1. Basic knowledge of mathematics: Mathematicians need to master the basic concepts, principles and theorems of mathematics, including algebra, geometry, calculus and probability theory. These basic knowledge are the basis for solving more complex problems.
2. Abstract thinking ability: Mathematicians need to have abstract thinking ability, be able to transform specific problems into abstract mathematical models and find solutions to problems.
3. Logical reasoning ability: Mathematicians need to have strict logical reasoning ability and be able to verify the correctness of mathematical conclusions through logical deduction and proof.
4. Ability to analyze problems: Mathematicians need to be able to analyze the complexity and difficulty of problems and find effective ways to solve them. This requires in-depth thinking and understanding of the problem.
5. Innovative thinking ability: Mathematicians need to have innovative thinking ability and be able to put forward new mathematical theories and methods to promote the development of mathematics.
6. Computer skills: Modern mathematics research can not be separated from the support of computers, and mathematicians need to master computer programming and data analysis techniques skillfully before they can use computers for mathematical modeling and calculation.
7. Teamwork: Mathematicians usually need to cooperate with other mathematicians to solve complex mathematical problems, so they need to have good teamwork and communication skills.
In short, mathematicians need to have extensive mathematical knowledge and skills, as well as the ability of abstract thinking, logical reasoning, problem analysis, innovative thinking, computer skills and teamwork. The comprehensive application of these knowledge and skills enables mathematicians to solve complex mathematical problems and promote the development of mathematics.