That cant be right
A decimal point followed by an infinite string of 9s is not merely close to this number. It is exactly equal to it.
1
___ is the smallest number equal to the sum of all its positive divisors except itself
6
Pick any positive integer aa and prime pp. If p ∤ a, this theorem guarantees
a^(p-1)≡1(mod p).
Fermat's Little theorem
Legend says that as a schoolboy, he stunned his teacher by quickly finding
1+2+3+⋯+100=5050
He later became known as the “Prince of Mathematicians.”
you can get bonus points for saying his FIRST name
Carl Friedrich Gauss
oll two standard six-sided dice. This sum has more ways to occur than any other.
7
In a group of ___ people, the probability that at least two share a birthday is already greater than 50%.
23
This three-digit number is apparently very attached to itself:
a^3+b^3+c^3=abc (as a three-digit number)
153
Draw three cevians in a triangle, one from each vertex. This theorem tells you they meet at one point exactly when
FB/AF * DC/BD * EA/CE =1.
Ceva's theorem
This mathematician introduced a revolutionary way to compare infinities, proving, for example, that the real numbers cannot be put into one-to-one correspondence with the integers
Georg Cantor
In the Monty Hall problem, you pick one of three doors. After the host reveals a goat, switching doors gives you this probability of winning the prize.
2/3
Among all positive integers, the fraction of pairs that are relatively prime approaches this expression, unexpectedly involving pi.
6/pi^2
142857
For a polygon whose vertices lie on lattice points, you can find its area by counting dots instead of measuring lengths
Pick's Theorem
This mathematician made fundamental discoveries about polynomial equations while still a teenager. At age 20, he died after being shot in a duel.
Évariste Galois
A family has two children, and you are told at least one is a boy. Assuming the four gender orderings are equally likely, this is the probability that both are boys.
1/3
This infinite series diverges, even though its terms get arbitrarily close to zero:
1+1/2+1/3+1/4+...
Harmonic series
Start with almost any four-digit number containing at least two different digits. Rearrange its digits largest-to-smallest and smallest-to-largest, subtract, and repeat. You will eventually become trapped at this number.
6174, the Kaprekar’s constant
Take any triangle and trisect each of its three angles. Three particular intersections of those trisectors will always form this surprisingly regular shape.
Equilateral triangle and Morley's Trisector Theorem
This mathematician refused all prizes for his solution to the Poincaré conjecture. Upon being called by The Guardian, he reportedly said "You are disturbing me. I am picking mushrooms."
Grigori Perelman
You repeatedly flip a fair coin until you get two heads in a row. This is the expected number of flips you’ll need.
6
This paradox says a solid ball can mathematically be split into a finite number of pieces and rearranged into two balls, each the same size as the original.
Banach–Tarski paradox
This pair of numbers has an unusually wholesome friendship: the proper divisors of the first add to the second, and the proper divisors of the second add back to the first. They are the smallest pair with this property.
220 and 284, and they were called amicable numbers
According to this theorem, every positive integer can be written as the sum of four integer squares, allowing zeros.
Lagrange’s Four-Square Theorem
This mathematician lost sight in one eye and eventually became almost completely blind, yet continued producing major mathematics. A huge amount of modern notation, including popularizing the transcendental e, imaginary i, and totient, is associated with him.
bonus points for full name
Leonhard Euler
Randomly put nn letters into nn addressed envelopes. As nn gets huge, the probability that not a single letter reaches the correct person approaches this famous constant.
1/e