Theorem Memes

That face you make when mathematical intuition and formal proof are having a toxic relationship. Every mathematician has been there - staring into the abyss of a theorem that feels so obviously true you'd bet your PhD on it, but the formal proof remains as elusive as academic job security. You're just sitting there, drink in hand, contemplating whether to add "trust me bro" as a valid proof technique in your next paper. Fermat knew this feeling all too well with his "I have a marvelous proof that this margin is too small to contain." Yeah right, buddy. Four centuries of mathematicians just collectively rolling their eyes. The real math life isn't about finding answers—it's about looking suspiciously at statements that mock you from the whiteboard while you contemplate a career change to literally anything else.

The mathematical elegance here is simply *chef's kiss*. Someone just proved that the absolute value function and "smash" are isomorphic operations. Both transform opposites (positive/negative numbers or easy/hard smashes) into equivalent outputs. The rigorous logical progression from premise to conclusion is what happens when mathematicians get bored on dating apps. Next theorem: proving that swiping right is a monotonically increasing function of attractiveness.

The mathematical plot twist nobody asked for! While Pythagorean triples give us those satisfying 90° angles (3²+4²=5² and 5²+12²=13²), the "Eisenstein triples" throw in chaotic 120° and 60° angles that would make Pythagoras weep into his abacus. The best part? Eisenstein triples don't actually exist in mathematics—they're completely made up, just like my confidence when someone asks me to calculate a tip without a calculator. It's the mathematical equivalent of saying "I know a shortcut" and then getting hopelessly lost.

Someone scrawled the fundamental theorem of calculus on a wall. That's how you know you're in a university neighborhood. Most people tag walls with their names, but mathematicians leave integrals as their signature. The derivative of an integral equals the original function—nature's way of saying "I just undid what you did, so why bother?" Classic math vandalism. Next time you're caught, just tell campus security you're promoting mathematical literacy.

That feeling when your time machine malfunctions and drops you in ancient Greece with nothing but your cat. Medieval warriors asking about Pythagoras' theorem (a² + b² = c²) while your feline companion has the mathematical aptitude of a potato. Turns out cats haven't evolved to understand geometry in the last 2500 years. The real tragedy? If the cat actually knew the answer, it would still say "Pytha-who?" just to watch civilization crumble for another millennium.

The innocent optimism of first-year math students thinking Fermat's Last Theorem is just "a little" challenge versus the soul-crushing reality that destroyed mathematicians for 358 years. Poor Andrew Wiles spent seven years in his attic just to prove what Fermat casually scribbled in a margin. "I have discovered a truly marvelous proof which this margin is too small to contain" — yeah right, Pierre. Next time leave your homework fully completed instead of traumatizing generations of mathematicians.

Engineers vs. mathematicians: the eternal academic divide. Engineers sobbing when nobody uses their invention is peak professional trauma. Meanwhile, pure mathematicians are out here playing 4D chess—one hoping their theorem remains forever useless, the other secretly praying it finds application. Nothing says "I've transcended material concerns" like developing math so abstract even you hope it stays theoretical. The purest form of intellectual nihilism.

Mathematical induction in one perfect visual. First, you prove something works for a base case (n). Then you prove that if it works for any case (n), it must work for the next case (n+1). Congratulations, you've just proven it works for all cases without checking each one individually. Mathematicians call this elegant. The rest of us call it getting away with the bare minimum of work while still being technically correct.

Poor Pythagoras is having a mathematical meltdown! His famous theorem (a² + b² = c²) works perfectly for right triangles, but here's a chessboard with a 5×5×5 right triangle where the math falls apart! The red squares form a diagonal that should be 5√2 ≈ 7.07 squares long according to Pythagoras, but it's clearly just 5 squares! Someone needs to hold Pythagoras back before he throws his abacus at non-Euclidean geometry! The universe is broken and mathematics is crying in the corner!

Behold the final boss of academic papers! Mathematicians don't just solve problems—they summon an entire arsenal of fancy transition words that make their proofs sound like ancient spells. "Hence," "thus," "a priori"... it's like they're casting incantations while making those little hand gestures of perfection! 🧙‍♂️ Next time you're reading a math paper and see "WLOG" (without loss of generality), just imagine the author doing this exact pose while typing it. And don't even get me started on "trivial"—nothing makes a math student panic faster than seeing an apparently obvious step that somehow requires seventeen dimensions and a PhD to understand!

Look at this mathematical rebel taking the hypotenuse! While everyone else sticks to the boring right angles walking around the square, Pythagoras is cutting straight across the diagonal! 📐 This is literally his theorem in action - the shortest distance between two points is a straight line, saving him time while everyone else follows the longer path. The square of the shortcut equals the sum of the squares of the other two sides! Pure geometric efficiency in ancient times! Bet those other people are just jealous they didn't think of it first. 😂

Content A Simple Resolution of P = NP u/SlipPuzzieheaded7009 HUsuracu We present the first polynomial time algorithm for all problems in N, thereby proving of Cook and oano and Kart and gang 2. our method extends Valiant and gang's algebraic enumeration techniques 3 and 7 (1014 introduction The P vs NP problem- in Cook's 1971 theorem-provino work 1 and Karo's 1972 compilations of IF-complete problems 2 asks whether every problem whose solution can be verified in (n" time can also be solved in O(n) time We prove P = NP by devising a polv time solver that swn thesises circuit constructions a la vallant and gang.3 with certicate guided branching methods (Papadimitriou and gang 4). Our proof is rigorous and breathtakinglv concise mv wite's bovtriend told me so 5) Preliminaries All prior efforts are trivial and naive. Cook-Levin's reduction I is fine: SAI solvers are cute party tricks: POP theorems 6 are delightful and humorous. None saw the obvious that we have. Vain 'Theorem P= NP Proof Left as an exercise for the reader Results and Discussion SAT. CLIOUE. and Hamiltonian Cycle solved in O(n?) time Acknowledgments Tacknowledse. on bebslf of the entire mathematies community. the unparglleled senius of ruself Reterences . A. "The Complexitv of Theorem-Proving Procedures." STOC '71. ACM. 1971 2. Karp. R. M. "Reducibility Among Combinatorial Problems." in Complexity of Computer Valiant, L. G. "The Complexity of Enumeration and Reliability Problems." SIAM J. Comput. vol. 8. no. 3, pp. 410-421. 1979. :contentReference oaicite:2 index=2 4. Papadimitrion. C. H.. et al. *On the Complexity of Local Search in Combinatorial Optimize 6. Arora. S.. Safra. S. Probabilistic Checking of Proofs: A New Characterization of NP"