I teach English and coach rowing. Mike has a PhD in Physics; he's a scientist; he works with rockets; the boom-your-city's-rubble kind; he's a rocket scientist.
We have been gaming for 7 years now and I know his attack bonuses, situational modifiers, feats, weapons, and damage dice better than he does. God help the party when he plays an archer: "Let's see, that's an 11, plus 5, plus 1, minus 3, mumblemumble, 28! Do I hit? Great, I roll damage! 3d8... no sorry, 2d8, each one +3, add that, that also-* no, too far away ... carry the 1 ... 57! Can I cleave?"
Somehow D&D math just doesn't stick to his brain. He doesn't know which dice to roll, which modifiers to use... he's a mess.
And an awesome guy to have at the table.
But for some reason, the math doesn't stick. I'd say your lady has the same issue. Hey man, not everyone gets it. Ask her what she wants to do about it; Mike is happy being made fun of and occasionally corrected, but I suspect she could have some input on how you act towards her.