#2. Tupper's Self-Referential Formula
Tupper's self-referential formula sounds like an impotence cure sold by a man slicking his hair with snake oil. In fact, it's a mathematical inequality ...
... which outputs the same mathematical inequality.
In places where X and Y satisfy the inequality you get black, where it doesn't it's white, and this Manichean math outputs itself. It's the Facebook formula, the mathematical equivalent of social media: You were expecting an intelligent answer, but it just refers to itself. In fact, it's the mathematical equivalent of infinite monkeys, as it eventually produces every possible 106 x 17 pixel image as you scroll through higher and higher numbers.
Though most monkey math is applied to fecal ballistics
The formula is just one of many bitmap decoding functions. Any image can be represented as numbers.
Strangely, Brockway's images are always triplets of sixes.
The number for the formula is 543 digits long, so you can expect another hellayottahellayottahellayottayotta-scale number for similar pictures. Making this the smartest, longest, and biggest dick joke we've ever shown:
Quite Excellent Dick.
#1. The Most Beautiful Equation in The World
Euler's identity is regularly chosen as the most beautiful in existence. It isn't just an equation, it's the haiku of mathematics. It's the only artwork that can objectively prove itself true. It's a more beautiful embodiment of numbers than 7 of 9.
This contains more understanding of the truths of the universe than a Shaolin monastery full of Greek philosophers full of magic mushrooms. If you're ever contacted by aliens, shout it quickly: It's the only thing you can possibly say fast enough before they detect reality TV. It contains the five most important numbers there are, more fundamental truths of reality than any five pantheons you care to mention.
The Greeks were more jock-gods
The imaginary unit is "i." When real numbers couldn't find the root of negative things, we found imaginary ones which could help us solve our problems. That's the calculation equivalent of a Disney movie. And if it sounds impossible, stop using electronics, AC power, and atoms, because imaginary numbers are essential for understanding all of them.
If pi is the keycode for space, Euler's constant "e" is the number of mathematics itself. The rate of change of e^x is e^x, making 2.71828 a perfect point in differentiation and integration, which are everything. Connecting calculus to numerals feels like connecting poetry to prehistoric pond water, but that's pretty much what happened: Something beginning with one trying to plus one to become two eventually led to everything we've ever known. The e is used to calculate so many things you'd swear it was Star Trek-nobabble. It's used in phasor notation, probability theory, calculus, compound interest, and more. It's so powerfully nerdy Google pledged to raise e billion dollars in their IPO.
So you've got the imaginary, oneness, nothingness and two irrational transcendental numbers. It could only be a better calculation of the meaning of life if it equaled 42. And it gets even smarter from there. e to the power of a complex number projects you into the complex plane. Which sounds like something you do to Superman villains when the writer thinks, "Damn, Superman doesn't kill anyone, but we really need to get rid of this guy."
Regular guns? Evil. Eternal banishment to a limbo dimension with inevitable mental breakdown, insanity, and escape to murder countless innocents? No problem
Two dimensional pictures have horizontal and vertical. The complex plane does the same thing with uses realistic and imaginary. Every real number you've ever seen is just a line, an antiquated slide-rule for counting, while complex numbers are the full page where math draws pictures of pure intellect. e^ix draws a circle around the zero point on this complex plane. It's a more incredible imaginary landscape than Dali's.
A curve hasn't been imagined by so many nerds since rumors of the Tomb Raider nude code
2pi takes you around a complete circle, so e^i pi is halfway round the circle at minus one. The formula combines transcendental truths with oneness to reveal nothing. Math is how humanity understands the former instead of the latter.
For more incredibly applications of intellect, behold 6 Badass Spacecraft Landings Humanity Totally Nailed and 9 Badass Lasers That Prove The Death Star Isn't Far Off.