There are a wide range of employment channels for Ph.D. in Mathematics, and the following are some of the major employment fields and positions:

1. Academia: Ph.D. in Mathematics can work as a professor, researcher, lecturer, etc. in a university or a research institution for teaching and research. In addition, they can apply for various research projects, such as the National Natural Science Foundation of China and the National Key Research and Development Program.

2. Financial industry: many financial institutions, such as banks, securities firms, insurance companies, etc., need mathematics majors to carry out risk management, investment analysis, quantitative trading and other work. A PhD in Mathematics can work as a data analyst, quantitative analyst, risk manager and other positions in these institutions.

3. Technology companies: many technology giants, such as Google, Microsoft, Alibaba, Tencent, etc., have a large number of math-related positions, such as algorithm engineers, data scientists, artificial intelligence researchers, etc.. A PhD in mathematics can work in software development, big data analysis, artificial intelligence research, etc. in these companies.

4. Government Departments: departments such as government statistics bureaus and national statistics offices need math majors to work on data analysis, policy making, and so on. A PhD in Mathematics can be used as a statistical analyst, policy researcher and other positions in these departments.

5. Manufacturing: Many manufacturing companies need mathematics majors for production optimization, quality control and other tasks. A PhD in Mathematics can be used in these companies as a production engineer, quality engineer and other positions.

6. Consulting industry: management consulting, strategy consulting and other industries need professionals with data analysis skills. A PhD in Mathematics can be used as a consultant, project manager and other positions in these companies.

7. Education industry: Ph.D. in Mathematics can also work as teachers, lecturers and other positions in colleges and universities, training institutes and other places for teaching and training.

8. Other industries: a PhD in Mathematics can also work as a researcher and developer in the fields of aerospace, physics and biology.