Abstract: Math is able to train logical, analytical, systematic, critical, and creative thinking of students. Mathematical critical thinking ability is a capability that supports a variety of other mathematical thinking abilities. The students' critical thinking ability is also closely related to the personality or character of the student. Personality can affect how a person behaves, thinks, or interacts with around. The personality types discussed in this study are examined from four types of temperaments by the theories of Hippocrates and Galenus. This research includes the type of qualitative research that uses descriptive qualitative research methodology. This research will be conducted on the students of class XI MIA SMA Negeri 2 Kota Jambi. The thing described in this research is the students' mathematical critical thinking based on the dominant personality type on linear program solution. The results of personality tests of the instrument adapted from the patterns of personality by Lana Bateman found 40 dominant students that is the type of phlegmatic personality. Furthermore, based on sampling technique that is purposive sampling technique, 2 students are taken as research subjects ie phlegmatic students with the highest level of critical thinking ability called first phlegmatic students and phlegmatic students with the lowest level of critical thinking ability is called second phlegmatic student. From the results obtained can be concluded that the first phlegmatic students have the level of critical thinking skills are very critical and the second phlegmatic students have a critical level of critical thinking is not critical. This is inversely between the ability to think critically and the type of phlegmatic personality. The first phlegmatic student with enough phlegmatic category has critical critical mathematical thinking and the second phlegmatic student with very high / dominant phlegmatic category, critical critical thinking ability is not critical.Keywords: Mathematical Critical Thinking Ability, Four Temperament Types