the thing about math is even if you understand it you actually don’t understand it
Prime numbers are like atoms. They are the building blocks of all integers. Every integer is either itself a prime or the product of primes. For example, 11 is a prime; 12 is the product of the primes 2, 2, and 3; 13 is a prime; 14 is the product of the primes 2 and 7; 15 is the product of the primes 3 and 5; and so on. Some 2,300 years ago, in proposition 20 of Book IX of his Elements, Euclid gave a proof “straight from the book” that the supply of primes is inexhaustible.
Assume, said Euclid, that there is a finite number of primes. Then one of them, call it P, will be the largest. Now consider the number Q, larger than P, that is equal to the product of the consecutive whole numbers from 2 to P plus the number 1. In other words, Q = (2 x 3 x 4 … x P) + 1.
From the form of the number Q, it is obvious that no integer from 2 to P divides evenly into it; each division would leave a remainder of 1. If Q is not prime, it must be evenly divisible by some prime larger than P. On the other hand, if Q is prime, Q itself is a prime larger than P.
Either possibility implies the existence of a prime larger than the assumed largest prime P. This means, of course, that the concept of “the largest prime” is a fiction. But if there’s no such beast, the number of primes must be infinite. “Euclid alone,” wrote Edna St. Vincent Millay, “has looked upon Beauty bare.”
Paul Hoffman (and Euclid) in The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth.
if you don’t think this is the coolest fucking thing idek what to say
There are a number of steps to follow when you come across an integration problem that requires trig substitution. The first step is to cry. The second step is to re-evaluate your life and wonder what you did to deserve this.
The cosine of 1/x is undefined at x=0. It is also visually disturbing near x=0.
the fact that 66 + 44 doesn’t add up to 100 really pisses me off
I understand this pain too well