As any Goofy Snob knows math is something you're really good at or really bad at, depending on what you were told at age 9. Below is a summary of our species' greatest math minds. Beautiful minds!
Euclid: The Man Who Organized Everything
Nobody knows who Euclid really was. We don’t have his birth date, his death date, or any certain facts about his life. What we have is The Elements, thirteen books that organized all of Greek mathematics into a logical system starting from five basic assumptions.
He worked in Alexandria around 300 BCE, probably running the mathematics department at the great Library. His approach was radical: start with things so obvious nobody can argue with them, then build everything else through pure logic. A point has no dimension. A line has length but no width. Two parallel lines never meet.
From these simple ideas, he constructed 465 propositions covering everything from basic geometry to number theory. For 2,000 years, The Elements was the second most printed book in the Western world after the Bible. Abraham Lincoln carried a copy in his saddlebag to learn clear thinking. 📐
Euclid taught us that mathematics isn’t just calculation—it’s proof. You don’t just show something works; you show why it must work. That standard of rigor defines mathematics today. Every theorem you’ve ever seen follows his template: state your assumptions, build your argument step by step, show the conclusion follows necessarily.
He created the instruction manual for logical thought itself. No cap, the man was the GOAT of organizing knowledge. 🎯
“There is no royal road to geometry.” - Euclid’s reply when King Ptolemy I asked if there was an easier way to learn mathematics than through the Elements.
Gangster Summary: Listen bruv, this Euklid guy, nobody know who he is proper yeah, but he write THE book bout geometry innit. Like he take all the maths and put it in order, make it all logical like. Start with simple shit everyone agree with, then build everything from there. Book was number two bestseller for 2000 years, only Bible beat it. Even Abraham Lincoln carry it round. Man basically invent how you prove things proper, not just say “trust me bruv it works.” King ask him for shortcut and Euklid say nah mate, no easy way. Absolute legend.
Archimedes: Death in Syracuse
The Roman soldier found him in 212 BCE, during the sack of Syracuse. Archimedes was 75 years old, drawing geometric figures in the sand. “Don’t disturb my circles,” he said.
The soldier killed him anyway. 💀
Before that moment, Archimedes had done more than any other ancient mathematician. He calculated pi accurately, understood the mathematics of levers and pulleys, invented a screw pump still used today. He created war machines that held off the Roman fleet for two years—catapults, grappling hooks, possibly burning mirrors. When the Romans finally breached the walls, General Marcellus had given orders to spare the old mathematician.
But Archimedes’ real achievement was something nobody understood for 2,000 years. He developed early versions of calculus and integral mathematics, using infinitesimals to calculate areas and volumes. He found the area under a parabola. He calculated the volume of a sphere. His Method wasn’t rediscovered until 1906, in a palimpsest that had been scraped clean and written over with prayers.
He asked to be buried with a sphere inscribed in a cylinder—his proof of their volume ratio was his proudest achievement. Cicero found the tomb 137 years later, overgrown and forgotten. ⚔️
Archimedes died defending his city, but what he was really defending was mathematics itself. The man’s work was absolutely bussin—so advanced that nobody understood it for millennia.
“Give me a place to stand, and I shall move the Earth.” - Archimedes, on the principle of the lever.
Gangster Summary: Yo so this Arkimedes bloke, he 75 years old drawing shapes in sand when Roman soldier come kill him during war yeah. Before he die tho, man was crazy smart bruv. Work out pi, make war machines that fuck up Roman navy for two years—catapults and shit. But real talk, he invent calculus like 2000 years before anyone else, nobody even understand it till 1906. He want sphere and cylinder on his grave cos that his best proof. Cicero find the grave later all fucked up and forgotten. Man die protecting his city but really he protecting maths innit. Legend say give him place to stand he move whole Earth. Mad ting.
Al-Khwarizmi: The Man Who Named Everything
In 820 CE, Caliph al-Ma’mun built the House of Wisdom in Baghdad and filled it with scholars. Among them was Muhammad ibn Musa al-Khwarizmi, a mathematician from Khwarezm in modern Uzbekistan.
Al-Khwarizmi wrote a book called Kitab al-Jabr wa-l-Muqabala—“The Compendious Book on Calculation by Completion and Balancing.” That word “al-jabr,” meaning restoration or completion, gave us “algebra.” His name, Latinized, gave us “algorithm.” 📚
He did something more important than inventing methods—he imported them. He brought Indian numerals and the concept of zero to the Islamic world, then to Europe. Before this, Europeans were doing arithmetic in Roman numerals. Try multiplying MCMXLIV by DCCCXVIII sometime and you’ll understand what he saved us from.
His algebra book showed how to solve equations systematically. Not just specific problems, but classes of problems. He created procedures that anyone could follow, step by step. That’s what an algorithm is: a recipe that always works if you follow it exactly. 🔢
When his work reached Europe through Latin translations, it revolutionized mathematics. The Hindu-Arabic numeral system he championed made complex calculation possible. Commerce, science, engineering—none of it works without the tools he transmitted.
He didn’t just do mathematics. He made it portable. Lowkey one of the most important knowledge transfers in human history.
“That fondness for science, that affability and condescension which God shows to the learned, that promptitude with which he protects and supports them in the elucidation of obscurities and in the removal of difficulties, has encouraged me to compose a short work on calculating by al-jabr and al-muqabala.” - Al-Khwarizmi, from the introduction to his algebra treatise.
Gangster Summary: Right so in Baghdad year 820, big boss Caliph build House of Wisdom, fill it with smart mans yeah. This al-Khwarizmi guy from Uzbekistan write book bout algebra—word “algebra” come from his book innit. His name give us “algorithm” too. But real talk, he don’t just invent shit, he bring Indian numbers and zero to Islam then Europe. Before him Europeans using Roman numerals for maths—try multiply MCMXLIV by DCCCXVIII bruv, impossible yeah. He show how solve equations step by step, anyone can follow. When his work get to Europe everything change—commerce, science, all that need his numbers. Man didn’t invent maths, he make it work for everyone. Massive ting.
Omar Khayyam: The Poet Who Solved Cubics
Omar Khayyam is famous in the West for the Rubaiyat, those quatrains about wine and roses and the moving finger that writes and moves on. What gets forgotten is that he was a mathematician first. 📖
Born in Nishapur in 1048, he wrote Treatise on Demonstration of Problems of Algebra in 1070. In it, he gave geometric solutions to cubic equations—equations with x³ terms. European mathematicians wouldn’t solve cubics for another 400 years.
He also reformed the Persian calendar, creating one more accurate than the Gregorian calendar Europe adopted five centuries later. His observatory in Isfahan produced astronomical tables that were used for centuries. He wrote on Euclid’s parallel postulate, trying to prove what turned out to be unprovable. 🌙
The poetry came later, maybe as consolation. He lived through the Seljuk conquest, through political instability and religious orthodoxy that didn’t always appreciate mathematicians asking questions. His verses are full of mortality and impermanence, the sense that everything passes.
But his mathematics remains. Those cubic solutions he found by intersecting conic sections? They work as well now as they did in 1070. The calendar he designed still governs Iran.
He understood that wine and roses fade, but that truth is different. Truth you can prove doesn’t age. It just waits for people smart enough to read it. Man was out here solving problems that Europe wouldn’t touch for four centuries—that’s straight fire.
“The moving finger writes, and having writ, moves on: nor all thy piety nor wit shall lure it back to cancel half a line, nor all thy tears wash out a word of it.” - Omar Khayyam, from the Rubaiyat.
Gangster Summary: So Omar Khayyam yeah, West know him for poetry bout wine and roses and shit. But bruv was mathematician first innit. Born 1048 in Nishapur, write book in 1070 solving cubic equations—them x³ things yeah. Europe don’t solve that for 400 more years. He also fix Persian calendar, make it better than one Europe use later. Run observatory, make star tables, try prove geometry shit that turn out impossible. Poetry come later maybe cos life hard—Seljuks taking over, religious mans don’t like questions. His poems all bout everything die and pass away. But his maths? Still work perfect. Calendar still used in Iran today. He know wine and roses fade but truth stay forever, just wait for smart people find it. Man was 400 years ahead, absolute fire.
Fibonacci: The Merchant’s Son
Leonardo Pisano, called Fibonacci—son of Bonacci—grew up in North Africa where his father was a merchant. He learned arithmetic from Arab teachers using Hindu-Arabic numerals. When he returned to Pisa around 1200, he wrote Liber Abaci, the Book of Calculation. 🧮
The book’s message was simple: these Arabic numerals are better than what you’re using. Stop counting on your fingers and calculating with Roman numerals. Here’s how merchants should do accounting, how to calculate interest, how to convert currencies. Practical mathematics for practical people.
But the book contained a problem about rabbits. Suppose a pair of rabbits breeds every month, producing another pair. Each new pair also breeds after one month. How many pairs after twelve months? 🐰
The sequence goes: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… Each number is the sum of the previous two.
Fibonacci probably thought it was just a clever puzzle. He couldn’t have known that this sequence appears in sunflower seed patterns, pine cones, nautilus shells, hurricane spirals, galaxy arms, stock market corrections, and thousands of other natural phenomena. The ratio between consecutive Fibonacci numbers converges to the golden ratio, approximately 1.618, which appears everywhere in art, architecture, and nature.
His real achievement was dragging Europe into modern arithmetic. But his accidental gift was discovering that nature itself seems to count in a particular way, and that way carries his name. Nature really said “bet” to Fibonacci’s sequence and started using it everywhere.
“The nine Indian figures are: 9 8 7 6 5 4 3 2 1. With these nine figures, and with the sign 0… any number may be written.” - Fibonacci, from Liber Abaci.
Gangster Summary: Leonardo Fibonacci, son of Bonacci yeah, grow up in North Africa where his pops was merchant. Learn Arab maths with proper numbers not that Roman numeral bullshit. Come back to Pisa round 1200, write book saying yo, use these Arabic numbers bruv, they better. Show merchants how do accounts proper, interest, currency exchange, all practical shit. But in book he got rabbit problem—how many rabbits you got after 12 months if they breed every month innit. Make sequence 1,1,2,3,5,8,13 and so on, each number is last two added up. He think it just puzzle but turns out this pattern EVERYWHERE—sunflowers, pine cones, shells, hurricanes, galaxies, even stock market. Nature use Fibonacci numbers for everything. Real achievement was bringing modern arithmetic to Europe but accidentally he discover how nature counts. Mans name on the sequence forever.
Descartes: Geometry Meets Algebra
René Descartes slept until noon every day. He considered it essential to his thinking. Queen Christina of Sweden, who hired him as a tutor, insisted on 5 AM lessons. He lasted four months in Stockholm before dying of pneumonia. ❄️
Before Sweden killed him in 1650, he’d revolutionized philosophy and mathematics. His Discourse on Method included an appendix called La Géométrie that changed everything.
The insight seems simple now: you can represent geometric points with pairs of numbers and geometric curves with equations. The horizontal x-axis, the vertical y-axis, coordinates (x,y) marking every point on a plane. Suddenly geometry became algebra and algebra became geometry. 📊
A circle isn’t just a shape anymore—it’s x² + y² = r². A parabola is y = x². Every curve has an equation; every equation has a curve. You can prove geometric theorems with algebra and solve algebraic problems with geometry.
Descartes created analytic geometry, which gave us the tools to describe motion mathematically. Without it, Newton couldn’t have written the Principia. Without it, we couldn’t do calculus, physics, engineering, or navigate spacecraft.
He wanted certainty in an uncertain world. “I think, therefore I am” was his philosophical bedrock—the one thing he couldn’t doubt. But his mathematical legacy might be more durable. The Cartesian coordinate system doesn’t require faith. It just works, whether you’re a philosopher or not. Man really cooked with that x-y axis concept.
“Cogito, ergo sum” (I think, therefore I am). - René Descartes, from Discourse on Method.
Gangster Summary: Rene Descartes sleep till noon every day yeah, say he need it for thinking. Queen of Sweden hire him, make him teach at 5 AM, he dead in four months from cold. But before he die, man change everything bruv. Write book with bit called La Géométrie that proper mental. His idea: you can write geometric shapes as numbers and equations. Make x-axis and y-axis, now every point got coordinates (x,y) innit. Circle ain’t just shape no more, it’s x² + y² = r². Parabola is y = x². Every curve got equation, every equation got curve. Now you can prove geometry with algebra and algebra with geometry. He invent analytic geometry—without it Newton can’t do shit, no calculus, no physics, no rockets to space. Famous for “I think therefore I am” but really his coordinate system change the game forever. Mans proper cooked with that one.
Fermat: The Amateur
Pierre de Fermat was a lawyer in Toulouse. Mathematics was his hobby, something he did between cases. He never published a book, never sought fame, just wrote letters to other mathematicians, filled with theorems he’d discovered. ⚖️
In 1637, he was reading a Latin translation of Diophantus when he wrote something in the margin: x² + y² = z² has infinitely many whole number solutions, but xⁿ + yⁿ = zⁿ has none for any n greater than 2. Then he added: “I have discovered a truly marvelous proof of this proposition, which this margin is too narrow to contain.”
That marginal note became the most famous unsolved problem in mathematics. Fermat’s Last Theorem. Mathematicians worked on it for 358 years. Andrew Wiles finally proved it in 1995, using mathematics that didn’t exist in Fermat’s lifetime. Whatever proof Fermat thought he had, he was probably wrong—but he was right about the theorem. 📝
Fermat also created modern number theory, proved theorems about primes, and with Pascal created probability theory through their correspondence about gambling problems. He developed early versions of calculus before Newton and Leibniz, finding maximums and minimums using what he called “adequality.”
He died in 1665, a successful lawyer who happened to be one of the greatest mathematicians who ever lived. His son published his notes. That’s the only reason we know what he did.
Sometimes the people who change everything aren’t the professionals. Sometimes they’re the obsessed amateurs who can’t help themselves. Fermat was highkey one of the greatest mathematicians ever and it was just his side hustle.
“I have discovered a truly marvelous proof of this proposition, which this margin is too narrow to contain.” - Pierre de Fermat, marginal note that created the most famous unsolved problem in mathematics for 358 years.
Gangster Summary: Pierre de Fermat was lawyer in Toulouse bruv. Maths was just hobby for him, something he do between cases innit. Never publish book, never want fame, just write letters to other maths mans with theorems he find. In 1637 reading book and write in margin: this equation x² + y² = z² got infinite solutions but xⁿ + yⁿ = zⁿ got none when n bigger than 2. Then he say “I got proof but margin too small to write it.” That note become most famous unsolved problem ever yeah. Take 358 years to prove—Andrew Wiles do it 1995 using maths that don’t even exist in Fermat time. Whatever proof Fermat think he had probably bullshit but he right bout theorem. He also invent number theory, probability with Pascal, early calculus and shit. Die 1665, successful lawyer who just happen be one of greatest mathematicians ever. His son publish his notes, only reason we know. Sometimes greatest people ain’t professionals bruv, just obsessed amateurs who can’t stop.
Pascal: Thirty-Nine Years
Blaise Pascal was sick his entire life and dead at 39. In between, he invented the mechanical calculator, created projective geometry, founded probability theory, explained barometric pressure and vacuums, and wrote philosophy that people still read. 🎲
At 16, he proved theorems about conic sections that made Descartes jealous. At 19, he built a calculating machine to help his father with tax calculations—adding and subtracting with gears and wheels. He built 50 versions. They worked, but nobody wanted to manufacture them.
In 1654, a gambler named Chevalier de Méré asked him about dice problems. When should you bet on rolling double sixes? How should you split the pot if you stop mid-game? Pascal corresponded with Fermat, and together they created probability theory—the mathematics of uncertainty. ⚔️
Then Pascal had a religious vision and mostly quit mathematics for theology. He joined Port-Royal, wrote the Pensées, argued about God and infinity. His famous wager: believe in God because the upside is infinite and the downside is finite. It’s not a proof of God’s existence—it’s game theory.
But he kept thinking mathematically. Pascal’s triangle—that pyramid of numbers where each entry is the sum of the two above it—appeared in his Treatise on the Arithmetical Triangle. It contains binomial coefficients, Fibonacci numbers, powers of two, and patterns mathematicians are still discovering.
He was always sick, always in pain, always thinking. Thirty-nine years was enough time to create multiple fields of mathematics and revolutionize how we think about chance, calculation, and infinity.
Some people just burn brighter. Pascal absolutely ate with everything he touched—no cap.
“The heart has its reasons which reason knows nothing of.” - Blaise Pascal, from Pensées.
Gangster Summary: Blaise Pascal sick his whole life, dead at 39 bruv. But in between he invent calculator machine, create geometry, invent probability, explain pressure and vacuums, write philosophy people still read today. At 16 he prove theorems make Descartes jealous yeah. At 19 build calculating machine for his pops—gears and wheels doing addition and subtraction. Build 50 versions but nobody want manufacture them. In 1654 gambler ask him bout dice problems—when you bet on double sixes? How split pot if stop mid-game? Pascal write letters to Fermat, together they invent probability theory, maths of uncertainty innit. Then Pascal have religious vision, quit maths for God shit. Write bout betting on God—upside infinite, downside finite, it’s game theory not proof. But he still do maths—Pascal’s triangle got all kinds patterns, still discovering new shit in it. Always sick, always in pain, always thinking. 39 years enough to create multiple fields and change how we think. Some people just burn brighter mate, Pascal ate with everything.
Newton: The Difficult Genius
Isaac Newton was born on Christmas Day 1642, three months after his father died. He was premature and not expected to survive. His mother remarried and left him with his grandmother. He grew up angry, isolated, and smarter than everyone around him. 🍎
When plague closed Cambridge in 1665-1666, Newton went home for eighteen months. During that time, alone at age 23, he invented calculus, began his work on optics and color, and developed his law of universal gravitation. Apples may or may not have been involved, but the math was real.
He didn’t publish any of it for twenty years. When he finally wrote Philosophiæ Naturalis Principia Mathematica in 1687, it explained why planets orbit the sun, why the moon affects tides, why apples fall—all from three laws of motion and one law of gravitation. He invented the mathematics needed to prove his physics. 📚
The calculus priority dispute with Leibniz was ugly. Newton never forgave anyone who crossed him. He used his position as president of the Royal Society to destroy rivals. He spent years on alchemy and biblical chronology, trying to decode God’s intentions through numbers.
But the Principia remains the most important scientific book ever written. It gave us the clockwork universe, the idea that nature follows mathematical laws we can discover. Everything from space travel to engineering relies on equations Newton wrote.
He died in 1727, wealthy and famous, buried in Westminster Abbey. He never married, had few friends, and was probably the most brilliant and difficult person of his century.
Genius doesn’t require being nice. It just requires being right. Newton’s work was absolutely fire, even if he was kind of mid as a person.
“If I have seen further it is by standing on the shoulders of Giants.” - Isaac Newton, in a letter to Robert Hooke (though possibly a subtle insult given Hooke’s short stature).
Gangster Summary: Isaac Newton born Christmas 1642, three months after his pops die. Premature baby, not expected live. His mum remarry and leave him with grandma. Grow up angry, alone, but smarter than everyone bruv. Plague close Cambridge 1665-66, Newton go home 18 months. During that time, age 23 yeah, he invent calculus, work out optics and colour, develop law of gravity. Apple story maybe bullshit but maths real. Don’t publish nothing for 20 years. Then write Principia in 1687—explain why planets orbit, why moon affect tides, why apples fall. Three laws of motion, one law of gravity, invent maths needed to prove his physics innit. Fight with Leibniz over calculus was nasty—Newton never forgive nobody, use position to destroy rivals. Spend years on alchemy and Bible numerology trying decode God. But Principia most important science book ever bruv. Give us clockwork universe, idea nature follow maths laws. Everything from rockets to engineering use Newton equations. Die 1727, rich and famous, buried Westminster Abbey. Never marry, few friends, most brilliant and difficult person of his time. Don’t need be nice to be genius, just need be right.
Leibniz: The Better Notation
Gottfried Wilhelm Leibniz learned about mathematics late—he was studying law and philosophy when he discovered Descartes and Pascal. By his thirties, he’d invented calculus independently of Newton, created binary arithmetic, invented a calculating machine that could multiply and divide, and was corresponding with every major intellectual in Europe. 💻
His calculus notation—dy/dx for derivatives, ∫ for integrals—was better than Newton’s. More intuitive, more flexible, easier to manipulate. Today we use Leibniz’s notation exclusively. Newton won the priority dispute during his lifetime, but Leibniz won the war that mattered.
Leibniz wasn’t just a mathematician. He was a philosopher, diplomat, librarian, historian, and inventor. He wrote about logic, metaphysics, theology, and linguistics. He tried to create a universal characteristic—a formal language that would make all reasoning as clear as arithmetic. He failed, but the attempt prefigured formal logic and computer science. ⚙️
In 1714, he was in Vienna trying to secure patronage when his employer, the Elector of Hanover, became King George I of England. Leibniz wanted to go to London. The king refused. Newton was there, still angry about calculus, and George I chose sides.
Leibniz died in 1716, alone in Hanover, his funeral attended only by his secretary. No royalty, no dignitaries, no scientific societies. His obituary in the Paris Academy of Sciences came from a friend, not an official tribute.
But his notation lived. His ideas lived. Binary arithmetic powers every computer. His logic work prefigured Boole and Frege. His calculus notation teaches every freshman.
Sometimes vindication takes centuries. Leibniz can wait. Man’s notation was so fire that we ghosted Newton’s version completely—lowkey the ultimate flex.
“It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used.” - Gottfried Wilhelm Leibniz.
Gangster Summary: Gottfried Leibniz learn maths late bruv—studying law and philosophy when he find Descartes and Pascal. By his 30s he invent calculus same as Newton but independent, create binary arithmetic, invent calculator that multiply and divide, talk to every smart person in Europe. His calculus notation—dy/dx for derivatives, ∫ for integrals—way better than Newton’s yeah. More intuitive, easier use. Today we use only Leibniz notation. Newton win argument while alive but Leibniz win long term innit. Man wasn’t just mathematician—philosopher, diplomat, librarian, historian, inventor, all that. Try make universal language for reasoning like arithmetic. Fail but it predict computer science. In 1714 his boss Elector of Hanover become King George I of England. Leibniz want go London but king say no—Newton there still mad bout calculus, king pick Newton side. Leibniz die 1716, alone, funeral only got his secretary. No royals, no dignitary, no scientific society mans. But his notation live, his ideas live. Binary arithmetic run every computer, his logic work predict Boole and Frege, his calculus notation teach every student. Sometimes vindication take centuries bruv, Leibniz can wait.
Euler: Blind and Unstoppable
Leonhard Euler went completely blind in 1771. He was 64 years old and had already published more than any mathematician in history. So he kept going, dictating papers to his assistants for twelve more years. 👁️
He published 886 books and papers during his lifetime. The St. Petersburg Academy was still publishing his backlog fifty years after he died. He wrote about everything: number theory, graph theory, calculus, mechanics, fluid dynamics, optics, astronomy, music theory.
He created so much mathematical notation we take for granted: e for the base of natural logarithms, i for the square root of -1, π for the ratio of circumference to diameter, Σ for summation, f(x) for functions. If you’ve done mathematics, you’ve spoken Euler’s language. 📐
His identity e^(iπ) + 1 = 0 connects five fundamental constants in one beautiful equation. He solved the Königsberg bridge problem, creating graph theory by proving you couldn’t walk across all seven bridges exactly once. He invented topology by studying polyhedra.
He had thirteen children. Several died young. His house burned down, destroying his library. He went blind from cataracts, probably worsened by observing the sun. None of it stopped him.
When he died in 1783, he was calculating the orbit of Uranus. His last words were supposedly “I am dying.” Then he stopped calculating and died.
Euler proved that genius isn’t about perfect conditions or good luck. It’s about relentless productivity and refusing to let anything—including blindness—stop the work. Man went blind and still cooked harder than everyone else—that’s sigma energy right there.
“Read Euler, read Euler, he is the master of us all.” - Pierre-Simon Laplace, advising a young mathematician.
Gangster Summary: Leonhard Euler go completely blind 1771 yeah. He 64 years old, already publish more than any mathematician ever. So he keep going, just tell assistants what write for 12 more years bruv. Publish 886 books and papers while alive. St Petersburg Academy still publishing his leftover work 50 years after he die. Write bout everything—number theory, graph theory, calculus, mechanics, fluids, optics, astronomy, music, all that. He invent so much notation we use today: e for natural log base, i for square root of -1, π for circle ratio, Σ for summation, f(x) for functions. You do maths, you speak Euler language innit. His identity e^(iπ) + 1 = 0 connect five fundamental constants in one beautiful equation. Solve bridge problem, invent graph theory and topology. Got 13 kids, several die young, house burn down with library, go blind from cataracts looking at sun. None of it stop him. When he die 1783, he calculating orbit of Uranus. Last words “I am dying” then stop calculating and die. Man prove genius ain’t bout perfect conditions or luck bruv, it’s bout never stopping even when you go blind. Laplace say “read Euler, he master of us all.”
Gauss: The Prince
Carl Friedrich Gauss discovered a pattern in prime numbers at age 15. At 19, he proved that a regular 17-sided polygon could be constructed with compass and straightedge, solving a 2,000-year-old problem. At 22, he proved the fundamental theorem of algebra for his doctorate. 👑
He was called the Prince of Mathematicians and he earned it. Number theory, differential geometry, statistics, astronomy, geodesy, magnetism—he dominated every field he touched. The Gaussian distribution (the bell curve) describes everything from test scores to measurement errors. His work on curved surfaces laid groundwork Einstein used for general relativity.
But Gauss was cautious about publishing. His notebooks, discovered after his death, contained theorems other mathematicians spent decades rediscovering. He’d proven them years earlier and never told anyone. His motto was “few, but ripe”—only publish work that’s perfect. 📊
This cost mathematics decades of progress. He discovered non-Euclidean geometry but never published it, afraid of controversy. When others published it later, they got credit for what Gauss had known privately for years.
He was difficult personally. His first wife died young. His relationship with his sons was cold. He opposed giving teaching positions to talented mathematicians, blocking their careers. He believed mathematics was a young man’s game and didn’t want competition.
But the work was undeniable. Gauss is on Germany’s old ten-mark note with a normal distribution curve. Seven things in mathematics are named “Gaussian.” He saw farther and deeper than almost anyone before or since.
Perfection has a price. Sometimes that price is progress shared too slowly. Gauss kept receipts in his notebooks showing he’d solved problems years before others, but that’s kind of sus when you never actually publish them.
“Mathematics is the queen of sciences and number theory is the queen of mathematics.” - Carl Friedrich Gauss.
Gangster Summary: Carl Gauss find pattern in prime numbers age 15 bruv. Age 19 prove you can make 17-sided shape with compass and straightedge—problem been unsolved 2000 years. Age 22 prove fundamental theorem of algebra for doctorate. They call him Prince of Mathematicians and he earn that shit yeah. Number theory, geometry, statistics, astronomy, magnetism—dominate everything. Gaussian distribution (bell curve) describe test scores, errors, everything innit. His work on curved surfaces Einstein use later for relativity. But Gauss cautious bout publishing. His notebooks found after he die, got theorems other mathematicians spend decades rediscovering. He prove them years earlier, never tell nobody. His motto “few but ripe”—only publish perfect work. This cost maths decades of progress bruv. He discover non-Euclidean geometry, never publish it, scared of controversy. When others publish later they get credit for what Gauss know years before. He difficult person—first wife die young, relationship with sons cold, block talented mathematicians from jobs cos he think maths is young man’s game and don’t want competition. But work undeniable. Gauss on Germany 10-mark note with bell curve. Seven things in maths named “Gaussian.” Saw farther than almost anyone. Perfection got price—sometimes that price is keeping shit to yourself too long.
Cauchy: Making It Rigorous
Augustin-Louis Cauchy made calculus honest. For 150 years after Newton and Leibniz, calculus worked but nobody could quite explain why. Proofs relied on intuition and loose language about infinitesimals. It was effective but imprecise—and precision is what mathematics demands. 📏
Cauchy, working in Paris in the 1820s, created the rigorous foundations. He properly defined limits, continuity, derivatives, and integrals using epsilon-delta arguments. He proved the theorems that had been assumed true. He created complex analysis, showing that calculus works with imaginary numbers.
He wrote prolifically—almost 800 papers—but was terrible at presenting his work. His lectures at the École Polytechnique were notoriously confusing. He’d digress, go too fast, assume too much. Students complained. He kept writing anyway. 🎓
He was also a royalist during revolutionary times, which meant exile and political trouble. He opposed the July Monarchy and refused to take loyalty oaths, costing him academic positions. His politics were reactionary, his religious views rigid. He wasn’t easy to like.
But modern analysis—the rigorous study of calculus, continuity, and convergence—starts with Cauchy. His definition of a limit is what every calculus student learns today. His integral theorem is fundamental to complex analysis. His work on differential equations shaped engineering and physics.
Mathematics doesn’t care about your politics or personality. It cares whether your proofs work. Cauchy’s proofs worked, and they form the foundation of how we think about continuous change and convergent series.
Sometimes being difficult doesn’t matter if you’re correct. Cauchy took calculus from vibes-based hand-waving to actually rigorous—no cap, that’s what math needed.
“Men pass away, but their deeds abide.” - Augustin-Louis Cauchy (inscription on his tomb).
Gangster Summary: Augustin-Louis Cauchy make calculus honest bruv. For 150 years after Newton and Leibniz, calculus work but nobody explain why proper. Proofs based on intuition and loose talk bout infinitesimals yeah. It work but not precise, and maths need precision innit. Cauchy working in Paris 1820s, create rigorous foundations. He properly define limits, continuity, derivatives, integrals using epsilon-delta arguments. Prove theorems people just assume true. Create complex analysis, show calculus work with imaginary numbers. Write almost 800 papers but terrible at teaching—lectures at École Polytechnique notoriously confusing. He digress, go too fast, assume too much. Students complain, he keep writing anyway. Also he royalist during revolution times, mean exile and political trouble. Oppose July Monarchy, refuse take loyalty oaths, cost him jobs. His politics reactionary, religious views rigid, not easy like. But modern analysis—rigorous study of calculus, continuity, convergence—start with Cauchy. His definition of limit what every student learn today. His integral theorem fundamental to complex analysis. His differential equations work shape engineering and physics. Maths don’t care bout your politics or personality bruv, care if proofs work. Cauchy proofs work, they foundation of how we think bout continuous change. Sometimes being difficult don’t matter if you correct.
Galois: The Night Before the Duel
Évariste Galois stayed up all night on May 29, 1832, writing mathematics. He was 20 years old and knew he was dying in the morning. The duel was over a woman—Stéphanie-Félicie Poterin du Motel—and Galois had no illusions about his chances. ⚔️
So he wrote. He filled sheets with theorems and scribbled notes in the margins: “I have not time; I have not time.” He explained which equations could be solved by radicals and which couldn’t—a 350-year-old problem. He invented group theory, though he didn’t call it that. He saw patterns in permutations that revealed deep structure in algebra.
At dawn, he fought the duel with pistols. He was shot in the stomach and died the next day of peritonitis. His funeral triggered a riot—Galois was a republican revolutionary, too radical even for most republicans. The police arrested dozens of mourners. 💀
His mathematical papers sat in obscurity for fourteen years until Joseph Liouville read them and realized what Galois had done. The boy had created an entirely new branch of mathematics the night before he died, and it was so advanced that mathematicians needed decades to fully understand it.
Galois theory now connects field theory, group theory, and polynomial equations. It explains why you can’t trisect an angle with compass and straightedge, why you can’t solve fifth-degree equations with radicals. It’s fundamental to modern algebra.
He wrote his mother a letter before the duel: “I beg patriots and my friends not to reproach me for dying otherwise than for my country. I die the victim of an infamous coquette. It is in a miserable brawl that my life is extinguished.”
Twenty years old. A woman’s name. A night of mathematics that would last forever. Man literally cooked an entire field of mathematics knowing he was about to die—that’s the most sigma thing ever.
“I have not time; I have not time.” - Évariste Galois, scribbled in the margins of his papers the night before his death.
Gangster Summary: Évariste Galois stay up all night May 29, 1832 writing maths bruv. He 20 years old, know he dying in morning. Duel over woman—Stéphanie-Félicie something—and Galois know he ain’t winning. So he write. Fill sheets with theorems, scribble in margins “I have not time, I have not time.” Explain which equations can be solved and which can’t—350-year-old problem yeah. Invent group theory though he don’t call it that. See patterns in permutations that reveal deep structure in algebra innit. At dawn he fight duel with pistols. Get shot in stomach, die next day. His funeral trigger riot—Galois was republican revolutionary, too radical even for republicans. Police arrest dozens of mourners. His maths papers sit forgotten 14 years till Joseph Liouville read them and realize what Galois done. Boy create entire new branch of maths night before he die, so advanced mathematicians need decades understand it. Galois theory now connect field theory, group theory, polynomial equations. Explain why you can’t trisect angle, can’t solve fifth-degree equations with radicals. Fundamental to modern algebra bruv. He write his mum before duel: “I die victim of infamous woman. My life extinguished in miserable brawl.” 20 years old, woman’s name, night of maths that last forever.
Riemann: Spaces Nobody Could See
Bernhard Riemann was shy, sickly, and poor. He stuttered when nervous and struggled through his doctorate at Göttingen. For his habilitation in 1854, he had to give a lecture. His supervisor, Gauss, chose the topic: the foundations of geometry. 🌌
Riemann delivered one of the most important mathematical lectures ever given. He described curved spaces of arbitrary dimensions—geometries where parallel lines could converge or diverge, where the Pythagorean theorem didn’t hold. Spaces that bent and twisted according to intrinsic properties, not because they were embedded in some higher dimension.
Gauss, who’d thought about non-Euclidean geometry privately for decades, was stunned. Riemann had gone far beyond what anyone imagined.
But Riemann’s health was failing. Tuberculosis was killing him slowly. He traveled to Italy for the climate, kept working, returned to Germany, went back to Italy. He married in 1862. He had one child. He was dying and he knew it. 💫
His work on complex analysis created Riemann surfaces. His zeta function, defined for complex numbers, seemed to encode mysterious patterns in prime numbers. In 1859, he published a paper on prime number distribution containing what’s now called the Riemann Hypothesis: all non-trivial zeros of the zeta function have real part equal to 1/2.
Nobody’s proven it yet. It’s the most important unsolved problem in mathematics, worth a million dollars from the Clay Institute. Riemann stated it almost as an aside—“one would of course like to have a rigorous proof of this; I have meanwhile temporarily put aside the search for such after some fleeting futile attempts.”
He died in 1866, age 39, in Italy. Sixty years later, Einstein used Riemannian geometry to describe spacetime in general relativity. The curved four-dimensional space that gravity creates? Riemann saw it coming in 1854, though he thought he was just talking about abstract geometry.
Some minds see geometries that won’t be discovered for generations. Riemann was out here describing spaces that didn’t exist yet—absolutely delulu in the best way possible.
“If only I had the theorems! Then I should find the proofs easily enough.” - Bernhard Riemann.
Gangster Summary: Bernhard Riemann shy, sickly, poor bruv. Stutter when nervous, struggle through doctorate at Göttingen. For habilitation 1854 he gotta give lecture. His supervisor Gauss pick topic: foundations of geometry. Riemann deliver one of most important maths lectures ever yeah. Describe curved spaces of any dimensions—geometries where parallel lines converge or diverge, where Pythagorean theorem don’t hold. Spaces that bend and twist according to intrinsic properties, not cos embedded in higher dimension innit. Gauss who been thinking bout non-Euclidean geometry private for decades, stunned. Riemann gone way beyond what anyone imagine. But Riemann health failing—tuberculosis killing him slow. Travel to Italy for climate, keep working, go back Germany, back to Italy. Marry 1862, got one kid, dying and he know it. His work on complex analysis create Riemann surfaces. His zeta function seem encode mysterious patterns in prime numbers. In 1859 publish paper with Riemann Hypothesis: all non-trivial zeros of zeta function got real part equal to 1/2. Nobody prove it yet—most important unsolved problem in maths, worth million dollars. Riemann state it almost like aside, say he put aside search after “fleeting futile attempts.” Die 1866 age 39 in Italy. 60 years later Einstein use Riemannian geometry for general relativity. Curved 4D space that gravity creates? Riemann see it coming 1854 though he think he just talking bout abstract geometry. Some minds see geometries won’t be discovered for generations bruv.
Cantor: Infinite and Mad
Georg Cantor proved that some infinities are bigger than others, and it broke him. 🔢
In 1874, he showed that the rational numbers (fractions) can be counted—you can list them in a sequence, one, two, three. Infinite, yes, but countable. The real numbers (everything on the number line) cannot be counted. The infinity of real numbers is a larger infinity than the infinity of counting numbers.
His proof was elegant: assume you could list all real numbers between 0 and 1, then construct a number not on the list by making its nth digit different from the nth digit of the nth number. Therefore your list was incomplete. Therefore the real numbers are uncountable. 🧮
His contemporaries hated it. Leopold Kronecker called him a “corrupter of youth” and blocked his appointment to the University of Berlin. Henri Poincaré called Cantor’s work a “disease.” The idea that mathematics dealt with completed infinities, that infinity came in different sizes, violated mathematical intuition.
Cantor kept going. He created set theory, defined ordinal and cardinal numbers for infinite sets, and built a hierarchy of infinities—aleph-null, aleph-one, aleph-two, climbing forever. He proposed the continuum hypothesis: there’s no infinity between the counting numbers and the real numbers.
The attacks and rejection drove him to depression. He was hospitalized multiple times, suffered nervous breakdowns, spent his final years in poverty and mental anguish. He died in a sanatorium in 1918.
But he was right. Set theory became the foundation of modern mathematics. His transfinite numbers are now standard. Infinity doesn’t mean “really big”—it means precisely what Cantor defined it to mean.
David Hilbert defended him: “No one shall expel us from the paradise that Cantor has created.” But paradise cost Cantor his sanity. Man proved some infinities hit different than others, and the math community lowkey destroyed him for it.
“The essence of mathematics lies in its freedom.” - Georg Cantor.
Gangster Summary: Georg Cantor prove some infinities bigger than others and it break him bruv. In 1874 he show rational numbers (fractions) can be counted—you can list them one, two, three. Infinite yeah but countable. Real numbers (everything on number line) cannot be counted. Infinity of real numbers is LARGER infinity than infinity of counting numbers innit. His proof elegant: assume you list all real numbers between 0 and 1, then construct number not on list by making nth digit different from nth digit of nth number. Therefore list incomplete. Therefore real numbers uncountable. His contemporaries hate it—Kronecker call him “corrupter of youth,” block his appointment to University of Berlin. Poincaré call Cantor work “disease.” Idea that maths deal with completed infinities, that infinity come in different sizes, violate maths intuition yeah. Cantor keep going. Create set theory, define ordinal and cardinal numbers for infinite sets, build hierarchy of infinities—aleph-null, aleph-one, aleph-two, climbing forever. Propose continuum hypothesis: no infinity between counting numbers and real numbers. Attacks and rejection drive him to depression. Hospitalized multiple times, nervous breakdowns, final years in poverty and mental anguish. Die in sanatorium 1918. But he right bruv. Set theory become foundation of modern maths. His transfinite numbers now standard. Infinity don’t mean “really big”—mean precisely what Cantor define. Hilbert defend him: “No one expel us from paradise Cantor created.” But paradise cost Cantor his sanity.
Poincaré: The Last Universal Mathematician
Henri Poincaré understood all of mathematics. He was the last person who could claim that—after him, the field became too vast, too specialized for any one mind to contain it all. 🧠
Born in 1854, he revolutionized topology, created qualitative dynamics (chaos theory before it had a name), made fundamental contributions to celestial mechanics, worked on special relativity before Einstein, and posed problems that took a century to solve.
His conjecture about three-dimensional spheres—that every simply connected, closed 3-manifold is homeomorphic to a 3-sphere—was finally proven in 2003 by Grigori Perelman. It took 99 years and earned a million-dollar prize that Perelman refused. 🌍
Poincaré discovered mathematical chaos in 1890 while working on the three-body problem—predicting how three planets interact gravitationally. He found that tiny changes in initial conditions could produce wildly different outcomes. The universe wasn’t the clockwork machine Newton implied. It was sensitive, unpredictable, chaotic.
He wrote philosophy of science, explaining that scientific theories are conventions we choose for convenience. He nearly developed special relativity before Einstein—he had the Lorentz transformations and much of the mathematics. But he couldn’t quite make the conceptual leap about the nature of time and space.
Poincaré died unexpectedly in 1912, at 58, from a blood clot after routine surgery. By then, mathematics had grown so large that no one person could master it all. Einstein had published special and general relativity. The twentieth century was arriving with specialization.
But Poincaré had seen it coming. His work on topology and chaos showed that mathematics was entering new territory—more abstract, more complex, more fragmented. He stood at the hinge point, the last mathematician who could see the whole landscape before it became too vast to map. Man really was the final boss of universal mathematical knowledge—absolutely bussin intellect.
“Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house.” - Henri Poincaré.
Gangster Summary: Henri Poincaré understand ALL of maths bruv. Last person who can claim that—after him, field become too vast, too specialized for one mind contain it all yeah. Born 1854, revolutionize topology, create chaos theory before it got name, make fundamental contributions to celestial mechanics, work on special relativity before Einstein, pose problems take century to solve. His conjecture bout three-dimensional spheres finally proven 2003 by Perelman—take 99 years, earn million-dollar prize that Perelman refuse innit. Poincaré discover mathematical chaos 1890 working on three-body problem—predicting how three planets interact gravitationally. He find tiny changes in initial conditions produce wildly different outcomes. Universe not clockwork machine Newton implied—it sensitive, unpredictable, chaotic. Write philosophy of science, explain scientific theories are conventions we choose for convenience. Nearly develop special relativity before Einstein—got Lorentz transformations and much of maths. But couldn’t make conceptual leap bout nature of time and space. Poincaré die unexpectedly 1912, age 58, from blood clot after routine surgery. By then maths grown so large no one person master it all. Einstein published relativity, twentieth century arriving with specialization. But Poincaré seen it coming. His work on topology and chaos show maths entering new territory—more abstract, more complex, more fragmented. He stand at hinge point, last mathematician see whole landscape before it become too vast to map bruv. Say “science built of facts like house built of stones, but accumulation of facts no more science than heap of stones is house.”
Hilbert: The Twenty-Three Problems
In 1900, David Hilbert stood before the International Congress of Mathematicians in Paris and announced twenty-three problems that would define mathematics for the twentieth century. Some were solved quickly. Some remain unsolved. Some were proven to have no solution. 📋
Hilbert believed mathematics should be complete and consistent—that every true statement could be proven from clear axioms using formal logic. He wanted to axiomatize all of mathematics the way Euclid had axiomatized geometry.
He formalized geometry, removing the ambiguities in Euclid. He pioneered functional analysis—infinite-dimensional vector spaces that became essential for quantum mechanics. He proved fundamental theorems about invariant theory. His name is on Hilbert spaces, Hilbert’s basis theorem, Hilbert’s Nullstellensatz, and dozens of other concepts. 🎯
But in 1931, Kurt Gödel proved that Hilbert’s program was impossible. Any formal system strong enough to include arithmetic must be either incomplete or inconsistent. There are true statements that cannot be proven. Mathematics cannot be fully axiomatized.
Hilbert never fully accepted this. He’d spent decades building toward completeness and consistency. Gödel showed it was impossible—not difficult, not complicated, but logically impossible. The dream was dead.
But Hilbert’s twenty-three problems still shaped mathematics. The Riemann Hypothesis (Problem 8) remains unsolved. The continuum hypothesis (Problem 1) was proven independent of standard axioms—neither provable nor disprovable. Problem 10, about Diophantine equations, was solved negatively—there’s no general algorithm.
Hilbert lived through World War I and into the Nazi era. He watched colleagues dismissed and exiled. When asked if mathematics in Göttingen had suffered from the loss of Jewish mathematicians, he replied: “Suffered? It doesn’t exist anymore.”
He died in 1943. The funeral was attended by fewer than a dozen people. The greatest mathematician of his generation, buried in wartime obscurity.
But his problems remain. They’re still guiding questions for mathematicians today. Hilbert really thought he could make all of math complete and consistent—highkey ambitious, but Gödel showed him why that’s literally impossible.
“We must know. We will know.” - David Hilbert (engraved on his tombstone, despite Gödel proving this impossible).
Gangster Summary: In 1900 David Hilbert stand before International Congress of Mathematicians in Paris, announce 23 problems that define maths for twentieth century yeah. Some solved quick, some still unsolved, some proven have no solution. Hilbert believe maths should be complete and consistent—every true statement can be proven from clear axioms using formal logic. He want axiomatize all maths like Euclid axiomatize geometry innit. He formalize geometry, remove ambiguities in Euclid. Pioneer functional analysis—infinite-dimensional vector spaces essential for quantum mechanics. Prove fundamental theorems bout invariant theory. His name on Hilbert spaces, Hilbert basis theorem, Hilbert Nullstellensatz, dozens other concepts bruv. But in 1931 Gödel prove Hilbert program impossible. Any formal system strong enough include arithmetic must be either incomplete or inconsistent. There are true statements cannot be proven. Maths cannot be fully axiomatized. Hilbert never fully accept this—he spend decades building toward completeness and consistency. Gödel show it impossible—not difficult, not complicated, but logically impossible. Dream dead. But Hilbert 23 problems still shape maths. Riemann Hypothesis (Problem 8) still unsolved. Continuum hypothesis (Problem 1) proven independent of standard axioms—neither provable nor disprovable. Problem 10 bout Diophantine equations solved negatively—no general algorithm. Hilbert live through World War I and into Nazi era. Watch colleagues dismissed and exiled. When asked if maths in Göttingen suffered from loss of Jewish mathematicians, he reply: “Suffered? It doesn’t exist anymore.” Die 1943, funeral attended by fewer than dozen people. Greatest mathematician of generation, buried in wartime obscurity. But his problems remain, still guiding questions for mathematicians today. Tombstone say “We must know. We will know” even though Gödel prove this impossible.
Emmy Noether: The Revolution Nobody Noticed
When Emmy Noether applied to the University of Erlangen in 1900, women weren’t allowed to enroll. She had to get special permission to audit classes. She couldn’t earn a degree until the rules changed in 1904. She couldn’t get a faculty position for another fifteen years. 👩🔬
In 1915, Hilbert and Felix Klein invited her to Göttingen. The faculty objected: “What will our soldiers think when they return to the university and find that they are required to learn at the feet of a woman?” Hilbert replied: “I do not see that the sex of the candidate is an argument against her admission. After all, we are a university, not a bath house.”
She lectured anyway, sometimes under Hilbert’s name. In 1918, she proved what’s now called Noether’s Theorem: every symmetry in physics corresponds to a conservation law. Time symmetry gives conservation of energy. Space symmetry gives conservation of momentum. Rotational symmetry gives conservation of angular momentum. ⚛️
This wasn’t just mathematics—it was fundamental physics expressed in mathematical language. Einstein studied her theorem and called it “penetrating mathematical thinking.”
But Noether’s real contribution was creating modern abstract algebra. She developed ring theory, group theory, and the axiomatic approach to algebra. She thought in terms of structures and mappings, not just calculations. Her influence shaped twentieth-century mathematics more than most realize.
In 1933, the Nazis dismissed her for being Jewish. She emigrated to America and taught at Bryn Mawr College. In 1935, she died suddenly from complications after surgery for an ovarian cyst. She was 53.
Einstein wrote her obituary: “In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began.”
But during her life, she couldn’t get a proper faculty position in Germany. She lectured for free, worked unpaid, and revolutionized mathematics anyway.
Sometimes the revolution happens without anyone noticing until it’s over. Noether’s work was so fire that Einstein himself had to stan—but she couldn’t even get a real job because of her gender.
“My methods are really methods of working and thinking; this is why they have crept in everywhere anonymously.” - Emmy Noether.
Gangster Summary: When Emmy Noether apply to University of Erlangen 1900, women not allowed enroll bruv. She gotta get special permission just audit classes. Can’t earn degree till rules change 1904. Can’t get faculty position for another 15 years innit. In 1915 Hilbert and Klein invite her to Göttingen. Faculty object: “What our soldiers think when return and find they gotta learn from woman?” Hilbert reply: “Sex of candidate not argument against admission. We university, not bath house.” She lecture anyway, sometimes under Hilbert name. In 1918 she prove Noether Theorem: every symmetry in physics correspond to conservation law. Time symmetry give conservation of energy. Space symmetry give conservation of momentum. Rotational symmetry give conservation of angular momentum yeah. This not just maths—fundamental physics expressed in maths language. Einstein study her theorem, call it “penetrating mathematical thinking.” But Noether real contribution creating modern abstract algebra. She develop ring theory, group theory, axiomatic approach to algebra. Think in terms of structures and mappings, not just calculations. Her influence shape twentieth-century maths more than most realize bruv. In 1933 Nazis dismiss her for being Jewish. She emigrate America, teach at Bryn Mawr College. In 1935 die suddenly from complications after surgery for ovarian cyst—she 53. Einstein write her obituary: “most competent living mathematicians say Fräulein Noether most significant creative mathematical genius produced since higher education of women began.” But during life she couldn’t get proper faculty position in Germany. Lecture for free, work unpaid, revolutionize maths anyway. Sometimes revolution happen without anyone noticing till it over. She say “my methods really methods of working and thinking, this why they crept in everywhere anonymously.”
Gödel: Starving for Truth
Kurt Gödel proved in 1931 that mathematics is necessarily incomplete. Any formal system strong enough to include arithmetic contains true statements that cannot be proven within that system. And no consistent system can prove its own consistency. 🤯
He was 25 years old.
Hilbert wanted completeness—all truths provable from clear axioms. Gödel showed this was impossible. Not difficult. Not impractical. Logically impossible.
The proof was ingenious: Gödel constructed a statement that essentially says “This statement is not provable.” If it’s false, then it IS provable, making the system inconsistent. If it’s true, then it’s an unprovable truth, making the system incomplete. Either way, you lose. 🧩
Mathematics would never be the same. There are limits to what we can know, built into the structure of logic itself. Some truths exist beyond proof.
Gödel kept working—on set theory, on the continuum hypothesis, on relativity. He found solutions to Einstein’s equations that allowed time travel. Einstein walked with him daily at Princeton’s Institute for Advanced Study, partly for the conversation, partly to make sure Gödel was okay.
Because Gödel wasn’t okay. He was paranoid, anxious, convinced people were trying to poison him. His wife Adele managed his meals, convinced him to eat. When she was hospitalized in 1977, Gödel stopped eating entirely. He starved himself to death, weighing 65 pounds when he died in 1978.
The death certificate listed “malnutrition and inanition caused by personality disturbance.” He thought logic could reveal all truth, then proved it couldn’t, then spent his life looking for truths beyond logic’s reach.
His incompleteness theorems stand among the most important intellectual achievements of the twentieth century. They changed philosophy, mathematics, computer science, and how we understand the limits of knowledge.
But they couldn’t save him from himself. Some truths you prove. Others you just live with. Gödel proved that some truths are literally unprovable and then starved himself to death from paranoia—man was delulu in the tragic sense.
“Either mathematics is too big for the human mind, or the human mind is more than a machine.” - Kurt Gödel.