A: I am insane.
B: I am pure.
C: I am applied.
D: I am sane.
A: C is pure.
B: D is insane.
C: B is applied.
D: C is sane.
You are also given that:
Pure mathematicians tell the truth about their beliefs.
Applied mathematicians lie about their beliefs.
Sane mathematicians beliefs are correct.
Insane mathematicians beliefs are incorrect.
Describe the four mathematicians.