Logic is actually a branch of mathematics just like trigonometry or calculus is. Logic is needed extensively in other branches of math. It's all over the place like pepperoni on pizza. That would be like someone saying they know the pizza industry but have never heard of a pepperoni pizza.

I should relate a famous story in math since you discussed your proficiency in math. First, though, congrats on learning it so efficiently. That is impressive. But, math is a never ending ladder into the sky. The higher you go, the more incredible it gets. And, everyone has their level at which they must really clamp down and study hard and some other level they cannot get passed.

In the ancient world of Euclid, they had what was called the Bridge of Asses problem. This was a particularly revealing problem. If a student could get the Bridge of Asses, then they would go on to do well in geometry. If they couldn't, Euclid was telling them to to move on to some other work and leave geometry behind.

So, it is good you didn't find your bridge of asses problem in your studies with your daughter.

My mom did run into her bridge of asses problem, but it was in college algebra. Specifically, it was Gauss-Jordan elimination. She couldn't get her degree (a Ph.D. in law) if she didn't pass college algebra. She was on her third time taking the class, and she was having an exam that was going to include this math concept. So, she asked me to help her. We lived in different states, so it was an incredibly long phone call. Man, that was rough.

Anyway, she took the test and got like a 40 on it. But, she scored enough to get a D in course. Previously, she was getting below 20 getting her an F in the course. A D was good enough to get her her degree. My mom never did practice law, but I helped her become a doctor (of law).

Peace.