Why Is Math So Hard? You Have to Do It Yourself

There is a strange thing about learning math.

You can watch a great teacher explain a problem and think:

“Yes. I get it.”

You can watch a YouTube video. Every step makes sense. You can read a beautifully written solution. Nothing looks confusing. You can ask ChatGPT, and within seconds it can explain exactly what to do.

And then you close the video, hide the solution, open a new problem… and you have no idea where to start.

This is one of the reasons math feels so hard.

There is a big difference between understanding someone else’s solution and being able to solve a math problem yourself. And in math, that difference is everything.

Why understanding math isn’t enough

When someone shows us a solution, our brain recognizes what they are doing.

Of course they divided by 3.

Right, I remember that formula.

Yes, that step makes sense.

Because every step looks reasonable, we feel that we understand the problem. But following someone else’s thinking is much easier than doing the thinking yourself.

When there is nobody telling you the next step, you have to decide:

What should I do first? Which information matters? Which rule should I use? Did I make a mistake? What should I try next?

That is the hard part of math. And that is also where much of the learning happens. It is also the part that asks the most of your attention — which is why math can feel especially hard with ADHD, even when the concept itself is clear.

Researchers have even found a difference between feeling like you are learning and actually learning. In a Harvard study comparing actual learning with the feeling of learning, students in actively taught classes learned more than students who received traditional lectures — but they felt as if they had learned less.

In other words:

A great explanation can feel easy. Solving a problem yourself can feel hard.

But feeling that something is easy is not the same as learning it.

You can’t learn math just by watching

Imagine trying to learn basketball by watching hundreds of videos about shooting. You might learn where to put your hands. You might understand the correct movement. You might even be able to explain exactly what a good shot looks like.

But at some point, you have to pick up the ball. Math works the same way.

Videos are useful. Teachers are useful. Textbooks are useful. Worked-out solutions are useful too.

But they are useful because they can help you understand how to approach a problem — not because reading them replaces solving problems yourself.

Research on how students study worked examples has found that students learn more when they actively think about why each step works instead of simply reading through the solution.

Eventually, the solution has to disappear. And you have to try.

A meta-analysis of 225 studies in science, engineering, and mathematics found that students in active-learning environments performed better than students taught primarily through traditional lectures.

The point isn’t that explanations are bad. The point is that explanations are the beginning of learning, not the end.

At some point, you have to take control of the problem.

Watching someone think is not the same as thinking.

Getting stuck is part of learning math

When you’re stuck on a math problem, the natural reaction is to look for help.

For a student, that might mean opening YouTube, checking the solution, or asking ChatGPT. For a parent helping a child, the instinct is often the same: show them the next step, remind them of the formula, or explain the solution.

It feels helpful because suddenly the problem starts moving again. But sometimes, moving the problem forward means taking the thinking away from the student.

Getting stuck for a while is not necessarily a bad thing. Researcher Manu Kapur has studied an idea called productive failure: giving learners opportunities to attempt difficult problems and generate possible solutions before receiving full instruction.

Of course, this doesn’t mean leaving someone frustrated for an hour. It means giving them just enough help to keep thinking, without doing the thinking for them.

There is a huge difference between:

“Here is the next step.”

and:

“What could you try next?”

The first moves the solution forward.

The second moves the student forward.

And getting through a hard problem yourself does something else, too — it’s how small wins build real math confidence instead of the feeling that you were never a math person.

Does ChatGPT actually help you learn math?

Now this problem has become much bigger. For the first time, almost every student has access to a tool that can solve math problems in seconds.

Take a photo. Ask ChatGPT. Get the answer.

Don’t understand it? Ask for an explanation. Get every step.

It feels like the perfect way to learn math. But there is an important question:

If the AI is doing the reasoning, who is actually practicing the math?

A large field experiment with nearly 1,000 high-school students learning math with GPT-4, published in Proceedings of the National Academy of Sciences, tested exactly this. While students had access to a standard GPT-4 interface, they performed much better on practice problems.

But then the AI was taken away. On the later exam, students who had used unrestricted GPT-4 performed 17% worse than students who had practiced without it.

The AI had helped them do the problems. But it had not necessarily helped them learn to do the problems themselves.

And there was another important result. The researchers also tested a specially designed AI tutor with safeguards intended to guide students instead of simply giving them answers, and those safeguards largely avoided the negative learning effect seen with unrestricted GPT-4.

That distinction is incredibly important:

AI that solves the problem for you and AI that helps you solve the problem are not the same thing.

A good AI math tutor shouldn’t do your math for you

This sounds strange at first. We usually think a great tutor should be able to answer every question.

And they should.

But that doesn’t mean they should give you every answer. Sometimes, the most helpful thing a math tutor can do is refuse to take over.

Give you a small hint. Then stop. Let you think. Let you write the next step.

If you’re wrong, help you understand why. Then let you try again. And again.

Until something important happens:

You solve it.

Not the teacher. Not the video. Not ChatGPT.

You.

Because that’s the moment when:

“I think I understand it”

starts becoming:

“I can actually do it.”

That’s why we built igni differently

igni isn’t designed to be the fastest way to get a math answer. There are already plenty of tools that can do that.

igni is designed for something more important:

Helping you become able to solve the problem yourself.

When you sit down to work on algebra, calculus, statistics, geometry — or any other math course — igni is the math tool you keep by your side.

You try the problem. When you know what to do, igni stays out of the way. When you get stuck, igni helps.

A hint. A question. Help understanding a mistake. A small push toward the next step.

But you still do the math. That’s the difference.

igni doesn’t replace the work required to learn math.

It helps you do that work.

How do you know if you really understand math?

So the next time you finish a math video and think:

“I understand it.”

Don’t trust that feeling just yet.

Close the video. Hide the solution. Pick a new problem.

Now solve it yourself.

That’s the real test. Because in math, understanding isn’t being able to follow someone else’s solution.

It’s being able to create your own.

And when you get stuck — and you will — don’t ask AI to do the thinking for you.

Open igni.

Keep it beside you while you study. Let it help when you need help. But keep the thinking yours.

Because the goal isn’t to finish this problem.

The goal is to become someone who can solve the next one.

Research behind this article

Deslauriers, McCarty, Miller, Callaghan & Kestin (2019), “Measuring actual learning versus feeling of learning in response to being actively engaged in the classroom.” Proceedings of the National Academy of Sciences. Students learned more through active instruction even though they felt that they learned less.

Freeman et al. (2014), “Active learning increases student performance in science, engineering, and mathematics.” Proceedings of the National Academy of Sciences. A meta-analysis of 225 studies found better student performance and lower failure rates with active learning compared with traditional lecturing.

Kapur (2014), “Productive Failure in Learning Math.” Cognitive Science. Research examining how attempting difficult mathematical problems before instruction can support subsequent learning.

Chi, Bassok, Lewis, Reimann & Glaser (1989), “Self-Explanations: How Students Study and Use Examples in Learning to Solve Problems.” Cognitive Science. Successful learners engaged actively with worked examples instead of simply reading their steps.

Bastani et al. (2025), “Generative AI without guardrails can harm learning: Evidence from high school mathematics.” Proceedings of the National Academy of Sciences. Unrestricted GPT-4 improved students’ performance while they had access to it, but students subsequently performed worse without AI. A tutoring-oriented version with safeguards largely avoided that effect.