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Life is nonlinear. So handle it using Math.

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Area of circle ⭕

Area of circle ⭕

1,156,544 views

There is a shape in mathematics that can hold a finite amount of paint, yet would require an infinite amount of paint to coat its surface. It is called Gabriel’s Horn. Imagine rotating the curve y=1/x around the x-axis. The result is a long, tapering surface that stretches infinitely, like a tunnel that never ends. Here’s where the paradox appears. The volume of this shape converges—if you add up all its infinitesimal slices, the total stops growing. In other words, you can completely fill it with a finite amount of paint. But the surface area diverges. No matter how far you go along the horn, there is always more surface to cover. The outer “skin” keeps extending, demanding more paint without end. So while you could pour paint inside and fill it entirely, you would never finish painting the outside. This is not a trick, but a consequence of how infinity behaves. The radius shrinks quickly enough for the volume to remain finite, yet not fast enough to keep the surface area from growing without bound. It reveals a deeper truth: infinity does not simply mean “very large”—it means unending. And sometimes, the infinite can exist within the finite in ways that defy our intuition, even while remaining perfectly consistent in mathematics.

There is a shape in mathematics that can hold a finite amount of paint, yet would require an infinite amount of paint to coat its surface. It is called Gabriel’s Horn. Imagine rotating the curve y=1/x around the x-axis. The result is a long, tapering surface that stretches infinitely, like a tunnel that never ends. Here’s where the paradox appears. The volume of this shape converges—if you add up all its infinitesimal slices, the total stops growing. In other words, you can completely fill it with a finite amount of paint. But the surface area diverges. No matter how far you go along the horn, there is always more surface to cover. The outer “skin” keeps extending, demanding more paint without end. So while you could pour paint inside and fill it entirely, you would never finish painting the outside. This is not a trick, but a consequence of how infinity behaves. The radius shrinks quickly enough for the volume to remain finite, yet not fast enough to keep the surface area from growing without bound. It reveals a deeper truth: infinity does not simply mean “very large”—it means unending. And sometimes, the infinite can exist within the finite in ways that defy our intuition, even while remaining perfectly consistent in mathematics.

278,658 views

Where lines meet at right angles, Pythagoras revealed a hidden poetry of numbers. 🎬credit: eeanimation

Where lines meet at right angles, Pythagoras revealed a hidden poetry of numbers. 🎬credit: eeanimation

124,497 views

Do you still think math is boring?

Do you still think math is boring?

206,092 views

There is a famous anecdote about mathematician Stanisław Ulam. In 1963, while attending a seminar, he became bored and started doodling in his notebook. He arranged the integers on a square grid in a spiral and marked the prime numbers. He noticed that the primes seemed to form noticeable diagonal patterns rather than appearing completely random. To me, this is a good example of how the way we represent mathematical objects can reveal patterns that are otherwise difficult to notice. I think it’s really surprising to most of us that a noticeable pattern appears in this doodling.

There is a famous anecdote about mathematician Stanisław Ulam. In 1963, while attending a seminar, he became bored and started doodling in his notebook. He arranged the integers on a square grid in a spiral and marked the prime numbers. He noticed that the primes seemed to form noticeable diagonal patterns rather than appearing completely random. To me, this is a good example of how the way we represent mathematical objects can reveal patterns that are otherwise difficult to notice. I think it’s really surprising to most of us that a noticeable pattern appears in this doodling.

20,206 views

When you realized that you forgot to write +c in all indefinite integrals on your final exam

When you realized that you forgot to write +c in all indefinite integrals on your final exam

75,938 views

The Math Dance

The Math Dance

41,876 views

This calculus meme 😢

This calculus meme 😢

41,511 views

Rotation 😂

Rotation 😂

35,873 views

what is differentiation?

what is differentiation?

22,331 views

Happy New Year 2026

Happy New Year 2026

39,535 views

Math is easy: Just the Alphabet

Math is easy: Just the Alphabet

14,726 views

These mathematical equations don’t just draw surfaces — they sketch a heart, turning cold symbols into something that feels deeply human. 📷: mathswithmuza

These mathematical equations don’t just draw surfaces — they sketch a heart, turning cold symbols into something that feels deeply human. 📷: mathswithmuza

11,533 views

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Can you turn a sphere inside out without cutting or tearing it? Remarkably, yes. If we allow the surface to pass through itself, it can be turned completely inside out while remaining smooth at every stage. This is called sphere eversion.
1:01
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Can you turn a sphere inside out without cutting or tearing it? Remarkably, yes. If we allow the surface to pass through itself, it can be turned completely inside out while remaining smooth at every stage. This is called sphere eversion.

Math Files

663,686 views • 1 day ago

Imagine solving a 150 × 150 × 150 Rubik’s Cube, where each face contains 22,500 colored squares!
0:49
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Imagine solving a 150 × 150 × 150 Rubik’s Cube, where each face contains 22,500 colored squares!

Math Files

1,684,336 views • 4 days ago

Suppose a straight line is rotating clockwise through a collection of points. Whenever it reaches another point, that point becomes its new pivot. Could it keep turning ever and ever without leaving a single point? It's a beautiful problem from the 2011 IMO.
0:35
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Suppose a straight line is rotating clockwise through a collection of points. Whenever it reaches another point, that point becomes its new pivot. Could it keep turning ever and ever without leaving a single point? It's a beautiful problem from the 2011 IMO.

Math Files

122,412 views • 4 days ago

(a + b)² = a² + 2ab + b²
0:21
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(a + b)² = a² + 2ab + b²

Math Files

2,941,863 views • 4 months ago

We often call Euler’s identity the most beautiful equation in mathematics. But sometimes we forget the beauty of the Gaussian integral. It is absolutely gorgeous. And if you don’t know this integral yet, can you really call yourself a math nerd? 😉
0:54
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We often call Euler’s identity the most beautiful equation in mathematics. But sometimes we forget the beauty of the Gaussian integral. It is absolutely gorgeous. And if you don’t know this integral yet, can you really call yourself a math nerd? 😉

Math Files

94,050 views • 17 days ago

Not a single curved line. Yet your eyes see a spiral.
0:38
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Not a single curved line. Yet your eyes see a spiral.

Math Files

12,864 views • 3 days ago

Math champs don’t need calculators. 😂
0:30
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Math champs don’t need calculators. 😂

Math Files

394,197 views • 6 months ago

It appears circular, but the balls are really moving in straight lines
0:26
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It appears circular, but the balls are really moving in straight lines

Math Files

410,590 views • 7 months ago

The history of π is not merely a search for more decimal places. It is the story of how mathematics continually invents new ways to reach the same truth.
0:51
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The history of π is not merely a search for more decimal places. It is the story of how mathematics continually invents new ways to reach the same truth.

Math Files

16,932 views • 6 days ago

A rotating circle that draws a perfectly straight line
0:46
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A rotating circle that draws a perfectly straight line

Math Files

17,675 views • 7 days ago

In 2014, a woman won the Fields Medal for the first time since it was established. Her story is fascinating because she was representing ordinary girls from all over the world. Her name was Maryam Mirzakhani, and she was from Iran. When Maryam was studying in Iran, there were separate schools for boys and girls. This did not make it easy for her to pursue science. Still, she did not give up. She worked hard and became one of the first Iranian girls to take part in the International Mathematical Olympiad, where she won a gold medal. The following year, she won another gold medal. She completed her early studies in Iran and later went to the United States, where she earned her PhD from Harvard University in 2004. Ten years later, she was awarded the Fields Medal for her important work in the geometry of Riemann surfaces and their moduli spaces. Stories like hers help inspire more women to be included in the world of mathematics.
0:21
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In 2014, a woman won the Fields Medal for the first time since it was established. Her story is fascinating because she was representing ordinary girls from all over the world. Her name was Maryam Mirzakhani, and she was from Iran. When Maryam was studying in Iran, there were separate schools for boys and girls. This did not make it easy for her to pursue science. Still, she did not give up. She worked hard and became one of the first Iranian girls to take part in the International Mathematical Olympiad, where she won a gold medal. The following year, she won another gold medal. She completed her early studies in Iran and later went to the United States, where she earned her PhD from Harvard University in 2004. Ten years later, she was awarded the Fields Medal for her important work in the geometry of Riemann surfaces and their moduli spaces. Stories like hers help inspire more women to be included in the world of mathematics.

Math Files

320,578 views • 5 months ago

Kepler’s Second Law says that a line joining a planet to the Sun sweeps out equal areas in equal intervals of time. So a planet moves faster near perihelion and slower near aphelion. The speed changes, but the rate at which orbital area is swept out remains constant. A beautiful geometric signature of angular momentum conservation.
0:42
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Kepler’s Second Law says that a line joining a planet to the Sun sweeps out equal areas in equal intervals of time. So a planet moves faster near perihelion and slower near aphelion. The speed changes, but the rate at which orbital area is swept out remains constant. A beautiful geometric signature of angular momentum conservation.

Math Files

32,297 views • 15 days ago

None of these points move in circles, so why does the flower rotate? Each dot only slides back and forth along its own straight line, following r = R cos(4θ − ωt). Because every line has a slightly different phase, the dots together form an 8-petal rose that turns at ω/4. No particle rotates, yet the pattern does. Math can make motion from phase.
0:40
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None of these points move in circles, so why does the flower rotate? Each dot only slides back and forth along its own straight line, following r = R cos(4θ − ωt). Because every line has a slightly different phase, the dots together form an 8-petal rose that turns at ω/4. No particle rotates, yet the pattern does. Math can make motion from phase.

Math Files

25,108 views • 15 days ago

Volume of sphere: a beautiful proof
0:43
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Volume of sphere: a beautiful proof

Math Files

19,615 views • 11 days ago

In 1696, Johann Bernoulli challenged Europe’s mathematicians with the brachistochrone problem: find the curve along which a particle falls from one point to another in the least time. The answer was not a straight line. It was a cycloid. Johann solved it using Fermat’s principle of least time. His brother Jakob found a more geometric approach and pushed the problem further, helping lay foundations for what became the calculus of variations. Their mathematics was brilliant. Their sibling rivalry was even more intense. Source: Hal Hellman, Great Feuds in Mathematics.
0:52
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In 1696, Johann Bernoulli challenged Europe’s mathematicians with the brachistochrone problem: find the curve along which a particle falls from one point to another in the least time. The answer was not a straight line. It was a cycloid. Johann solved it using Fermat’s principle of least time. His brother Jakob found a more geometric approach and pushed the problem further, helping lay foundations for what became the calculus of variations. Their mathematics was brilliant. Their sibling rivalry was even more intense. Source: Hal Hellman, Great Feuds in Mathematics.

Math Files

17,927 views • 11 days ago

Gas molecules are always moving, but not all at the same speed. The Maxwell–Boltzmann distribution shows how those speeds are spread out. Heat the gas → more molecules move faster, and the speed range becomes broader. Cool it → speeds cluster more tightly at lower values. Temperature changes the whole distribution, not every molecule in the same way.
0:48
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Gas molecules are always moving, but not all at the same speed. The Maxwell–Boltzmann distribution shows how those speeds are spread out. Heat the gas → more molecules move faster, and the speed range becomes broader. Cool it → speeds cluster more tightly at lower values. Temperature changes the whole distribution, not every molecule in the same way.

Math Files

17,316 views • 11 days ago

Synchronization is one of nature’s quiet surprises: independent oscillators can discover a common rhythm without a conductor.
0:45
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Synchronization is one of nature’s quiet surprises: independent oscillators can discover a common rhythm without a conductor.

Math Files

13,146 views • 8 days ago

Mathematics is the art of patterns, and equations are the tools that bring them to life.
1:10
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Mathematics is the art of patterns, and equations are the tools that bring them to life.

Math Files

19,205 views • 13 days ago

Math becomes beautiful the moment you can see it. a² − b² = (a + b)(a − b)
0:38
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Math becomes beautiful the moment you can see it. a² − b² = (a + b)(a − b)

Math Files

178,939 views • 6 months ago

Differentiation gave mathematics a language for changing slopes. Integration gave it a language for accumulating quantities and areas. Together, they transformed the study of motion, change, and modern analysis.
0:45
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Differentiation gave mathematics a language for changing slopes. Integration gave it a language for accumulating quantities and areas. Together, they transformed the study of motion, change, and modern analysis.

Math Files

18,878 views • 15 days ago