The Joy of Not Knowing (Yet)

Everyone meets math questions they cannot answer—and that is where the real learning starts.

Here's a secret that mathematicians know but rarely say out loud: they spend most of their time confused.

Not slightly puzzled. Not momentarily stuck. Genuinely, deeply, sometimes frustratingly confused. The difference between a professional mathematician and someone who "hates math" isn't that the professional finds it easy. It's that the professional has learned to sit with confusion, to trust that understanding will come, and even—strange as it sounds—to enjoy the not-knowing.

This post is an invitation to reframe how you think about struggle. That uncomfortable feeling when a problem won't yield? It's not a sign you're bad at math. It's a sign you're doing math.

Why Struggle Is Normal in Math

Somewhere along the way, many of us picked up a toxic belief: that being good at math means being fast at math. You see the problem, you know the answer, you move on. Hesitation equals failure.

This is backwards.

Real mathematics—the kind that matters, the kind that builds bridges and cures diseases and sends robots to Mars—is slow. It involves dead ends, wrong turns, crumpled paper, and long walks to clear your head. Andrew Wiles spent seven years proving Fermat's Last Theorem, mostly in secret, mostly stuck. He describes the process as "groping in the dark."

The problems worth solving don't come with obvious paths. If they did, someone would have solved them already.

For students, this means that struggling with a problem isn't a sign to give up or ask for the answer. It's a sign you've found something worth working on. The struggle is the learning. Neurons are connecting. Understanding is being built, brick by brick, even when it doesn't feel like it.

For professionals, this means that the project that makes you feel incompetent might be the one that grows you most. Comfort is nice, but confusion is where growth lives.

How Curiosity Beats Speed

If speed isn't the goal, what is? Curiosity.

Curious learners ask different questions than anxious ones. An anxious learner asks: "What's the answer? How do I get this done?" A curious learner asks: "Why does this work? What happens if I change this? Is there another way?"

The anxious approach gets you through the test. The curious approach makes you a mathematician.

Here's the thing: curiosity is trainable. You can practice it. When you hit a wall, instead of thinking "I can't do this," try asking:

• What do I actually know so far?
• What would make this easier?
• Have I seen something like this before?
• What if I tried a smaller version of the problem?
• What if I worked backwards from the answer?

These questions don't guarantee success, but they keep you engaged. They turn passive frustration into active exploration. And exploration, even failed exploration, teaches you things.

The phrase "I don't know" can be a full stop or a launchpad. Adding "yet" turns it into the latter. "I don't know yet" implies a future where you will know—and that future gets closer every time you try.

Tiny Challenges for Each Age Group

Growth mindset isn't about tackling impossibly hard problems. It's about consistently working at the edge of your ability—not so easy that you're bored, not so hard that you're overwhelmed.

For kids, this might mean puzzles where the answer isn't immediately obvious, but persistence pays off. The goal is to experience the satisfaction of solving something that seemed hard at first.

For teens, the challenges get more abstract. Algebra and geometry introduce problems where the path forward isn't clear, where you have to try things and see what happens. This is also the age where mathematical dead ends become common—and learning to recover from them is essential.

For professionals, the challenges often aren't purely mathematical. They're about making decisions with incomplete information, estimating when precision isn't possible, and communicating uncertainty honestly. These are math-adjacent skills that benefit from the same growth mindset.

At every level, the advice is the same: find problems that make you a little uncomfortable, and sit with that discomfort. That's where the magic happens.

Try These

Here are three puzzles calibrated for different levels—but don't be fooled by the labels. The "kid" puzzle might stump adults. The "professional" puzzle might click instantly. The point isn't to succeed. The point is to try, notice how it feels, and keep going.

Puzzle 1: The Frog's Journey (Kid-Friendly)

A frog sits at the bottom of a 10-metre well. Each day, it climbs up 3 metres. Each night, it slides back down 2 metres.

How many days does it take for the frog to escape the well?

Hint: Don't just calculate 10 ÷ 1. Think about what happens on the last day.

Puzzle 2: The Locker Problem (Teen-Level)

A school has 100 lockers, all closed. Student 1 walks down the hall and opens every locker. Student 2 then closes every 2nd locker (2, 4, 6...). Student 3 changes the state of every 3rd locker (if open, close it; if closed, open it). This continues with all 100 students.

After all 100 students have passed, which lockers are open?

Hint: A locker ends up open if it's toggled an odd number of times. When does that happen?

Puzzle 3: The Envelope Paradox (Professional Brain-Teaser)

You're given two sealed envelopes. You're told one contains twice as much money as the other, but you don't know which is which.

You pick one envelope and find £100 inside. You're now offered the chance to switch to the other envelope.

Here's the puzzle: The other envelope contains either £50 or £200. The expected value of switching seems to be (0.5 × £50) + (0.5 × £200) = £125. That's more than £100, so you should switch!

But wait—you could make the same argument no matter what amount you found. This implies you should always switch, which can't be right.

Where's the flaw in the reasoning?

Hint: The argument assumes something about the probability distribution that may not be valid. What exactly is being assumed?

Final Thought

The next time you hit a math problem that makes you feel stupid, try something radical: say "good."

Good, because you've found the boundary of what you know. Good, because you're about to learn something. Good, because this uncomfortable feeling is exactly what growth feels like.

You don't know the answer yet. But that "yet" is everything.

Mathematicians aren't people who never get stuck. They're people who've learned that being stuck is part of the job—sometimes the best part. Because when you finally break through, when the fog clears and the answer appears, there's no feeling quite like it.

That feeling is waiting for you. You just have to be willing to not know for a while first.

What's a problem that stumped you before you finally cracked it? How did it feel when you got there? Share your "yet" moments in the comments!