"Can I use math to impress women ?"
As other answers already noted this will strongly depend on the individual woman. But yes, I think that there could be cases in which math may be of use to you to impress women. This will generally require the person to be intellectual (i.e. sensitive to intellectual topics and to mastery of these, do not mistake this term for "intelligent"), although
I have zero experience on using mathematics to date (without playing on syntactic functions, this time: yes, I mean "in order to date", not "until now" ;) ) but my educated guess would be that:
• The more mathematically knowledgable the woman is, the more likely she will be able to distinguish studying and/or accumulating knowledge one side, from discovering or exhibiting non-trivial ideas on another side.
• The more mathematically talented the woman is, the less likely she will be "impressed" by you merely studying and/or accumulating knowledge about the field and the more likely she will be "impressed" by you discovering or exhibiting non-trivial ideas, assuming she is able to discriminate both well from one another.
• The more sensitive the person is to mathematics, the more she will be "impressed".
Hence, I hope that you will be satisfied with the following formula to approximate the efficiency of "impressing" women with mathematics:
I=S(1+KT)Discovery+S(max(0,1-KT))Studying.
If you really are motivated you can begin by putting this in matrix form.
So now, you know about using math to impress women.
With that out of the way, let's get to the real dish, i.e. the non-identity permutations of the symmetry group.
What about:
(2,3): "Can I use women to impress math ?"
(1,2,3): "Can women use me to impress math ?"
(1,2)(1,3):"Can women use math to impress me ?"
(1,2): "Can math use me to impress women ?"
(1,3,2): "Can math use women to impress me ?"
That's right. You just frowned a bit because you were reminded of "When you look into the abyss, the abyss also looks into you." You felt increasingly tricked by sheer Machiavellianism as the possibilities went on and on, and quickly returned to the sentences to check that they weren't applicable to the situation. You just shivered as you noticed that all were.
Sweet dreams !