Because the topic only mentions that the female teacher can teach high school mathematics and is young and beautiful, and does not mention her personality, it is difficult to determine her personality characteristics.

However, generally speaking, female teachers who can teach high school mathematics well usually have the following personality characteristics:

1. Patience and meticulousness: Teaching students mathematical knowledge requires patience and meticulousness, which can simplify complex problems and help students understand.

2. Enthusiasm and passion: The love and pursuit of mathematics will infect students and stimulate their interest and motivation in learning.

3. Flexibility: We can flexibly use different teaching methods and strategies according to students' different needs and levels to achieve the best teaching effect.

4. Rational and calm: able to analyze and solve problems rationally, and will not affect teaching because of personal emotions.

5. Good at communication: able to communicate and cooperate effectively with students, parents and other colleagues to complete the educational task together.

Of course, these are just some common personality traits. Everyone's personality is unique, and this female teacher's personality may have other characteristics.