Greedy Irrationals

The mathematical satisfaction of a factorion is enough to make even Thanos smile. For the uninitiated, a factorion is a number equal to the sum of the factorials of its digits. 40585 = 4! + 0! + 5! + 8! + 5! is one of only four such numbers in base 10. Finding these rare mathematical unicorns brings balance to the numerical universe in a way that would make the Mad Titan proud. Mathematicians spend years hunting these creatures, only to find that perfectly balanced equations are indeed as rare as infinity stones.

The eternal battle of theoretical physics in one image! Time-independent perturbation theory is the hot date you bring home to your parents—simple, well-behaved, and solvable before dinner. Meanwhile, time-dependent perturbation theory lurks in the shadows like that homework problem that made you question your life choices. For the uninitiated: perturbation theory is how physicists solve problems they can't actually solve. Time-independent versions let you calculate stuff without worrying about that pesky fourth dimension. Add time dependence? Suddenly you're drowning in partial differential equations while questioning why you didn't just become an accountant. The face transformation is every grad student halfway through their quantum mechanics final. Pure emotional damage.

Ever had that moment when math breaks your brain? 85÷17=5. That's it. No decimals. No remainders. Just a clean, whole number that feels like finding a perfectly symmetrical potato in nature—it shouldn't exist but somehow does! The mathematical universe is having a laugh at our expense. Those "ugly" fractions with weird denominators like 17 are supposed to give us messy answers that drag on forever, not wrap up neatly with a bow! It's like expecting your cat to ignore a cardboard box—theoretically possible but deeply unsettling when it happens. My calculator and I are having an existential crisis right now! 🧮🤯

Someone clearly skipped their high school geometry classes. Flying higher doesn't mean traveling in a triangle! The Earth is curved, so the shortest path between two points is actually a great circle route (geodesic), not whatever this bizarre triangular flight path suggests. If pilots actually flew like this diagram, we'd all have enough time to watch the entire Lord of the Rings trilogy—extended editions—before landing. The real kicker? Even if this were true, the Pythagorean theorem is sobbing in the corner right now because those distances don't remotely add up. Next they'll tell us planes need to dodge the firmament.

What starts as an innocent question about why 0! equals 1 quickly spirals into the mathematical abyss of the gamma function. The top panel shows our naive beginning—just a curious mind pondering factorial basics. The bottom panel reveals the mathematical horror show that follows, complete with complex integrals and conditions on the real part of z. This is the mathematical equivalent of opening Wikipedia to look up a simple fact and finding yourself, three hours later, reading about obscure Romanian folk dances. The gamma function is essentially the factorial function's evil twin that works for non-integer values, and once you start trying to understand it, your brain turns into that screaming skull. The definition shown (Γ(z) = ∫₀^∞ t^(z-1)e^(-t) dt) is what mathematicians call "elegant." The rest of us call it "the reason we switched majors."

The eternal statistician's dilemma! While normies see a simple coin toss, statisticians see a philosophical crisis. That coin might say 50/50 chance, but is anything truly random? The subtle physics of the flip, the air resistance, the initial position—all deterministic factors that make statisticians question reality while everyone else just wants to know heads or tails. This is basically the difference between theoretical probability and the crushing weight of knowing too much about variables.