What are the main research problems in mathematics at present?

The research field of modern mathematics is very extensive, covering many different directions and problems. The following are some frontier fields and problems that are currently being studied in the field of mathematics:

1. Quantum Computing and Quantum Information: This is a very hot field in the field of mathematics at present, involving quantum algorithms, quantum error-correcting codes, quantum communication and other issues.

2. Topology: Topology is a branch of mathematics that studies the nature of space, involving many abstract concepts and skills. For example, given a closed n-dimensional manifold m, how to find its dimension and so on.

3. Geometric analysis: Geometric analysis is an interdisciplinary subject of differential geometry and real analysis, involving curve and surface theory, partial differential equations, boundary value problems and so on.

4. Dynamic system: Dynamic system theory studies systems that evolve with time, such as Naville-Stokes equation problem, variational theory and geometric analysis.

5. Stochastic systems and financial mathematics: This involves stochastic processes, stochastic calculus, stochastic matrices, and how to apply these tools to practical problems such as financial markets.

6. High-performance calculation method of mathematical physics: This is an interdisciplinary field, which involves how to use computer technology to solve complex mathematical physics problems.

7. Seven Millennium Problems: This is a series of unsolved mathematical problems, involving number theory, algebra, geometry and other fields. For example, researchers at the University of California, San Diego, have found the answer to the r (4, t) problem that has puzzled the mathematics community for decades.