Notes - The MANIAC

April 26, 2025

Chapter 1: Paul or The Discovery of the Irrational

Paul's Tragic Death and His Son's Suffering

On September 25, 1933, the Austrian physicist Paul Ehrenfest entered Professor Jan Waterink’s Pedagogical Institute for Afflicted Children in Amsterdam, where he fatally shot his fifteen-year-old son, Vassily, who suffered from Down syndrome, before taking his own life. Paul died instantly, but Vassily endured agony for hours before being pronounced dead by his doctors. Vassily, known as Wassik, had been moved to Amsterdam in January 1933 because his father feared for his safety in Jena, Germany, due to the Nazi regime. Wassik had severe mental and physical disabilities, experiencing knee pain that often prevented him from standing, yet he maintained a boundless enthusiasm. Albert Einstein, a close friend of Paul, affectionately called Wassik "patient little crawlikins". Despite spending most of his life institutionalized, Wassik was cheerful, sending postcards and letters to his parents, describing new learnings, his best friend's illness, his efforts to be a good boy, and his affections for two girls and his teacher, Mrs. Gottlieb. Paul, primarily a teacher, was moved to tears by Wassik's thoughts.

Paul's Lifelong Depression and Intellectual Gifts

Paul Ehrenfest suffered from extreme melancholy and crippling depression throughout his life, having been a weak and frequently ill boy. He often feigned ailments to stay home with his mother, as if foretelling her death when he was ten. This anticipation of loss, followed by his father's death six years later, haunted him until his suicide at age fifty-three. Despite his internal struggles, Paul was intellectually gifted, excelling as a student and being well-liked by peers and teachers, though he lacked self-worth. He was not an introvert; he openly shared his vast knowledge and remarkable ability to simplify complex ideas into understandable images and metaphors, connecting concepts from diverse fields. His mind was "fully porous," absorbing everything without differentiation, making him feel "raw and exposed" to constant information flow. Even after becoming a distinguished professor, succeeding Hendrik Lorentz at Leiden University, his only true joy came from selflessly giving to others, to the point where he "distributed all that was living and active in him" without building personal reserves.

Paul's Scientific Contributions and Critical Acumen

As a physicist, Paul Ehrenfest did not make earth-shattering discoveries but commanded immense respect from figures like Niels Bohr, Paul Dirac, and Wolfgang Pauli. Albert Einstein felt an immediate kinship with Paul, noting their shared "dreams and aspirations". These friends admired his critical and intellectual abilities, his ethics, character, and an overwhelming desire to understand the "heart of the matter," which he called "der springende Punkt". For Ehrenfest, deriving a logical result was insufficient; true understanding was a "full-body experience" that involved one's entire being. An atheist, doubter, and skeptic, his rigid standards for truth sometimes made him a figure of fun among peers, as seen in a 1932 parody of Faust where he was cast as Heinrich Faust, unwilling to be convinced of the neutrino's existence. Known as the "Conscience of Physics," a nickname with a hidden barb due to his opposition to the direction physics was taking, he was nonetheless sought out by colleagues who would test their ideas on him and his wife, Tatyana Alexeyevna Afanassjewa, an accomplished mathematician.

The Influence of Ludwig Boltzmann

Tatyana co-authored some of Ehrenfest’s most significant scientific papers, including a summary article on statistical mechanics that helped him succeed Lorentz. This subject was favored by Ehrenfest's mentor, Ludwig Boltzmann, a trailblazer who discovered the role of probability in atomic behavior and a strong advocate of the atomic hypothesis. Like Ehrenfest, Boltzmann suffered from severe bouts of mania and depression, compounded by harsh criticism for his revolutionary ideas, especially from Ernst Mach, who questioned the existence of atoms. Boltzmann, nicknamed "the Bull" for his tenacity, despaired at his critics' ferocity, and despite laying down a fundamental equation of modern physics (statistical interpretation of thermodynamics' second law), his mental disorder constantly worsened, akin to increasing entropy. He feared losing his mind during lectures and, towards the end of his life, suffered severe asthma, failing eyesight, and unbearable headaches. In September 1906, Boltzmann committed suicide by hanging himself at a hotel in Duino, while his wife and daughter were swimming. Boltzmann's motto, "Speak the truth, write with clarity, and defend it to your very end," was deeply embraced by Paul.

Paul's Struggle with Quantum Mechanics and Antisemitism

Ehrenfest was admired for his ability to clarify others' ideas and passionately transmit knowledge. Arnold Sommerfeld, a German theoretical physicist, described him as lecturing "like a master," making difficult concepts concrete and intuitively clear, though he also feared Ehrenfest's reputation as "the grand inquisitor of physics". Paul would pitilessly point out flaws in arguments, including his own, a role particularly vital at the 1927 Solvay Conference, where he mediated between Einstein (who abhorred chance in quantum mechanics) and Bohr (who championed a new physics for the subatomic world). Ehrenfest famously scribbled a Bible verse about the confounding of languages during the raging arguments, which quantum mechanics ultimately won. Despite siding with the new physics, Paul felt a "fundamental line had been crossed," sensing a "demon" or "genie" had infiltrated physics, making the world seem less solid and real. He humorously, yet despairingly, wrote to Einstein about "a special section in purgatory for professors of quantum mechanics!". By May 1931, he confessed to Niels Bohr a complete loss of contact with theoretical physics, unable to grasp the "flood of articles and books," feeling like a "dog that, totally exhausted, was running after a streetcar carrying his master out of sight". He saw quantum revolution as "stagnation and even degeneration," detesting its "awful abstractions," "incessant focus on tricks and techniques," and the "mathematical plague" that replaced intuition with "brute-force artillery" and formulae. He particularly disliked John von Neumann's "terrifying mathematical guns" and the "infinite Heisenberg-Born-Dirac-Schrödinger sausage-machine factory". He lamented that younger students were becoming "relays in a telephone network" without realizing mathematics was "inhuman, like every truly diabolic machine" that could kill those not conditioned to it. His self-criticism and inferiority complex worsened, as he was not a "computer" who could calculate with ease. By 1930, his letters were filled with "death and despair," likening his life to a "chaos" seen by a gambler or alcoholic. This inner turmoil mirrored Europe's economic and political instability. Though officially nondenominational (having given up his religion to marry Tatyana in 1904), rising antisemitism fueled morbid thoughts. In 1933, he proposed a mass suicide of eminent Jewish academics to "prick the German conscience," an idea Samuel Goudsmit furiously rejected as absurd. Hitler's regime, barely two months old, had enacted laws risking Jewish government employees, which convinced Ehrenfest that the extermination of the "Jewish 'plague'" would be "90 percent effective". In his final year, he helped Jewish scientists find work outside Germany, despite having lost all hope for himself. His suicidal fantasies, initially self-focused, began to include Wassik, as he could not bear to leave his wife with his care, or burden his older children, Tatyana, Galinka, or Paul Jr.. He expressed a wish that his daughters "should not in the future have to work themselves to the bone simply to keep their idiot brother alive" to his lover, Nelly Posthumus Meyjes.

The Affair with Nelly and the Concept of the Irrational

Paul's intense love affair with Nelly Posthumus Meyjes brought him some joy but also worsened his mental state. His wife, Tatyana, initially condoned the affair, hoping it would soothe his mind and distract him from his obsessions with chess and unfinished physics work. Their marriage had been happy, based on mutual understanding and shared intellectual interests, but Nelly, an art historian, possessed a dark side and control over her own death wish that Paul lacked. Paul was captivated by Nelly's intelligence, looks, and her lecture on a Pythagorean myth about the "disharmony of the world and the discovery of the irrational," which became a central obsession in his final year, contrasting with his worries about the Nazis. Nelly explained that nature contains things beyond proportion and categorization, "outliers, singularities, monstrosities" that defy measurement and lie at the root of disharmony and chaos. For the Greeks, discovering the irrational was a heinous, death-punishable crime, with legends speaking of the discoverer being banished or drowned. This knowledge, she said, had to be suppressed to preserve natural harmony, as existence depended on "unseen threads that bind all things together". Nelly stated this taboo wasn't just ancient, but central to Western philosophy and science, as Kant argued science needed to view nature as a totality. She warned that nature might be "utterly chaotic," a "terrifying possibility" that would be a "death blow to science, philosophy, and rationality," but which artists had embraced as the driving force behind vanguard movements—a "rush of madness" that permitted everything and recognized no laws or truth. Paul was entranced, bombarding Nelly with questions and spending the night with her. The affair, coupled with his depression, convinced him he was related to the Pythagorean sage and caused him to see "disharmony and turbulence everywhere," losing all sense of order in the universe. He saw the irrational in Hitler Youth chants, warmongering politicians, "blind proponents of endless progress," and even his colleagues' "revolutionary ideas" as the "industrialization of physics". He wrote to Einstein, whose son Eduard was schizophrenic, lamenting a "dark, unconscious force" confusing reason with its opposite, making them "pray to the wrong god". Afraid, Nelly urged Paul to write his childhood recollections, but he felt increasingly disconnected, unable to recognize himself in the mirror. Torn between Tatyana and Nelly, he felt an "unknown force" leading him to suicide. He wrote to Nelly, "Why are people like me condemned to continue living?" and confessed that love brought suffering, suggesting it was one's "duty to put an end to one’s life as soon as possible, before causing hideous destruction". Tatyana sought divorce, then agreed to stop proceedings if he left Nelly. Paul agreed but could not, and eventually filed for divorce himself, having already written his suicide note to friends, including Bohr and Einstein. In the note, he spoke of his unbearable burden, his inability to follow physics, and his concentration on "the precise details of suicide," stating he would kill Wassik first.

The Nazis and Paul's Last Act

In May 1933, Paul traveled to Berlin, witnessing Nazi storming of trade unions and the burning of twenty thousand "un-German" books outside the State Opera. He saw soldiers marching and heard Hitler's speeches. By May, eugenic sterilization was legalized in Germany, and in July, the "Law for the Prevention of Offspring with Hereditary Diseases" was approved, allowing forced sterilization for various hereditary defects and severe alcoholism. Paul then took Wassik from the Johannes Trüper Youth Sanatorium in Jena to the Waterink Institute in Amsterdam. Over sixty-four thousand people were forcibly sterilized in the first year of this law. In July, despite his dark mood, Paul outlined a new investigation with Hendrik Casimir into turbulence, a complex, unpredictable phenomenon in fluid dynamics that fascinated him due to its chaotic nature. His mind, "frenzied and fractured," developed an "affinity for fluid equations," leading to nightmares of being consumed by a maelstrom, yet paradoxically, a feeling of "enlightened calm" and certainty that his loved ones and country would be safe. He worked feverishly, sending Casimir contradictory letters, driven by the joy of working free from melancholia. He believed this work, a solution to turbulence's randomness, would tie his name to history. He questioned why this gift came now, after wasted years and trivial romantic worries, theorizing it was "possession, a sudden invasion from without," requiring him to "get out of the way". This manic phase ended abruptly, leaving him with flawed and incomplete equations. In August, he wandered alone on Schiermonnikoog island. In September, he visited Niels Bohr in Copenhagen, mediating a conference. Afterward, he confided his depression and suicidal thoughts to Paul Dirac, fearing Nazism's spread and the rise of an "inhuman form of intelligence" in science, a "deranged reason" or "specter haunting the soul of science". He sensed its "budding influence," but could not name it, fearing it was a delusion. A confounded Dirac praised Paul's role as a mediator, a "modern-day Socrates," but Paul, in tears, said such praise meant nothing to a man who had lost the will to live. At first light on September 25, 1933, Paul had a sparse breakfast, took a gun, and went to Leiden train station. He visited a former student, Arend Rutgers, discussing physics and religion, appreciating pious men who found hope in a "sacred order". Paul felt let down by physics, now "retreating into a darkness deeper than the abyss within atoms" due to quantum mechanics and the "mathematical plague". He refused lunch and left, almost sprinting. At the station, he felt an urge to turn back, seeing the clock hands stop. He recalled playing with broken clocks as a child at his grandmother's, a game he never succeeded in, yet found blissful. He remembered his "calendar craze" at Wassik's age, and singing "Chad Gadya," a Passover song about an unbroken chain of cause and effect, whose true meaning he only now understood as the train arrived. He knew he had time to turn back but stood "machinelike, propelled by a force he neither recognized nor understood," boarding the train. He arrived by ten.

Chapter 2: John or The Mad Dreams of Reason

Introduction to John von Neumann

The chapter begins by introducing George Boole's "religious vision" in the 1840s, where he conceived of using mathematics to describe human thought processes in binary form, publishing "An Investigation of the Laws of Thought" in 1854. Bertrand Russell doubted Boole's connection to human thought, believing it was something else entirely. The text then hails Neumann János Lajos, also known as Johnny von Neumann, as "the smartest human being of the 20th century" and "an alien among us". David Hilbert, a prominent mathematician, was so stunned by the 22-year-old Hungarian student during his doctorate examination that he only asked about his tailor. Later, when cancer destroyed von Neumann's mind at 53, he was sequestered by the U.S. military at Walter Reed Army Medical Center with armed guards and top-secret clearance personnel. High-ranking officials, including the Chairman of the Atomic Energy Commission and the Secretary of Defense, sat by his bedside, awaiting "one final spark" from the individual who had birthed the modern computer, laid quantum mechanics' mathematical foundations, wrote atomic bomb implosion equations, fathered Game Theory, heralded digital life and AI, and promised "godlike control" over Earth's climate.

Eugene Wigner: Only He Was Fully Awake

Eugene Wigner, a Nobel Prize winner, states there are "two kinds of people in this world: Jancsi von Neumann and the rest of us". Wigner first met Jancsi in 1914 at the Fasori Gimnázium in Budapest, a rigorous Lutheran secondary school renowned for producing top scientists and mathematicians. He ties Jancsi's arrival to the outbreak of war, remembering him as a "luciferin boy" and a "harbinger of something grand and terrible". Wigner's mother, a staunch rationalist, reacted superstitiously to Halley's Comet in 1910, fearing "pestilent vapors," which Wigner believes contributed to her dislike of Jancsi despite their later friendship. Jancsi's parents hired Gábor Szegő, a respected mathematician and friend of Wigner's mother, to tutor the boy before school started. Szegő reportedly wept after meeting the ten-year-old Jancsi, who effortlessly solved complex problems that had stumped him for months. Szegő later confirmed the story to Wigner, admitting he still possessed those pages written on Jancsi's father's bank stationery, and knew then that von Neumann would "change the world". Szegő felt Jancsi's "enormous head" signified something "completely Other". Rumors about Jancsi's prodigious abilities included reading by age two, fluency in Latin, Ancient Greek, German, English, and French, dividing eight-digit numbers by six, and self-teaching calculus and memorizing Wilhelm Oncken's "General History" by being locked in his father's library. Wigner initially felt disappointed by Jancsi's waddling, rotund walk but found his quirks endearing. He notes Jancsi's behavior was "almost like he was doing his best impression of the way a regular human being walked, but having never seen one before". Jancsi's immediate liking and unusual mannerisms made Wigner, a year older, overcome his wariness of being ostracized.

Margit Kann Von Neumann: Spoiled, Savage

Margit Kann, John von Neumann's mother, describes her son as "different from the beginning," born three days after Christmas 1903, not crying after the doctor's slap, and unnervingly smiling at her. She recalls him as precocious and happy but lonely, making his own toys. He was not shy but always by her side, with few friends initially, then too many, acting like a clown. Margit notes he loved his little brother, was strong and healthy but prone to fever spells, vomiting, and confusion, requiring things to be repeated "like before" in an "endless loop". He loved bugs, dogs, and cats, was polite, and too generous, once bringing home a poor boy who was given his father's watch. He sometimes slept in servants' rooms and was jealous. She also described him as flirtatious, in love with all maids and cousins, nicknamed "Little Prince," eating all day and reading all night, reckless, nosy, mischievous, spoiled, strange, and possibly savage.

Nicholas Augustus Von Neumann: At the Head of His Horde

Nicholas Augustus von Neumann, Johnny's younger brother, recounts how their father brought home a "monstrous device": a mechanical textile loom. Nicholas likened it to Kafka's machine in "In the Penal Colony," describing it as a "giant metal insect" that "gobbled up instructions and excreting silken threads". The loom wove tapestries using patterns from punched cards. While Nicholas quickly got bored, Janos was "bewitched" and bombarded their father with questions about how holes transmitted information and if he could keep it. Janos's later computers would use the same punched-card method for memory. The loom, the most extravagant investment their banker father brought home, took hold of Janos for two days straight. Their father explained it took roughly four thousand punched cards for a single textile and that a portrait of the inventor, Joseph-Marie Jacquard, required over twenty-four thousand. Janos "squealed with delight" when told Jacquard was nearly lynched for putting hundreds of thousands out of work and that original looms were destroyed. Janos tinkered with the loom, taking it apart, skipping meals, and working on it until Nicholas went to bed. That night, Janos woke Nicholas in a panic, unable to reassemble it, terrified their father would take it away. Nicholas stayed up till dawn helping him, feeling safe with Janos, who seemed to know and solve everything. He recounts their dangerous childhood adventures, like chasing trains on horseback and setting off homemade explosives, feeling protected by Janos. To distract Janos from their father's potential chastisement, Nicholas asked him to explain the loom. Janos explained Leibniz's 17th-century idea of using ones and zeros for logic and arithmetic, stating that any pattern could be translated into the loom's "language" of holes. These cards stored information in its "purest and most abstract form," allowing new patterns without altering the machine. Nicholas still finds it unbelievable that holes could create intricate designs or that such primitive machinery contained the "seed of another technology that would transform every aspect of the human experience". He asked Janos what else could be done with such a mechanism, a question Janos would later help resolve. Nicholas believes Janos had a "vague yet intense foreshadowing of the future" upon seeing the loom, which gripped him with the same "macabre attraction" he felt for games and explosions. Nicholas himself felt "slightly repulsed" by the scattered loom remains, a sensation that evolved into a recurring nightmare of the loom coming alive, with "bloodred threads trailing behind," and his brother "riding atop, like a Mongol conqueror at the head of his horde".

Mariette Kövesi: The Devil at Your Door

Mariette Kövesi, Johnny von Neumann’s first wife, states she entered his life on a tricycle at age two and a half, when he was eight. Both were "rich brats". She recalls he spent the Great War moving imaginary troops on his "Kriegsspiel" board, recreating battles using newspaper information. This war game, adopted by the Prussian military, obsessed him, and he always won due to its mathematical outcomes. She found it embarrassing that she envied their immersion, as she was "willfully ignorant of the larger world," enjoying her "coddled existence" despite the continent "catching fire". Hungary, a "plutocracy" enjoying a "belle epoque," saw its rich grow richer during the war. Many acted as if nothing was happening, teaching her the truth that "you can dance even with the devil knocking at your door". Budapest, Europe's fastest-growing city, had 600 coffeehouses, the first underground subway, and an opera house rivaling Vienna's. People knew the "wonderful world" was ending, so their games were "urgent. Necessary".

Mariette's family lived lavishly like Johnny's, in Pest, and spent summers in country houses, traveling with a "sprawling caravan" despite the short distance. Their early lives differed: she was an only child; he had two younger brothers. His mother was a "wafer-thin chain-smoker" he adored; hers was a hypochondriac who feigned illness. His father was "headstrong but kind and supportive"; hers was a "chronic womanizing drug addict" who was violent. Mariette feels no shame about her life or the fun she and Johnny had, nor guilt for leaving him for a younger man in the U.S.. They remained on good terms, sharing custody of their daughter Marina, who benefited from living with Mariette when young and with Johnny after sixteen. Marina became a gifted economist and the first female officer of General Motors. Mariette states she "never loved him for his brains," calling it Klari's mistake, and married him because he made her laugh. They remained in lust, despite driving their spouses crazy. Mariette implies Johnny was useless in practical matters, saying he "could not tie his shoes" and would have starved if left alone. She worried about him until his death. Johnny's father, Max, was awarded a hereditary "von" title by Emperor Franz Joseph for financial services, which Johnny kept in Princeton due to its German association, despite his hatred for Nazis. He enjoyed the "von" for better service in restaurants. Johnny loved self-deprecating jokes, including a dark one about a Jewish community reacting to a murdered Christian girl turning out to be Jewish. They re-met in the late 1920s when he was gaining fame in Germany. Mariette accepted his marriage proposal out of boredom. Her parents demanded Johnny convert to Catholicism, but he was "completely secular," his only real attachment to Jewish people being his Yiddish jokes, often directed at "goyim," and his put-down, "Nebbish!".

George Pólya: What Kind of a Boy Is This?

George Pólya, a professor of mathematics, vividly recalls the first time he saw Janos von Neumann in his seminar for gifted students in Budapest, despite having been warned by Gábor Szegő. Pólya was unprepared for Jancsi's quickness. Jancsi was quiet but always smiling. Pólya presented a difficult, unproven theorem he had been working on for decades, using the class to test his proofs. He believes mathematics is a "feeling" that guides towards the answer. While other students discussed the problem loudly, von Neumann remained silent, closed his eyes, and then raised his hand. When called upon, he walked to the blackboard and, "in a second. With no effort. No thinking even, only doing," wrote down a "completely stunning proof". Pólya was astonished, his years of work surpassed in a second by a solution so "beautiful, so elegant". He wondered, "What kind of a boy is this?" and admitted to being "afraid of von Neumann" afterward. The section notes that David Hilbert proposed an ambitious program in the early 1920s to build the entire mathematical universe from a unique set of axioms, establishing a complete and consistent foundation to avoid paradoxes. Young von Neumann found Hilbert's program irresistible, convinced that science needed immutable mathematical truths and fearing "dangerous unreason" emerging from his colleagues' search for truth.

Theodore Von Kármán: Some Lost Their Minds

Theodore von Kármán recalls a Budapest banker, Johnny's father, asking him to dissuade his son from becoming a mathematician, calling it a "breadless art". Kármán, who himself was forbidden from mathematics as a child, found the boy "spectacular," already studying infinity on his own. Recognizing it would be a shame to deter him, Kármán mediated a compromise: the boy would become both a chemist and a mathematician. Janos enrolled in chemical engineering at ETH Zurich and mathematics at the Universities of Berlin and Budapest simultaneously, completing both a chemical engineering degree and a mathematics doctorate in four years. Pólya noted he graduated summa cum laude from Budapest without hardly attending classes, spending most time in Germany with David Hilbert. This made him the youngest privatdozent in German history, a professor by age twenty-two. Von Neumann sent Kármán his ambitious doctoral thesis, which aimed to find the "purest and most basic truths of mathematics" and express them as "unquestionable axioms". This attempt to capture mathematics in a formal axiomatic system was the essence of Hilbert's program, which von Neumann embraced.

Kármán views Hilbert's absolutist program as a "symptom of its time," a desperate search for security amidst emerging fascism, quantum mechanics unsettling matter's behavior, and Einstein's theories revolutionizing space and time. He emphasizes mathematics' historical role as "the true light of reason," but notes its foundations were questioned in the early 20th century, leading to the "crisis of the foundations of mathematics," a profound questioning since the Greeks. This crisis, though involving brilliant minds, seemed like an "Arthurian quest" yielding an "empty chalice". The mathematical universe is depicted as a pyramid, with theorems resting on deeper substrates. The crisis revealed the potential for mathematics to float on a "void," unraveling at the edges. Logicians suffered "nervous breakdowns" due to paradoxes, as basic geometry concepts proved inadequate for non-Euclidean space where parallel lines could intersect. This forced mathematicians to either work on faith or seek the core "cornerstones" of mathematics, a "risky undertaking" that cost some their reputations, and others, like Georg Cantor, "lost their minds".

Cantor, the creator of set theory, expanded infinity, previously considered a pure mental construct, into a "great variety of them," throwing mathematics into "pandemonium". His expanded theoretical landscape was "teeming with dangerous, self-contradictory notions, and logical absurdities". He seemed to prove that a one-inch line had as many points as all of space. Critics argued his infinities were not for serious study, but Cantor's proof seemed "airtight," though many struggled to accept this "new and confounding article of faith". Cantor, born in Russia, was a pious Lutheran and sensitive soul. He privately confessed to his daughter that his infinities questioned God. These theological struggles, along with "vicious attacks" from peers who called his work a "pathological disease" or "mathematical insanity," pained him. Henri Poincaré called his work "un beau cas pathologique". He also disliked the "excessive admiration" from figures like Hilbert, who said, "Not even God will expel us from the paradise which Cantor has created," as he worked for a "higher calling". Compelled by an "unknown, secret voice" since boyhood, he believed his infinities came from "divine intervention," meant to lead humanity to "greater, transcendent certainty," though the opposite occurred. His opponents hindered his career, leaving him to languish in Halle. He wrote that fear of his work was "myopia," and his theory stood "as firm as a rock". To complete his theory, Cantor developed a hierarchy of infinities, but suffered "uncontrollable mania," followed by "deep melancholy and the darkest possible depression," rendering him unable to work on mathematics. He instead pursued proving Shakespeare's plays were by Francis Bacon and Christ was Joseph of Arimathea's natural son, views that fueled claims of his insanity. In May 1884, he had a "massive mental breakdown" and was institutionalized. During crises, he shrieked, yelled, or became silent, exhibiting paranoid fantasies of persecution. Between breakdowns, he continued teaching but was haunted by his own results, stuck in a loop of proving his continuum hypothesis true, then false. This "vicious cycle of truth and falsehood" marked his later years. He died from a heart attack in January 1918, after suffering his youngest son's death, illnesses, bankruptcy, and malnutrition during WWI.

Cantor's death did not quell arguments about infinities. Bertrand Russell, in 1901, found a "fatal paradox" in set theory that obsessed him, leading to recurring nightmares. Russell and Alfred North Whitehead wrote "Principia Mathematica" to reduce mathematics to logic, taking 762 pages to prove one plus one equals two. Their attempt failed, and Russell's new nightmare depicted a young librarian burning books, approaching his "Principia Mathematica". Russell would wake screaming, unaware of his work's fate. While Russell and Whitehead used over two thousand pages, von Neumann's doctoral thesis on axioms was concise enough for a single page. Though unsuccessful, his audacity earned him fame. His style involved stripping subjects to axioms and turning them into pure logic problems, an "otherworldly capacity to see into the heart of things," or "characteristic shortsightedness" that explained his "almost childlike moral blindness".

Gábor Szegő: A God-Shaped Hole

Gábor Szegő, von Neumann's former teacher, describes him as a "little devil" but also "an angel" to those who fled Nazi Germany. Szegő regretted only teaching Jancsi as a boy, seeing him as a "mathematical behemoth" but also a "fool, and a dangerous one at that!". He found him contradictory: brilliant yet childish, insightful yet shallow, constantly gossiping and wasting time with "idiotic friends" and "high-priced whores," morbidly interested in trivialities like family marriages. Szegő recounts Jancsi spending half an hour explaining the advantages of Pekinese over Great Danes, despite his countless contributions to mathematical theories. Szegő sought Jancsi's help to migrate his family to America, meeting him in Berlin at Horcher, a lavish restaurant favored by senior Nazis. Szegő shivered at the memory of discussing escape plans in "that lion's den".

They discussed mathematics, and Szegő sensed Hilbert's "perverse influence" on Jancsi, seeing a "single-minded obsession with logic and formal systems". Jancsi's fanaticism was common in Mitteleuropa. Jancsi claimed to be close to axiomatizing mathematics free from contradictions, which Szegő scoffed at, asking what kind of Eden such a "strict reduction" would create. Szegő urged him to stay in America, but Jancsi refused, feeling he needed to interact with Hilbert's Göttingen circle to develop an important idea. He believed mathematics, not chemistry or politics, would shape the future, stating that quantum physics entities "behave like numbers". Jancsi's absolute confidence in America's welcome relieved Szegő, but he doubted him when Jancsi gave no details, instead flirting with women. Szegő despairs over Jancsi's later actions, wondering if he could have "warmed his heart" or "saved some part of his soul". He feels guilty for failing to teach Jancsi the "sanctity" of pure mathematics, which he believes is "the closest we can come to the mind of Hashem" and a dangerous power if misused. Szegő saw Jancsi's "sinister, machinelike intelligence that lacked the restraints that bind the rest of us". He remained silent due to Jancsi's superiority, feeling "belittled and debased". He acknowledges Jancsi's "burning vision" to understand the world but critiques his spiritual ignorance and dangerous faith in logic, which, if betrayed, leaves a "god-shaped hole" that demands to be filled. Leaving the toilet, Szegő witnessed a loud ruckus, finding Jancsi laughing maniacally while wiping blood from his mouth as waiters picked him up and soldiers dragged a massive man outside. Jancsi refused to explain, calling the man an idiot lacking humor. Walking through the Tiergarten, Szegő saw Jancsi entranced by a military parade's armored division, salivating "like a dog," realizing there was "very little hope for him, indeed very little hope for any of us".

Eugene Wigner: A Mathematician’s Nightmare

Jancsi was outsmarted by only one person in his life, and it changed him. This happened in Königsberg in September 1930, at the Second Conference on the Epistemology of the Exact Sciences, where he represented Hilbert's program. Jancsi, then at the peak of his terrifying output in Germany, was known for proving "what he wants". Wigner and Jancsi met in Budapest before the conference; Jancsi asked Wigner to help Szegő find work in America and made him promise they would emigrate together. Wigner questioned Jancsi's delay, who stated he was so close to the "foundations of mathematics" he felt a "tingle in his brain!". Despite the Nazis becoming Germany's second strongest political force and Mariette's nagging, Jancsi, obsessed with history and the fall of empires, trusted his ability to know when to leave. He believed he was "many moves ahead," acting as if looking back at past events. He told Wigner they would enjoy Europe "to the very last," seeing farthest "in the darkest times". Jancsi was adamant about rooting out the paradoxes Cantor introduced to mathematics. Wigner couldn't comprehend this obsession, wondering if it was academic or a deeper need. As Wigner put Jancsi on the train, he never suspected Jancsi's grand dream would be "ripped away" by a 24-year-old graduate student.

During the final moments of the conference, Kurt Gödel, a skeletal and awkward young Austrian, spoke so softly and stuttered that his words were almost lost to history. Gödel's comment, unheard by many, was: "I b-believe that we can p-p-postulate, within any consistent f-formal system, a statement that is t-t-true but that can never be pr-proven within the rules of said system". This struck only Jancsi, who broke out in a sweat and had trouble breathing, realizing it was the end of Hilbert's program. Gödel had shown that any consistent formal system of axioms would be incomplete, containing unprovable truths, an "ontological limit" and a "personal catastrophe" for Jancsi. Gödel's incompleteness theorems are now considered a fundamental discovery. Bertrand Russell initially refused to accept it, saying, "Are we to think that 2 plus 2 is not 4, but 4.001?" but later bitterly conceded. Jancsi, with his unique brain, immediately understood and expanded on Gödel's ideas, holing himself up for two months in Budapest, screaming in six languages, to Mariette's worry. He emerged with a corollary: if a system was complete (proving every true statement), it would be inconsistent (full of contradictions). This meant mathematicians had to choose between paradoxes or unverifiable truths. Gödel politely informed Jancsi that he had already developed this as his second incompleteness theorem. Jancsi never worked on the foundations of mathematics again, remaining in awe of Gödel, calling his achievement "singular and monumental" and a "landmark". Ten years later, Jancsi worked to rescue Gödel from Nazi Germany after he was beaten by Brownshirts in Vienna. He wrote, "Gödel is absolutely irreplaceable; he is the only mathematician alive about whom I would dare to make this statement," helping him secure a U.S. visa.

Kurt Gödel achieved a "godlike status" among scientists. Albert Einstein admired Gödel so much he would go to his office at the Institute for Advanced Study just to walk with him. Gödel, as a birthday gift, devised a solution to general relativity allowing time travel, appealing to him because he was only happy as a young boy. His paranoia, starting in adolescence, worsened in America, leading to a severe eating disorder (subsisting on butter, baby formula, laxatives) and delusions that mathematicians wanted to kill him with refrigerator gases or poisoned food. He refused to eat anything not prepared or tasted by his wife, Adele. His descent was slow and painful. When Adele was hospitalized in 1977, Gödel starved himself to death. Most agree Gödel's paranoia caused both his downfall and his achievements, with one professor questioning if his work made him unstable or vice versa. Wigner sensed the inextricable link between Gödel's logic and derangement, as "paranoia is logic run amok". Gödel believed "Every chaos is a wrong appearance," a small step to seeing hidden manipulations. His ideas, "self-referential nightmares of logic," gnawed at both him and Jancsi.

Jancsi and Gödel are connected even in death, buried feet apart. Jancsi's reaction to Gödel's ideas was profound, affecting his worldview and making it darker. The Nazi rise to power further confirmed his disillusionment with human decency and the sway of irrationality. The strange boy Wigner knew became "more alien still," resigning his professorship in Berlin even before Jews were dismissed and publicly renouncing his German Mathematical Society membership. Jancsi saw it as a personal affront that Nazism was chosen over minds like Einstein's. Wigner and Jancsi traveled to America on the same boat, both changing their names. Jancsi's life seemed magnificent, teaching at Princeton University then the Institute for Advanced Study, where he had free rein. Oppenheimer headed the institute, and Alan Turing almost became Jancsi's assistant. Jancsi continued at breakneck speed, but Wigner saw his inner suffering, a "craving or an itch," like a tiger pacing. After Gödel, Jancsi abandoned his "juvenile faith in mathematics," becoming more practical and effective, but also dangerous and "set free". In the U.S., von Neumann became a "renegade mathematician," working for IBM, RCA, CIA, and RAND Corporation, charging exorbitant fees. After gaining citizenship, he sought an Army Reserve commission but was rejected. During WWII, he joined the Manhattan Project in New Mexico.

Chapter 3: Lee or The Delusions of Artificial Intelligence

Prologue

The prologue introduces the legendary Emperor Yao, one of China's mythical sage-kings, who invented the game of Go to enlighten his vicious son, Danzhu. Danzhu, born of the concubine San Yi, prized cruelty, ripping birds' wings, gouging their eyes, and tying bells to their talons. He opposed world order, delighting in contravening his father's rules. In spring, he hunted pregnant mares; in summer, he crippled fawns for wolves. Fall was his favorite, reveling in executions of criminals and the infirm. In winter, he kidnapped, raped, and strangled children, leaving their bodies for snow and wolves. His mother, Yao-Mu, revealed Danzhu was not human but a "fallen star" and a "harbinger of death," bearing marks on his forehead: "Heaven bestows a hundred grains upon mankind. Man offers not a single good deed to recompense heaven. KILL, KILL, KILL, KILL, KILL, KILL, KILL!". Emperor Yao was a "bastion of moral perfection," whose reign was marked by natural beauty and prosperity. However, two unicorns, omens of peace, fled on Danzhu's birth and had not returned, as he organized hunts to slay every living creature, including dragons and unicorns. With his mother's help, Emperor Yao prayed to the gods for permission to divide the cosmos into a 19x19 grid (361 intersections), creating a Go board. He explained the rules to Danzhu: place black or white stones to conquer space and encircle opponents' stones, with the most territory winning. Yao would use white clamshell stones, Danzhu black slate. Whoever won would rule the world.

The Strong Stone

Lee Sedol, the "Strong Stone," a 9 dan Go master, lost his voice at thirteen, in 1996. Five years after moving to Seoul and six months into his professional career, an affliction paralyzed his vocal cords and caused temporary aphasia, affecting his ability to read some words. Though the cause was unknown, it left his bronchial nerves permanently paralyzed, giving him an "odd, shrill, wheezy, almost toylike voice". Ashamed, he rarely spoke publicly or attended award ceremonies. At thirteen, he trained twelve hours a day at Kweon Kab-yong's Go Academy, a renowned teacher who recognized Lee's talent at the 12th National Children’s Go Competition in 1991, where eight-year-old Lee, the youngest winner, displayed his "wild, violent, and unpredictable" style. Kweon described Lee as shy with eyes that "shone with a different light". Lee learned Go from his amateur father, surpassing all siblings and his father by age five. He struggled to make friends, teased for his naiveté, asking what kind of trees pizza grew on. His training involved studying 6,000 problems from his dojo's manual, playing lightning games, and memorizing ancient masters' matches. His favorite was the "blood-vomiting game" of 1835, where Honinbo Jowa's three "unthinkable" moves caused his youthful opponent, Akaboshi Intetsu, to collapse and die. Lee's main strength was creating "daring, almost unthinkable moves" that seemed chaotic but revealed a unique logic as the game progressed, a skill honed by "reading" the empty board to foresee branching possibilities. Lee desired a new, unique Go style. His style became more "dogged and powerful, angrier, impulsive, less predictable" after his father died when Lee was fifteen. His friend, Kim Ji-yeong, described playing him as playing a "wild animal". Lee, though shy, was never modest, becoming the youngest 9 dan player and often taunting rivals. His boasts ("I have no confidence in this game. No confidence in losing, that is") and bravado earned him fans and detractors. He claimed to be the best and wanted his games to "endure, to be studied and contemplated as works of art". His gameplay was defined by risk, seeking out complicated fights and escaping disaster with speed and grace. He relied on creative talent, seeing Go as an art form arising from nothing, unlike chess. His mercurial character sometimes betrayed him, leading him to abandon a tournament out of boredom. Despite his intense dedication, Lee was a fan of K-pop and soap operas. He stated that Go was like breathing, a constant mental process. He believed understanding Go's deepest nature was paramount, surpassing winning or losing, as it mirrored the mind's inner workings and rivaled the universe's beauty and chaos. By 33, Lee had won the second-highest number of international titles (18 international, 32 national) and over a thousand games, dominating the global circuit. His mentor, Kweon, expressed pride in him. In early 2016, Lee was challenged to a five-game match against AlphaGo.

AlphaGo

AlphaGo was conceived by Demis Hassabis, a North London "wunderkind" who, at four, learned chess and within two weeks, could beat his father and uncle. He won his first tournament at five and was England's junior team captain by nine. A chess master by his early teens, Hassabis decided to abandon professional chess to dedicate his intellect to something more important: Artificial General Intelligence (AGI). This pivotal choice followed a humiliating defeat at age thirteen in an international tournament in Liechtenstein. Hassabis, a kind and thoughtful boy, taught himself to code on a Commodore Amiga he bought with chess earnings. His first AI agent, created at age eleven, played a simplified Go game (Reversi) and beat his five-year-old brother five times. He was fascinated by how his program, full of bugs, seemed to externalize a part of his mind, exhibiting personality through its flaws and tendency to stall.

In the tournament, after dispatching early rivals, Demis faced the Danish champion, a middle-aged veteran, for a grueling eight hours. In the endgame, Demis, with only a king and queen against a rook, knight, and bishop, struggled for four more hours to avoid checkmate. Exhausted, he resigned, but his opponent mocked him, revealing Demis had missed a stalemate opportunity by sacrificing his queen. This humiliating defeat, where a part of his mind "had been somewhere else," fueled his deeper obsession with understanding his own intelligence and the human mind. He wondered why he enjoyed what others found boring and why evolution burdened humans with consciousness, seeing that thousands of years of civilization hadn't brought understanding. Recognizing science's rapid progress would soon push humanity "off the edge," he concluded that "something radically new was needed. A different type of mind". He formulated a twenty-year plan to create AGI. He finished his A levels at fifteen, worked at a computer game company, creating "Theme Park" to pay for Cambridge, where he studied computer science. He founded Elixir, a gaming company that failed due to lack of computing power. He then studied cognitive neuroscience, becoming obsessed with John von Neumann’s unfinished manuscripts, "Computing Machines and the Brain" and "Theory of Self-Reproducing Automata". His research on memory and imagination, linking them to the hippocampus, was a top ten breakthrough of 2007. After a PhD in computational neuroscience, he founded DeepMind in 2010 with Shane Legg and Mustafa Suleyman, aiming "to solve artificial general intelligence, and then use that to solve everything else".

Initially, funders avoided DeepMind due to AI's "dark age" and the company's lack of short-term products. Hassabis eventually secured investment from Peter Thiel by explaining the fascination of chess and the dynamic tension between the bishop and knight. Google acquired DeepMind in 2014 for over $625 million, allowing founders creative control. Speculation arose about DeepMind's first move, with Hassabis confident they would start with Go, "the most complex and profound one that humankind has ever conceived".

In 1997, computers surpassed humans in chess when IBM's Deep Blue defeated Garry Kasparov, the world champion. Kasparov, who had beaten an earlier version, was shocked by his defeat and suffered a mental breakdown for a year. The loss was particularly traumatic due to two moves in the second game. Kasparov, on the defensive, laid a trap that a logic-driven computer should fall for, but Deep Blue refused, making a "brilliant play". His suspicions grew when Deep Blue made a "shocking mistake" just moves later. Kasparov wondered if he faced a hidden human opponent or a cunning ruse. Unable to focus, he forfeited the game despite being able to force a stalemate. He lost or tied the remaining games and his crown. Kasparov became paranoid, claiming a "human mind inside the machine" and demanding access to Deep Blue's hardware, software, and logs, which IBM refused, eventually dismantling the computer. Years later, an IBM programmer confessed the "flagrant mistake" was a software bug: unable to calculate an optimal move, the computer chose one at random. Modern chess programs like Fritz, Komodo, and Stockfish are unbeatable, using "brute force" calculation (200 million positions per second) rather than human creativity or imagination. Unlike humans who use intuition and pattern recognition, chess engines don't truly "understand" the game; they compute every possibility in a search tree.

Go, however, is different; its vast complexity makes brute-force search unviable. Go has 200 possibilities per move (vs. 20 in chess), typically lasts over 200 moves (vs. 40 in chess), and has astronomically larger possible interchanges and board positions (over 10^700 potential games, exceeding a googolplex). In Go, all pieces have equal value, their worth tied to position and relation to other stones and spaces, making good moves subjective and relying on intuition. Professionals train for years to "read the board," recognizing patterns like "eyes," "ladders," and "bamboo joints," and understanding concepts like "alive," "dead," "unsettled" stones, and "aji" (potential). They must alternate attacks, distinguish formation "thickness," invade, counter, capture, and master moves like "sente" (initiative) and "tenuki" (gambit). Go has traditional proverbs ("Don’t make empty triangles," "Play fast, lose fast," "If you don’t understand ladders then don’t play Go"). For centuries, Go was an art, not a game, considered too profound for computation. In 2016, DeepMind published an article in Nature showing their AI, AlphaGo, had beaten European champion Fan Hui, a stunning achievement that prompted widespread scrutiny and debate. Before this, AI was expected to be a decade away from competing in Go. AlphaGo's victory led to ridicule of Fan Hui, prompting DeepMind to seek a better opponent. Lee Sedol was chosen as the best.

A Sharp, Sudden Invasion

Lee Sedol made his opening move, a black stone in the upper right corner. Over 200 journalists and commentators, along with 100,000 YouTube viewers and 60 million television viewers, watched from Seoul's Four Seasons Hotel. Across from Lee sat Aja Huang, a DeepMind programmer, who played AlphaGo's moves displayed on a terminal. Lee later joked about Huang's "uncanny stillness," like a "puppet" who never left his seat or made eye contact, only taking "tiny sips of water," making Lee feel uncomfortable, like playing a "robot" or "simpleton". Huang was not allowed to use the bathroom or show emotions to avoid giving anything away. Opening moves in Go are usually quick, but after Lee's slightly unconventional opening, the clock ticked for nearly 30 seconds, causing panic among DeepMind technicians, including Demis Hassabis and David Silver. Lee, mocking the delay, initially felt AlphaGo was unimpressive compared to him and Fan Hui. Everyone expected the human to win. Lee's pre-match boast, "What worries me is if I will win five to zero, or four to one," reflected this confidence. After over a minute, AlphaGo made a standard move at the opposite side. Initial moves showed AlphaGo as unimpressive, even "amateurish" to commentators. Lee was clearly in the lead. Then, two hours into the game, Huang placed white stone 102 on the tenth line, two squares from the left edge, a "sharp, sudden invasion" into Lee's territory. This aggressive move, typical of Lee's own style, "flabbergasted" him; he rocked in his chair, then smiled, pinching three moles on his neck. He felt "shock, disbelief, and puzzlement, eventually leading to fear, then amusement, then something akin to sheer joy," wondering how a computer could play such a bold move. It was a wholly different level of play from the Fan Hui match, and Lee spent over ten minutes on his next move, knowing the tide had turned. Eighty moves later, Lee resigned.

A Thing of Beauty, Not of This World

Future historians might pinpoint "move 37" in the second Lee Sedol vs. AlphaGo game (March 10, 2016) as the "first glimmer of a true artificial intelligence". This move was unprecedented for both computers and humans, a "radical departure from thousands of years of accumulated wisdom". It offered a glimpse into a future that inspires both hope and horror. AlphaGo's first victory stunned the world, but many deemed it uninspired, attributing it to Lee's mistakes. Despite AlphaGo's impressive efficiency, its game lacked beauty. Though confidence in Lee waned, most still bet on him, some viewing the AI's win as a fluke. Lee, however, was deeply shaken and scared. He had taken over two decades to develop his skills, while AlphaGo had made an "incredible leap forward" in just months. In the post-game press conference, he retracted his bravado, admitting AlphaGo played "in such a perfect manner" and that the match was "fifty-fifty". Worn out, Lee appeared frail, losing almost eighteen pounds during the tournament. His daughter hugged him for strength before the second game.

Lee adopted an uncharacteristically cautious opening, avoiding violence and focusing on a firm base, realizing his usual impulsive pace was useless against a machine. He drank coffee and periodically smoked on a terrace overlooking Seoul. Commentators criticized Lee's caution, noting AlphaGo's occasional "amateurish" or "nonsensical-looking" moves that Lee didn't capitalize on. AlphaGo's "peep" at black 15 was dismissed as crude, but Lee remained cautious. DeepMind programmers were unaware of AlphaGo's internal choices; the moves were "emergent phenomenon from its training," beyond human control. The game remained balanced through move 30, with AlphaGo assessing its win probability at 48 percent. Standard play continued until Lee placed white stone 36. Then, AlphaGo played black 37, a "shoulder hit" on the fifth line, a move considered "outrageous and counterintuitive," against all Go wisdom, even for beginners, as it typically aids the opponent. Commentators and judges thought it was a mistake; Aja Huang, who placed the stone, felt ashamed. Few recognized its potential. Fan Hui, the recently defeated European champion hired by DeepMind, immediately recognized move 37 as a "stroke of genius". He noted it "casts an invisible net across the board" and linked all previous stones. His logbook entry read, "Here?! This goes beyond my understanding. It’s not a human move. I’ve never seen a human play this move". After the game, Fan Hui kept repeating, "Beautiful, beautiful, so beautiful!". Other commentators were flummoxed, some believing Huang had misread the monitor. Demis Hassabis and David Silver, in the control room, were excited to see AlphaGo's evaluation. Lee Sedol, returning from a cigarette break, reacted with initial disgust, then a "huge beatific smile," as if seeing "a thing of beauty, not of this world". He spent over twelve minutes pondering it, his thoughts almost visible on his face. Lee later recalled thinking, "This machine is still imperfect," until move 37, which made him realize, "I didn’t have a chance. . . . It tricked me. With that move, I was finished, it had already won". The move changed his mind about AlphaGo's creativity, calling it "meaningful". Lee fought for three more hours, but AlphaGo only got stronger, winning at white 211. In the post-game conference, a "broken man," Lee apologized for his powerlessness, conceding a "very clear loss" and a "near-perfect game" from AlphaGo, but vowed to fight on.

One of the Ten Thousand Things

Lee spent his day off before the third game with four other Go professionals, analyzing previous matches to understand how computer scientists, with little Go background, created a system that "wiped away centuries of tradition with a single move". The truth was, DeepMind hadn't programmed move 37; AlphaGo created it "with no human input" and knew it was a move no human master would consider. Demis Hassabis explained AlphaGo wasn't handcrafted or given comprehensive rules like Deep Blue. It taught itself through "self-play and reinforcement learning". First, it mimicked humans by analyzing 150,000 amateur games using an artificial neural network, a complex mathematical model mirroring the brain's neurons. This "Policy Network" learned "common sense," allowing AlphaGo to play at an amateur level. To reach professional level, it needed to "read the board" intuitively. AlphaGo played millions of games against itself, learning from mistakes, making billions of tiny, human-unfathomable adjustments to its model. It initially flailed like a clumsy human newcomer, but learned to recognize and strengthen good patterns. A second neural network, the "Value Network," trained on 30 million self-played games, could estimate the numerical value of any board configuration, far surpassing human capability. The combination of these two networks, refined through millions of self-play games, allowed AlphaGo to surpass human knowledge and devise "radical strategies and counterintuitive moves" like move 37. AlphaGo's internal systems assessed move 37 as having a probability of "one in ten thousand" for a human player.

The third game on March 12 saw Lee Sedol struggling from the start. Fan Hui observed Lee's trembling hand and haggard appearance, knowing the mental toll of high-level play. Online commentators had lost faith in Lee, criticizing his character. Fan Hui, having played against AlphaGo, understood the "uncanny" feeling of playing a "merciless, unfeeling opponent" that was "immune to weariness" and only cared about winning, even by a single point. He noted AlphaGo's "lazy" moves were pure calculations, making tiny imperceptible gains. Fan described playing AlphaGo as being "pulled down into a void," like a "black hole". Lee tried a "sudden and unexpected attack," but it was rash, and AlphaGo countered with an "inspired" two-space jump. Fan realized AlphaGo had advanced beyond the version he played, seemingly "looking down from the heavens" and anticipating Lee's moves. Lee became infuriated, losing his temper and making gruesome mistakes. By move 48, AlphaGo's win probability soared to 72 percent. Lee resorted to his "zombie" style of wild, unpredictable attacks, which stood no chance against AlphaGo. The AI secured a vast territory, reaching 98 percent likelihood of winning. The game continued for an "excruciating" twenty-eight more moves. AlphaGo won the game and the tournament.

God’s Touch

Despite losing the match, tournament rules required Lee Sedol to play two more games. The thought of losing all five was an "unbearable disgrace". The DeepMind team unintentionally shamed him by sending champagne for his wedding anniversary after his third loss. He apologized for his powerlessness, feeling immense pressure. He looked thinner and more childlike for the fourth game, bowing deeply to Aja Huang. AlphaGo, playing black, took control immediately, playing more aggressively. Lee was criticized for sluggishness, but cracked a smile at AlphaGo's vicious shoulder hit, as if playing a younger version of himself. Lee's lack of response shocked onlookers, letting AlphaGo barricade the board. A commentator, an old classmate, believed Lee was playing possum. Lee entered a state of absolute concentration, avoiding confrontation and giving up territory. Fan Hui felt Lee's anticipation, falling into a trance. By move 69, Lee had only 34 minutes left, AlphaGo over an hour. AlphaGo pounded Lee, taking a large group, and its win probability climbed to over 70 percent. With 11 minutes on his clock, Lee picked up a stone and "smacked it down right in the center of AlphaGo’s territory".

Gu Li, a rival, shouted, "The hand of God! That is a divine move!". Lee's 78th stone, a wedge move, tore AlphaGo's position apart, an "unthinkable move" no one had anticipated. Commentators were stunned, scrambling to understand it. AlphaGo's response "made no sense whatsoever," making "obvious blunders". Lee hesitated, wondering if it was a new strategy or trap. Only the DeepMind team knew AlphaGo had "lost its mind" and was playing nonsense. Demis Hassabis stormed into the control room, seeing AlphaGo's win probability plummet. The programmers confirmed everything was normal until Lee's wedge move; AlphaGo had "searched so deeply, that it lost itself". Hassabis screamed at AlphaGo's next consideration, realizing it knew it made a mistake but was evaluating it incorrectly. DeepMind watched in despair as commentators demanded answers. Aja Huang played AlphaGo's next stone, causing the audience to burst out laughing. It took AlphaGo over twenty moves to regain sanity, by which point it had lost control. Lee, playing under time pressure (byoyomi), maintained his composure, while reporters rushed back. AlphaGo made "pointless" last-ditch attempts, allowing Lee to increase his lead. When AlphaGo's win probability fell below 20 percent, it displayed "W+Resign" and Aja Huang bowed to Lee. Commentators and onlookers erupted in applause, seeing it as a victory for humanity. Lee remained still, analyzing the game, not smiling until Hassabis tapped his shoulder. He called it a miracle and a precious moment. In the press room, Lee was met with thunderous applause, humbly accepting congratulations despite having lost the match. He described the experience as "unbelievable," saying he wouldn't give it up for anything. Lee's victory, creating "something out of nothing," showed his "creative genius". Hassabis and his team confirmed move 78 had thrown AlphaGo into madness. Lee confessed his move was sheer inspiration, not planned. DeepMind ran the match through AlphaGo's systems, which assigned Lee's move 78 a probability of "Zero point zero zero zero one"—one in ten thousand, identical to AlphaGo's own groundbreaking move 37. This meant AlphaGo couldn't handle Lee's wedge move because it was "too far from human experience, and past even where AlphaGo’s seemingly boundless capabilities could reach". Lee and the computer had strayed beyond Go's limits, creating a "new and terrible beauty, a logic more powerful than reason".

Game Over

Lee lost his final game against AlphaGo, lacking the "hand of God" or blinding inspiration. Over 200 million people watched worldwide. Lee requested to play black, giving AlphaGo a slight advantage. Initial moves made commentators joke AlphaGo was short-circuiting, playing "useless and out of place" moves. The DeepMind team believed AlphaGo was wrong in its judgments, expecting embarrassment. However, others recognized AlphaGo's merit. Kim Ji-yeong noted, "White is winning now," describing AlphaGo's play as "what 10, or 11, dan play looks like? It looks weird, it looks ugly, it just doesn’t make sense to us". AlphaGo's decisions were based on a different kind of thinking: it calculated precisely how much it needed to win and did no more, valuing winning by a hair's breadth the same as a landslide. The game stretched over five hours, 280 moves, before Lee resigned, by only two and a half points. At the award ceremony, Lee appeared dignified but shrunken. He stated he had "grown through this experience," and AlphaGo showed that "moves humans may have thought creative were actually conventional," bringing a "new paradigm to Go". He was thankful to have found "the reason why I play Go" and called it "an unforgettable experience". Hassabis expressed it was the "most mind-blowing experience" and the "culmination of a twenty-year dream," highlighting moves 37 and 78 as ones that would be discussed for a long time. Lee apologized to his fans, convinced his defeat was due to his own weakness, not AlphaGo's superiority. He believed "there is still more that human beings can do against artificial intelligence," and that "enjoyment is the essence of Go," which AlphaGo cannot know. DeepMind received an honorary 9 dan ranking for AlphaGo from South Korea’s Go Association, recognizing its efforts to master Go's Taoist foundations and reach "a level close to the territory of divinity".

Calculate, Abandon Instinct

In the months following his defeat, Lee Sedol won every tournament game by relying on calculation instead of instinct. His consecutive victories suggested a continued illustrious career, but in November 2019, he suddenly announced his retirement. Go players typically compete into old age, and Lee was only thirty-six. Despite public outcry, he explained he had dedicated his life to Go since age five and now sought something new. For his farewell match, he chose to play HanDol, a South Korean AI, which had already defeated Korea's top five players. Lee started with a two-stone advantage. He won the first game after his 78th move confused HanDol, reminiscent of his AlphaGo match. Experts called his move "unthinkable," and HanDol's team was astounded by his ability to find software bugs, leading to irrational moves and HanDol's resignation. Lee Sedol became front-page news as the only human to defeat two advanced AI systems. However, HanDol crushed him in the subsequent game without advantage. The tournament was held near Lee's home island of Bigeumdo, with his family, old classmates, and teachers attending. After five hours and 181 stones, Lee resigned the third game. Weeks later, on a talk show, Lee stated AI had put "the final nail in my coffin," saying it was "simply unbeatable". He reflected that Go, once an art form, had "changed" since AI, becoming a "devastating force". He concluded that even if he became the world's best human player, "there is an entity that cannot be defeated".

Epilogue: The God of Go

Shortly after Lee's retirement, a player called "Master" emerged on the online Go circuit, winning fifty consecutive games against top players. DeepMind revealed Master was a stronger version of AlphaGo, attributing its single loss to an internet time-out. DeepMind then challenged Ke Jie, the world's highest-ranked Chinese prodigy, at the Future of Go Summit. Ke Jie, only nineteen, had criticized Lee Sedol's performance against AlphaGo and boasted he would restore human supremacy. Master "annihilated" Ke Jie, winning all three games. Ke Jie cried, expressing a sense of helplessness and describing Master as "a god of Go. A god that can crush all who defy him". He felt Master could see the "whole universe of Go," while he saw only a "tiny area". He concluded, "I think the future belongs to AI". With both Lee Sedol and Ke Jie defeated, DeepMind had reached a fundamental milestone. Ke Jie's question—how much further could the program evolve through self-learning?—haunted Hassabis.

DeepMind made a "radical departure," stripping Master (AlphaGo's successor) of all human knowledge—the millions of games it learned from—leaving only its "bare bones". Their goal was a more powerful, general AI, not relying on human understanding. This new program, AlphaZero, defeated the version of AlphaGo that retired Lee Sedol one hundred games to zero. Applied to chess, AlphaZero became better than any human in four hours and defeated the reigning AI chess champion, Stockfish, in eight. English grandmaster Matthew Sadler described its style as "a human on fire," aggressive and reminiscent of Garry Kasparov. AlphaZero mastered shogi in under twelve hours, beating the world's strongest program, Elmo, in 90 percent of games. For all these games, AlphaZero considered no human experience; it was given only the rules and allowed to play against itself. It started with random moves but quickly evolved into an unbeatable force, now the strongest entity in Go, chess, and shogi. The book itself is described as a work of fiction based on fact, and the author thanks various sources including George Dyson's "Turing's Cathedral," Marina von Neumann Whitman's memoir, Norman Macrae's biography, and the documentary "AlphaGo".