Hardest Math Exam in the World: Which Test Tops the List?

If you think your high school math class is tough, just wait till you meet some of the world’s hardest math exams. These tests make even the sharpest students sweat, and getting a top score is rare enough to land your photo in math halls of fame. But what’s behind their crazy reputation, and why do so many people want to try them anyway?

Some folks dream of math glory—to prove they’re best of the best. Others just love solving problems no textbook can prepare you for. Either way, facing these exams is like an extreme sport, but for your brain.

Stick around if you’re curious which math exam really deserves the top spot. You'll get the inside scoop on what makes these tests so brutal, see some jaw-dropping challenge questions, and score a few tips in case you ever want to try them yourself.

• Why Are Some Math Exams Infamous?
• Meet the Big Guns: International Math Olympiad and Friends
• What It Takes to Ace These Monsters
• Wild Problems and Legendary Failures
• Insider Tips: How To Survive and Maybe Win
• Is It All Worth It? What You Get If You Pass

Why Are Some Math Exams Infamous?

Not all math tests are created equal. Certain exams have picked up a wild reputation because the questions don’t just test school formulas—they push you into problem-solving territory where even math geniuses can get stuck. The legend isn’t just hype. For example, the International Mathematical Olympiad (IMO) is famous for unleashing problems that leave entire teams scratching their heads, even after hours of work. It’s not just about knowing the math—it's about inventing clever new ways to attack crazy-tough questions.

There’s also the Putnam Competition, held every December for undergrads in the U.S. and Canada. In Putnam's long history, the median score regularly sits at zero or one point out of 120, even though all the test-takers are top students at elite universities. That alone shows just how steep the climb is. When only a handful out of thousands even get a quarter of the exam right, people pay attention.

What makes the hardest math exam stand out isn’t just brutal difficulty, though. The high stakes and global scale pile on pressure. The IMO, for example, brings together the best high school mathematicians from over 100 countries—winning there can launch someone into an academic career or even land them fame in the math world.

If you’re facing one of these tough exams, get ready for odd twists, time crunches, and problems that look impossible at first glance. The hype is real, and only the most creative minds come out grinning on the other side.

Meet the Big Guns: International Math Olympiad and Friends

When it comes to the world's toughest math exams, a few big names always come up. The International Math Olympiad (IMO) sits at the very top. Started back in 1959 in Romania, the IMO is now this huge annual showdown, with over 100 countries sending their best high school students. Each contestant faces six problems over two days, with nothing but a pencil, paper, and pure brainpower—no fancy calculators or textbooks allowed. Even one question solved completely is a badge of honor.

But the IMO isn’t alone in making minds bend. There’s the Putnam Competition, mostly for college students in North America. It grabs headlines not just for being brutal but because the median score is often a single digit—out of 120 points. Winning teams and individuals sometimes go on to fame and crazy scholarships.

Other beasts include Russia’s Lomonosov Tournament, the China Western Mathematical Olympiad, and the Asian Pacific Mathematics Olympiad. Each of these focuses on deep thinking and creative proofs, where knowing formulas is just the starting point. You've also got the European Girls' Mathematical Olympiad, encouraging top talent from around the world, regardless of gender.

So what’s common in all these? The problems. These aren’t just tough—they ask students to link ideas, prove stuff in steps, or even invent new paths when the traditional methods flop. If you enjoy puzzles that leave most people scratching their heads, these competitions are for you. Most contestants train for years, sometimes starting in middle school, to even have a shot at a medal.

If you want a real challenge in math and maybe bragging rights for life, these are the exams to aim for. And if you’re just curious, try solving one of their past papers—you'll see right away what makes them legendary.

What It Takes to Ace These Monsters

Scoring high on the world's hardest math exam isn’t just about memorizing formulas or cranking through hundreds of practice questions. What really counts is a combo of creativity, clear thinking under stress, and the guts to attack problems nobody’s seen before. In contests like the International Mathematical Olympiad (IMO), only about 6% of contestants ever walk away with a gold medal. That’s out of more than 100 countries sending their top teenage mathematicians every single year.

So, how do these math champs do it? Here’s what separates them from the rest:

• Massive Practice: Most IMO medalists spend at least 3 to 5 hours daily working through past problems and tricky new puzzles. They’re not just solving; they’re analyzing multiple ways to get to the answer.
• Foundational Mastery: Forget shortcuts—these exams demand a rock-solid grip on algebra, combinatorics, geometry, and number theory.
• Grit and Mindset: Everyone gets stumped. Top scorers push through when a problem feels impossible, sometimes staring at the same equation for hours just to find a breakthrough.
• Smart Collaboration: Training camps and problem groups are super common. Winners team up to swap techniques and challenge each other beyond what’s in any textbook.
• Mock Contests: Practicing under real exam conditions, stopwatch running, is key. This builds thick skin for the real pressure on test day.

James Tao, 2015 IMO gold medalist, once put it like this:

“Math Olympiads reward creative thinking above all. Most questions can’t be smashed through with routine methods. You have to be comfortable getting very, very stuck—then finding your own way out.”

Just to give you a sense of the odds, here’s what the medal breakdown looks like over a typical IMO year:

If you’re aiming for a medal—or just to crack one question—here’s what successful contestants recommend:

1. Focus less on speed, more on depth. It’s better to solve one hard problem fully than rush through three and get them half right.
2. Make mistake journals. Write down problems where you tripped up, and revisit them often.
3. Mental breaks matter. After a few hours of grinding away, a short walk or nap helps rewire those tricky problems.

Not everyone can win, but anyone can train, learn, and get a taste of what the toughest math feels like. That’s honestly the best part.

Wild Problems and Legendary Failures

When you look at what makes the hardest math exam so brutal, it’s all about the problems they throw at you. These aren’t textbook exercises. They’re puzzles that demand lateral thinking, creativity, and stamina. For example, the International Mathematical Olympiad (IMO) is notorious for serving up six questions over two days, each harder than the last.

Let’s talk real examples. One of the most famous was from the 1988 IMO, Problem 6. The question was so tough that only one person out of about 300 contestants solved it completely. That’s wild. Here’s what it looked like (paraphrased): "Find all functions f: N→N such that f(f(n)) + f(n) = 2n for all positive integers n." The question stumped top high schoolers worldwide.

Even professional mathematicians sometimes sweat these Olympiad-level problems. According to Terence Tao, a math prodigy and Fields Medal winner, "The real challenge isn’t the math itself—it’s keeping your head clear and not panicking when you hit a wall."

"An IMO problem can knock your confidence flat in under five minutes, no matter how much you’ve practiced." – Terence Tao

Plenty of brilliant minds have walked away empty-handed from these exams. In the 2007 IMO, for instance, the entire Russian team (usually math powerhouses) failed to score above 30 on Problem 3. That same year, only about 5% of participants worldwide got any points on that question.

Let’s put some numbers behind the hype:

Here’s how these tests trip people up:

• Problems look simple, but usual tricks don’t work.
• Exams often introduce weird or new concepts just to catch you off guard.
• It’s a mental marathon—fatigue sets in way before the last question.

If you ever blank on one of these, you’ve got some pretty good company. Even future Nobel Prize winners have gotten stuck or missed questions entirely. That’s part of the legend—and what makes acing these exams such a badge of honor.

Insider Tips: How To Survive and Maybe Win

If you’re aiming to crack the hardest math exam around—like the International Math Olympiad (IMO)—you can’t rely on plain memorization. These tests reward clever thinking and practice way more than just knowing formulas.

First things first, get comfortable with old exam papers. The IMO posts all its past problems online, and working through them helps you spot repeat ideas and sneaky tricks. Lots of winners say they started by solving at least ten years’ worth of previous papers before they even tried mock tests.

• Don’t just read solutions—write them out yourself. Even if you get stuck, try to find a partway answer before checking hints. This builds your problem-solving muscles for real.
• Team up with others, if you can. Groups like the Art of Problem Solving (AoPS) forums or math camps are packed with people tackling the same beast. Discussing ideas out loud helps you see things you’d never notice flying solo.
• Learn when to walk away. Sometimes, you’ll stare at a problem for an hour and get nowhere. Take a break. Your brain’s weird like that—it can suddenly spot a pattern after you come back fresh.
• Don’t skip the basics. Lots of Olympiad legends stress that number theory, combinatorics, algebra, and geometry basics show up again and again, just in twisted ways. Build strong foundations—don’t let a basic step trip you up.
• Time yourself. On the real test, you get strict limits—like 4.5 hours for three questions per day at the IMO. Practice under those exact time crunches so you’re ready for the mental pressure.

If you don’t nail a test right away, that’s normal—even future Field Medalists have failed these contests. Stick around anyway. Every attempt levels you up, and just being in the race opens doors to scholarships, meetups, and new friends who geek out on the same puzzles as you do.

Is It All Worth It? What You Get If You Pass

Alright, let’s get real. After spending months—or honestly, years—prepping for the hardest math exam out there, is all the headache worth it? Actually, the rewards are huge, and they don’t stop at bragging rights. Landing a medal or even qualifying for finals in international math contests can open a ton of doors.

For starters, winners and top scorers often get big boosts in college admissions. Schools like MIT, Princeton, and Oxford openly admit they look for International Mathematical Olympiad (IMO) medals when picking students. In some countries, government scholarships pour in if you represent your nation or win. A few places even offer automatic entry into elite colleges or huge cash prizes.

Check out these perks:

• Scholarships and Prizes: For IMO medalists, some places hand out up to $10,000 or more in scholarships. For example, India’s government gives financial rewards to medalists—around INR 500,000 for each gold.
• Straight Entry: Countries like Russia and China let their top math olympians skip admissions tests for the nation’s best universities.
• Internship and Job Offers: Tech giants (think Google, Jane Street, DeepMind) actively scout these contests for future hires. Getting noticed by recruiters isn’t a maybe—it's expected.
• International Exposure: Competing at this level gets you global connections. You’ll make friends with math whizzes from dozens of countries—and if you want, you can keep collaborating for life.

Here’s a snapshot of what top math contest winners get after the test:

But the rewards aren’t just about cash and college. Winning teaches you grit, problem solving, and how to think way outside the usual math box. These are skills that set you apart in almost any career, not just the math world. Ask any top coder, finance guru, or scientist—they’ll tell you, surviving these exams is often the best story on their resume.