In the midst of all the uncertainty surrounding practicing mathematics in an age of AI, I thought it would be good for state some goals and things to keep in mind while teaching mathematics.

Is my goal to have people do as well on math competitions as possible?
No. That should be a side product though. If you learn mathematics well, (mathematics for math competitions), doing well in math competitions should be a side product. This takes a lot of time though.

Is my goal to have as many of my students major in math as possible?
No, I don’t think doing math competitions means you should major in math in college. And you can study math without studying math competitions. I am perfectly happy to talk about non-competition math (School math, other math)

In school, you aren’t really enabled to become a mathematician. I hope that in teaching classes, I enable my students to achieve their math and science goals from the theoretical side.

Part of why I teach to fill the holes created by school math. In school, we are taught the proofs of everything. I think it’s good to be rigorous and prove everything you know. This isn’t a necessary skill per se in real life, but having this experience has some benefits.

Developing a probabilistic view of the world (on conditionals) is probably a good reason to learn mathematics. Math competitions don’t always force this view, but it can be helpful to have this view rather than a fixed view of the world. Ex: If it’s cloudy, then it’s likely to rain.

Why do you learn mathematics?