual curiosity in pursuit of the unknown.

We promote advanced research in mathematics in each member's area of expertise, and create new research fields beyond the existing framework by combining them. The NTT-IFM will serve as a research institute where many researchers with various backgrounds work together, by inviting leading researchers and organizing colloquia, seminars and lecture series.

Head of NTT-IFM

Fundamental Mathematics Research Principal

Masato Wakayama

**Seiseki Akibue**

**Reimi Irokawa**

**Kaoru Sano**

**Seiichiro Tani**

**Ryosuke Nakahama**

**Shuji Horinaga**

**Hiroyasu Miyazaki**

**Cid Reyes Bustos**

**Cornelie Mitcha**