gl/ripetizioni

Using AI to study maths and physics: what works, what hurts

How to use AI to study maths and physics without switching your brain off: what to hand to artificial intelligence, what not to, and mistakes to avoid.

by Gaetano Livornese

Read the original in Italian

I use artificial intelligence every day for work: I write software with the help of models like Claude, and part of this site was built that way. So when a student asks me “can I use ChatGPT to study?”, I answer neither no, it’s cheating nor yes, everyone does it now. Both are lazy answers.

The real answer is that AI is a tool that amplifies the method you already have. If you study well, it helps you study better and faster. If you study badly, it lets you study very badly much more quickly, and you only notice on the day of the test, when the page is blank and the model isn’t there.

Here I explain where the line is, with concrete examples from maths and physics.

The test that exposes everything

Before any other consideration, a simple criterion you can apply by yourself:

After using AI, can you do the exercise on your own, blank page, no help?

If yes, you used it well, whatever you did. If not, you produced an assignment and learned nothing, no matter how clear it seemed while you were reading.

It is exactly the same criterion as “I understood it by looking at the solution in the textbook”: the feeling of understanding while you read is not understanding. The brain mistakes fluency for mastery. AI makes that trap much easier to fall into, because the explanation arrives tailor-made and always seems perfectly clear.

Four uses that really work

1. Getting it explained a different way

This is where AI beats the textbook. The textbook explains limits in one way only; if that way doesn’t get through to you, you are stuck. A model you can question until you find the angle that works for you.

“Explain the concept of a limit the way you would to someone who understands inequalities well but has never seen calculus. No epsilon-delta for now.”

And then keep pushing: “I didn’t understand step X, try again with a numerical example”. It is a patience that no teacher can have at eleven at night, and it is a 100% legitimate use.

2. Having it generate exercises to order

This is the best of all and almost nobody uses it. Don’t ask for the solutions: ask for more exercises of the same type.

“Generate 5 absolute-value inequalities of increasing difficulty, modelled on this one. Give me only the questions, not the solutions. I’ll ask for the solutions after I’ve tried.”

The number one problem for anyone preparing for a test is that they have few exercises and have already seen them. Here the constraint disappears. Note the important part: don’t give me the solutions now. It is the friction that makes you learn.

3. Having it check your reasoning, not give it to you

A huge difference. Not “solve this for me”, but:

“This is my working. Don’t give me the solution: just tell me, at the first step, where I go wrong, and why.”

That way the AI does what a tutor does in person: it stops you at the exact point where you derailed, without taking the work away from you. It is also how you discover your recurring mistakes, which are the ones that cost you marks.

4. Getting unstuck when you are really stuck

If you have been stuck for twenty minutes and are about to give up, asking for a hint is better than closing the book. But ask for a hint, not the solution:

“I don’t want the solution. Just give me the first step, or tell me which theorem I need.”

What ruins you

Copying the working and moving on. It is the digital equivalent of looking at the solutions at the back of the book, but worse, because the explanation is personalised and so the feeling of having understood is stronger and more deceptive.

Having it write the lab report or the essay. Besides being dishonest, it takes away the only part of the exercise where you learn to organise your thinking. And it shows: the gap between what you hand in and what you can produce in class becomes a signal that teachers read very well.

Using it during an assessed test. Here it isn’t a question of method but of rules: more and more universities cancel the exam, sometimes for the whole room. It is not worth the risk, ever.

Trusting the calculations. And here comes the part that almost nobody explains.

AI gets the calculations wrong, and for you that is an opportunity

Language models predict text, they don’t calculate. On long algebraic steps, on signs, on simplifications, they make mistakes with exactly the same confidence with which they write the right things. There is no signal that tells a correct derivative from a wrong one: the tone is always the same.

This makes them unreliable as an oracle and excellent as a sparring partner. Which, for someone who has to learn, is better.

The habit to build: when it gives you a result, check it: with a dimensional check in physics, by substituting a numerical value in maths, or by asking for a second solution by a different route and comparing. If the two don’t match, you have found an error, and working out which of the two is wrong, and why, is worth more than the exercise itself.

It is exactly the same scepticism I use when I write software with AI: I always read and verify the code it proposes, because sometimes it is convincing and wrong. With maths the same applies.

It doesn’t replace the hard part

There is one thing AI can’t do for you, and it is the reason tutoring still exists: it doesn’t know what you don’t know.

A model answers the question you ask. But a struggling student typically can’t formulate the right question, because the real gap is three chapters further back from where they got stuck. They ask for help with trigonometric equations when the problem is absolute values. The AI will diligently help with the trigonometric ones, and the gap will still be there.

Finding that gap, by watching how you write, where you hesitate, which mistakes you repeat, is diagnostic work that at the moment needs someone watching you work.

In practice

If you want to start tomorrow, three habits:

  1. Ask for exercises, not solutions.
  2. Have your own working corrected, one step at a time.
  3. Always check the calculations, especially when the answer seems convincing.

And every so often, redo the test from the start: blank page, no help. It is the only one that doesn’t lie.

You can do the blank-page test with a timed mixed Year 4 test: if you can’t hold up without help, that is the gap to close. Around this you need a method (studying maths without stress, how to build a real study plan), and for checking a model’s calculations the first list to know is the five maths mistakes that look right. For the real work on exercises there is tutoring in maths.

If you are dealing with a test or a resit at university, what to ask a chatbot and what not to applies there too: a concrete example of targeted recovery is in OFA in maths: how to clear it within the first year.

If you are preparing for a test, an exam or an admission test and want to understand where your gaps really are, the ones no model will find for you, look at the packages or write to me.

Keep reading

Want to put what you read into practice?

Let's talk for 30 minutes, free: we look together at where you are stuck and I tell you honestly how I can help.

Or message me on WhatsApp.