Rui Wang
Department of Mathematics, UC Berkeley
AI tools can be useful in learning mathematics, but they can also quietly weaken the very habits that mathematical learning is meant to build. The question is not simply whether to use AI, but how to use it in a way that supports your own thinking rather than replacing it.
In the past one or two years, as AI tools have become much more powerful, I have noticed a clear pattern in some courses: homework and take-home quiz scores often look stronger, while exam performance can become weaker. This does not mean that students have become less capable. Rather, it suggests that some students may be completing assignments with more outside assistance than before, without developing the same level of independent understanding.
I also understand why this is difficult. When AI is available, and when you believe that your peers may be using it to finish assignments more quickly or earn higher homework scores, it can feel unfair or inefficient not to use it yourself. The temptation is real.
But this is exactly why you need to be careful. If AI helps you produce polished homework solutions while quietly replacing the struggle through which understanding is formed, the cost may not appear immediately. It often appears later: on exams, in later courses, or when you need to solve a problem for which no ready-made explanation is available.
In proof-based mathematics, the goal is not only to get the correct final answer. The goal is to learn how to read definitions carefully, choose a useful strategy, identify hidden assumptions, write a complete argument, and judge whether a proof is actually correct.
These skills are built through the process of trying, getting stuck, revising, discussing, and trying again. If AI removes that process too early, you may still be able to recognize a correct-looking solution, but you may not be able to produce one independently.
This distinction matters. Recognizing a proof is not the same as writing a proof. Following an explanation is not the same as creating an argument. In upper-division mathematics, the real goal is to develop your own mathematical judgment.
I also often need to learn new mathematics myself. In that process, working through exercises is indispensable: it is one of the main ways to turn passive reading into real understanding. This is also how I try to use AI when I am learning something new.
A good way to approach homework is to begin before you look at the homework problems themselves: read the lecture notes, review your class notes, consult the textbook, and work through typical examples. Only after that should you start the assigned problems.
On your first attempt, you may be able to solve problems that are similar to examples from lecture or the text. That is good. Write these solutions yourself, without using AI. This is where you begin to build confidence and fluency.
For harder problems, you may not know how to begin immediately. That is also normal. Let the problem stay in your mind for a while. Think about it over a day or two, and try several possible approaches. If you still cannot solve it after serious effort, then it is a good time to discuss it with classmates or ask your instructor.
If you decide to ask AI for help, do not ask it to solve the problem for you. Instead, choose the approach you most want to pursue and ask whether it is a reasonable way to start, or what the next small step might be. AI may give you much more than you need. You should read only the parts that you already mostly understand, take a small hint, and then return to thinking on your own.
After you have written your own solution, AI can sometimes be useful for checking your reasoning. You might ask whether your argument has any gaps, or whether there are alternative approaches. Even then, you should verify every step yourself. The goal is not to replace your thinking, but to sharpen it.
The way you prompt AI matters. Try to make AI behave like a tutor, not like a solution writer.
Use AI after you have thought seriously, not before. Use it to clarify, test, and deepen your understanding, not to avoid the process by which understanding is formed.
Mathematics is learned by doing mathematics. In upper-division courses, this means reading carefully, writing carefully, making mistakes, repairing arguments, and gradually developing your own mathematical judgment. AI can support this process, but it cannot do it for you.