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Mathematics has evolved while maintaining close links with classical physics. Modem mathematics, too, is fusing with quantum statistical mechanics to form mathematical physics, becoming an increasingly sophisticated and diverse field. At the same time, it has also become a basic analytical tool in all fields of scholarship. The mathematical theories of John Von Neumann made possible the development, evolution, and spread of the computer, which has become the symbol of modern civilization. The various theories that have supported the development of information science and information theory, including probability theory, statistics, cryptography, and chaos theory, are also applications of mathematics.

Knot theory, which is derived from geometry, is used not only in quantum statistical mechanics and other aspects of theoretical physics, but also in biochemistry to classify deoxyribonucleic acid (DNA) nodes. Other elements of mathematics, such as analysis, algebra, probability theory, and statistics, have made possible the development of the mathematical and metrical analytic tools used in economics and other social sciences. In recent years, progress has also been made in applications for game theory and linear planning. In addition, there has been reciprocal stimulation and fusion among different fields of mathematics, leading to the formation of fields like algebraic geometry, complex analysis, and differential geometry.

In the field of particle physics, researchers are moving toward an understanding of particles, which are the ultimate forms of matter, and the four forces (gravitational, electromagnetic, strong nuclear, and weak nuclear) that operate between them. Standard models have been proposed to explain three of the four forces (except gravity). In 1994 the top quark was discovered through an experiment involving proton-proton collisions at the Fermi National Accelerator Laboratory in the United States. The crucial task remaining for this model is the investigation of the Higgs boson, which will enable us to understand the origins of mass.

Researchers have proposed Grand Unified Theory (GUT) to account for the three forces other than gravity, and the supersymmetry GUT appears to have particular potential. Future research will need to focus on the verification of GUT's prediction that protons decay into positrons and other particles, and the discovery of supersymmetry particles, the existence of which the supersymmetry GUT hypothesizes.

Another focus of future research will be the breakdown of the basic symmetry of particles (violation of CP symmetry). It will also be necessary to explain neutrino oscillation in order to verify the mass of neutrinos, which is assumed to be zero in the standard model.

Researchers in Japan are also working to solve these riddles. Projects include the B-Factory Plan, which involves the use of an electron-positron collider maintained by the High Energy Accelerator Research Organization. Another focus of research is Super-Kamiokande, which is a large-scale water Cherenkov cosmic particle detection system established by the University of Tokyo's Institute for Cosmic Ray Research to monitor cosmic particles. Other projects involving the use of large-scale accelerators are currently in progress at facilities in the United States, such as the Stanford Linear Accelerator Center (SLAC), and in Europe, including the European Organization for Nuclear Research (CERN).

Nuclear physics takes a more macroscopic view of the atomic nucleus than particle physics. Future research themes will include the creation of high-density nuclear matter, especially a high-temperature quark-gluon plasma, by using heavy ion collisions to establish conditions similar to those that existed at the beginning of the universe.

Researchers in the field of space physics are working to explain the evolution and structure of the universe, starting with the Big Bang. Progress is now being made in step with advances in particle physics. High-energy experiments using accelerators have an important role to play in this context. The observation and study of cosmic rays are also extremely important. Goals for the future include solving the solar neutrino question (why the number of neutrinos detected is about one-half of the theoretical number emitted by the sun) and elucidating the nature of superhigh-energy gamma rays and dark matter.

Researchers are working to find answers to these questions, especially in relation to solar neutrinos, using equipment like Japan's Super-Kamiokande; Canada's Sudbury Neutrino Observatory (SNO), a heavy water Cherenkov detection device; and Italy's Borexino, a liquid scintillator detector.

Solid state physics explores the diverse characteristics and phenomena exhibited by matter created through the combination of atoms and seeks to explain the mechanisms involved. It is also the basis of materials science and bioscience.

Among the substances to attract interest in recent years are high-temperature superconductors (substances that lose all electrical resistance below a certain temperature) made from copper oxides, fullerines, and carbon nanotubes, which are stable molecular structures made up of carbon atoms arranged like soccer balls or cylinders and quasi-crystalline structures that remain stable in a thermal equilibrium state. Also significant are mesoscopic substances, artificial substances of a size midway between atoms and matter that are produced using semiconductor processing technology. Research into new substances is expected to lead to new discoveries In the future.

Key tasks in this field include theoretical research into closely related areas, such as electronic superconductivity and chemical reactions, as well as the explanation of quantum effects and the development of applications. Future work could lead to the emergence of nonequilibrium and complex physics-new forms of physics and science that transcend traditional frameworks and create new paradigms.