One thing I have noticed while teaching and just generally from observing people learn maths (or in fact anything) nowadays is how quickly they reach for AI tools to make difficulty disappear.
In the past, when a student gets stuck on a problem there were only so many ways out. They could stare at it for a while, try a few examples, draw a picture, go back through their notes, ask a friend, drag themselves begrudgingly to office hours, or my personal favourite method: to give up, do other things then fall asleep, and wake up with an epiphany that turns out to be completely wrong but inspires you enough to try again and that eventually leads to the right idea. Cause not all of us are lucky enough to have solutions revealed in dreams 😉 but no one will ever be able to take away my ability to say my proof is too large to fit in the margins of the page (more so because I typeset the TeX wrong). I digress. The point is that, often, one would take some strange, roundabout route that didn’t solve the problem at all, but in doing so it did reveal something about why they were stuck.
Today there’s another option: just copy paste the problem into a whichever model of your choosing and Bob’s your uncle of course this is obviously useful because you get an instant fix. But I feel that, it is also sometimes exactly the wrong thing to do since a lot of learning mathematics seems to happen in the period where you do not yet know what to do. You try an approach that fails. You discover that you have misunderstood a definition. You work through a special case. You realise that the obstacle is not the calculation you thought it was, but some earlier gap in your understanding etc. Finally, after all that desperation does eventually something click. Those failed attempts are not incidental to that process; cause quite often, they are the process. (Would recommend skimming Poincaré’s Science et Méthode)
This is what worries me about using these AI tools as a shortcut through every difficulty: if the objective were simply to obtain the solution, then of course we should use the fastest available tool; but when learning mathematics, obtaining the solution and understanding the problem are not necessarily the same objective and sometimes the inefficient roundabout path is doing useful work. In fact, I’d argue sometimes this is what allows us to make those insanely creative leaps in logic to dig into other seemingly unrelated problems in the future cause of understanding some structure in our mistake that allows for some other exploit later.
In principle, we can now increasingly prompt the many mathematical objects we require, for whatever we are doing, be it a proof sketch, an explanation, an example, or a calculation , into existence within seconds (within reason of course) ; but if you are a student, the fact that something can be produced for you in an instant does not mean that having it produced for you will teach you much
—
However, at the same time, I think focusing only on this danger misses something remarkable about these tools. These AI tools in their current state may also be one of the best educational technologies we have had for learning maths.
One difficulty that plagues a textbook is that it has to imagine its reader. In fact, so does a math stack exchange answer, your lecture notes, or a blog post. What I mean by this is that the author cannot know exactly what you already understand, what notation you have seen, which analogy will make sense to you, or which sentence you have just failed to understand.
VS these modern AI systems which now can be that glue sit in between the text and the reader. For example, you can ask it to explain analysis assuming you learned from physicists to differentiate without restraint using vibes when you see an integral sign 😉 . You can ask for an example in a context you already understand. You can tell it exactly which step lost you and in fact you can even copy paste in your work and ask it where you have gone wrong and it will find you the fix. You can ask it to try again without using a theorem you have not learned yet or find links to theorems you have yet to learn. In that sense, it can act as a kind of middleware for mathematical exposition, translating a fixed piece of mathematics into something adapted to a particular reader.
That possibility is genuinely new to me yet so very familiar in the best parts of my journey in learning. Good lecturers have always done this by dynamically adjusting to the audience (you’d be surprised how rare but much appreciated of a skill this is), but sadly a book cannot do it for every reader at every moment.
So perhaps the question is not whether students should use AI, but instead we should more deeply think about what role we ask it to play.
There is a big difference between typing
> Give me the answer to “XYZ ” / Solve this problem for me.
and typing
> This is what I am thinking, this is what I have done, where have I gone wrong? (give me hints not the full solution).
Or, even better still:
Ask me questions that help me work out where I am stuck then give me a hint only when I need one.
In the first case, the model replaces part of the learning process. In the second, it participates in it. Cause I think, at least in my own naive ways, that challenging yourself is where you really learn and, in this age, where the barrier to be challenged is getting more liquid, I increasingly think that it is a useful principle to keep yourself engaged by being a learner in the loop.
Use the model to change the level of an explanation. Use it to generate examples. Ask it what prerequisite you might be missing. Ask for a counterexample, an analogy, or a smaller version of the problem; or even a variant of the problem once you have solved it. Let it nudge you when you have exhausted an idea. But perhaps, please do not be too eager to let it remove the struggle.
Getting stuck is frustrating. Yet, it is also one of the most wonderful places where the seed for learning gets sown and are ready to be reaped later 🙂
Received 12 August 2026.
Add to the discussion