In terms of curriculum development, I think using AI to write routine solutions to basic linear algebra problems saves time on routine boring stuff. Using AI on Asymptote diagrams, I’m less sure about. Never writing asymptote code engenders laziness.

In terms of learning math, never let the AI do all the work for you. Only ask for hints, next steps in possible solutions etc.

AI is a better version of Google, though.

Not everyone who learns from me or learns math in general needs to do math competitions. In fact, it’s kind of weird how mathematics has been turned into competitions.

However, I’d encourage anyone who has never done a math competition to try participating in one.

Here are some benefits:

Helps you find a job later on. Some companies’ job interviews ask similar questions to those you might see on some math competitions.

Helps you transition to other sciences, mathematics, or something else.

You may meet people you would not have otherwise met through competitions.

Teaches you to think rigorously.

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?

Congrats to Soham for making the US computing training camp. Congrats to Kailash for making the Swiss computing training camp and the Swiss Math Olympiad training camp I.

Good job to Allan for making it to tiebreaker round at ARML 2025.

Good job to Mikayla for placing in the top 42 at ARML 2024. Good job to Nikhil for getting bronze at the first American Masters in Math. Good job to Alexei for competing in AMM.

Congrats to Alex and James for doing well at Mathcounts Nationals 2026

Congrats to Sounak for making USAMO. Congrats to Anthony for making USAMO. Congrats to Charles for getting first in Mathcounts state.

Congrats to former students Andrew and Allan for placing in the top 12 in the USAJMO!

Congrats to former student Sohan for making CT ARML!

Congrats to Nikhil for making Mathcounts Nationals for MA!