People Share The Coolest Mathematical Facts They Know

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While many of us rushed through our required math classes as quickly as we could in high school and college, some people really found joy in those classes.

After spending several more years studying the subject, they also discovered there were many more fun facts to mathematics than Geometry and Calculus may have suggested.

Redditor xxTick asked: 

“What’s the coolest mathematical fact you know of?”

Two Redditors joked about the Banach-Tarski paradox.

“Banach-Tarski paradox, in a nutshell what it says is that if you take a (let’s make it simpler) 3-dimensional ball, you can partition it in finite number of pieces (which is only true for 3-dim case, otherwise it’s countably infinite).”

“Then if you rotate and translate some of the pieces, you can get two exactly identical balls that we started with. So you might think we doubled the volume, indeed we did.” – I_luv_your_mom

“There was an old Reddit post about this that made me giggle. The user found out that if you order an extra tortilla with one of those massive Chipotle burritos, then separate the contents between the two, you will get two burritos of equal size to the original.”

“They called it the Banach–Tarski burrito.” – buggy65

Others were in awe over the power of doubling numbers.

“I had a coworker how refused to believe that if you multiply a penny by 2 every day for a month that you’d be a millionaire by the end of the month, even after I had walked her through it with a calculator.” – Old_man_at_heart

“This blew my mind, I saw something somewhere saying to start investing a penny on the first and you won’t believe what you’d get by the 30th. I was thinking like $500!! I was wrong.” – DranoDrinker

One Redditor wanted to talk about circles.

“I like to draw this one out to explain to people.”

“Circles (people) and lines (relationships) with every other circle. It’s easy to see how quickly the number of lines increase, which shows that adding more people is not a linear increase in probability, but a … exponential or multiplicative… I’m not sure which one at the moment.”

“1 person = 0 lines”

“2 people = 1 line”

“3 people = 3 lines”

“4 people = 6 lines”


“23 people = 253 lines”

“24 people = 276 lines”

“25 people = 300 lines”

“26 people = 325 lines” – SalAtWork

Some talked about the Birthday Problem and probability.

“The Birthday Problem.”

“If you have 23 people in a room, there is a 50% chance that at least two of them have the same birthday. If you put 70 people in, the probability jumps to 99.9%.”

“It seems f**king weird to me but I haven’t done math since high school so what do I know.” – honeyimsorry

“The reason this is confusing for most people is that they’re thinking of how many people they’d have to meet to find someone who shares their birthday. You need to think of how many potential pairs there are, which grows fairly quickly.”

“And, you need to do the calculation in negative: as we add each person, calculate the odds that no one shares a birthday, and the odds that there is a match are 1 – that.”

“You start with one. Obviously no match. Second one: 364/365 says they’re different. But when we add a third, there are two potential matches, so only a 363/365 chance he doesn’t match, and 362/365 for the fourth.”

“The odds there is a match are 1 – the product of the other fractions. Since the fractions are close to one, they almost equal one, but as each person comes in, we’re multiplying a number that starts to be significantly less than one by a fraction that each time is more notably less than one, so the odds there is no match start to fall quickly until they dip just below half at the 23 mark.” – TheAlpacaLives

Then there was the Collatz Conjecture.

“The Collatz Conjecture: It’s an unsolved mathematical conjecture that can be summarized as follows; Take any positive integer, or ‘n.'”

“If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1.”

“For example, start with 21. it’s odd so I multiply by 3 and add 1, to get 64. 64 is even so I divide by 2 to get 32, again to get 16, 8, 4, 2, 1. No one has found a number that doesn’t follow this rule.” – AsiaWaffles

One Redditor talked about Rubik’s cubes.

“The maximum number of moves needed to solve a Rubik’s cube from any configuration is a mere 20.”

“Expecting Numberphile subscribers to have a strong showing in this thread.”

“To clarify, I mean the OPTIMAL solution from any given configuration will require fewer than or equal to 20 moves to solve.” – AlexVX_

One Redditor loved talking about multiplication. 

“1 x 1 = 1”

“11 x 11 = 121”

“111 x 111 = 12321”

“1111 x 1111 = 1234321”

“And on it goes” – IAmSomewhatHappy

A few talked about Pascal’s Triangle.

“Also, Pascal’s Triangle gives you the powers of 11 if you look at each row as a number.” – Aurora320

“I realized that in algebra class and tried to explain to my teacher why I thought it was so cool and he just didn’t get it. F**k you, Mr. Chase.” – 1stonepwn

One Redditor talked about Shizuo Kakutani.

“Shizuo Kakutani”

“If you take enough random steps in two dimensions, you’ll always eventually get back to your starting point. The same cannot be said of three dimensions.”

“I just find the idea that you will always get back to where you started by making random moves absolutely mind-boggling, and the fact things change just because you can go up and down is even weirder.” – _9tail_

One Redditor shared how they got into math.

“As a PhD student in mathematics, this is not a sexy answer, but one of the reasons I fell in love with math was in my differential equations course when we discussed modeling epidemic using mathematical equations.”

“It was so incredible to me that back in 1927, Kermack and McKendrick came up with a simple formulation of how to model a disease.”

“This idea has been expanded greatly, but their original version of the S-I-R compartmental model is still one of the coolest things. And it can also model rumors as well!” – hpmetsfan

Mathematics and similar subjects may have not been everyone’s favorite subject while they were going through school, but it’s clear now there was more to it than addition, subtraction and solving for X.

With facts like these, it’s almost enough to want to study math a little more again.

Written by McKenzie Lynn Tozan

McKenzie Lynn Tozan lives in North Chicago, where she works as a poet, freelance writer, and editor. She received her MFA in Creative Writing from Western Michigan University, and her BA in English from Indiana University South Bend. Her poems have appeared in Rogue Agent, Whale Road Review, the James Franco Review, Thank You for Swallowing, and elsewhere; and her essays and book reviews have appeared with Memoir Mixtapes, The Rumpus, BookPage, and Motherly, among others. When she's not reading and writing, she's in her garden or spending time with her family. For more, visit