A thousand years of discovery

Open the full timeline as a list

c. 300 BC — Euclid: proves there are infinitely many primes — Elements IX.20, the oldest proof still taught unchanged [INST·70 The Prime]
c. 300 BC — Euclid: the greatest-common-divisor algorithm — Elements VII.2, subtract the smaller from the larger and repeat; run against 1 it writes any number’s continued fraction, the oldest algorithm still in daily use [INST·88 (Elias Edition) The Fraction]
c. 240 BC — Eratosthenes: the sieve — strike out the multiples of each prime in turn and the survivors are the primes; the algorithm this instrument still runs [INST·70 The Prime]
c. 480 — Zu Chongzhi: finds 密率 355/113 — π to seven digits from a three-digit denominator, the luckiest fraction in the catalogue, unbeaten for nine hundred years [INST·88 (Elias Edition) The Fraction]
984 — Ibn Sahl: On Burning Mirrors and Lenses states the refraction ratio geometrically — the law later called Snell’s, six centuries early [INST·61 The Ray]
1602 — Galileo: times swinging lamps against his own pulse and declares the pendulum isochronous — the swing takes the same time whatever its width. The observation that would define the second, and (for wide swings) a lie [INST·84 (Elias Edition) The Metronome] [INST·85 (Elias Edition) The Tangle]
1621 — Snell: rediscovers the sine law of refraction n₁ sin θ₁ = n₂ sin θ₂ (published by Descartes 1637); the empirical bend the principle of least time must explain [INST·61 The Ray]
1656 — Huygens: hangs Galileo’s pendulum inside a clock — timekeeping error collapses from a quarter-hour a day to seconds, and for the next 271 years the pendulum is how civilisation knows what time it is [INST·84 (Elias Edition) The Metronome]
1659 — Huygens: proves the cycloid is the tautochrone — a bead released anywhere on it reaches the bottom in the same time — and hangs a pendulum from cycloidal cheeks to keep true time [INST·62 The Bead] [INST·84 (Elias Edition) The Metronome]
1662 — Fermat: derives Snell’s law from a deeper premise — light takes the path of least time — the first physical law stated as a minimum principle [INST·61 The Ray]
1665 — Huygens: two pendulum clocks on one beam fall into step — synchrony, first noticed [INST·23 The Chorus]
1669 — Newton · Raphson: root-finding by sliding down the tangent — De analysi’s iteration, simplified by Raphson in 1690 into the z − f/f′ update still running inside every solver [INST·80 (Elias Edition) The Basin]
1669 — Huygens: settles the laws of elastic collision for the Royal Society (beside Wallis and Wren) — momentum and live force both conserved, the update every clack still obeys [INST·83 (Elias Edition) The Clack]
1687 — Newton: universal gravitation — and the two-body ellipse, solved exactly [INST·17 The Orbit]
1690 — Huygens: Traité de la Lumière: each wavefront point is a source of secondary wavelets — refraction as the geometry of slower wavefronts, the wave companion to Fermat’s ray [INST·61 The Ray]
1696 — Joh. Bernoulli: poses the brachistochrone as a public challenge and solves it by an optical analogy; Newton, Leibniz, l’Hôpital and Jakob Bernoulli answer — the curve of fastest descent is a cycloid [INST·62 The Bead]
1733 — de Moivre: the first normal curve, as the limit of many coin flips [INST·19 The Walk]
1736 — Euler: settles the seven bridges of Königsberg by refusing to enumerate routes — a walk crossing every bridge once needs zero or two land masses of odd degree, and the city has four; the paper that founds graph theory by weighing the shores instead [INST·92 (Noa Edition) The Bridges]
1737 — Euler: writes ζ(s) as a product over primes, and from Σ 1/p diverging gives a new proof they never run out [INST·70 The Prime]
1738 — D. Bernoulli: resolves the St. Petersburg paradox by proposing that people maximise expected utility, not expected money, with utility growing like the logarithm of wealth — the seed of growth-optimal betting [INST·75 The Wager] [INST·86 (Elias Edition) The Ensemble]
1744 — Maupertuis: proposes the principle of least action — nature is thrifty with a quantity ∫ p dq — generalising Fermat’s least time from light to matter [INST·63 The Action]
1744 — Euler: Methodus inveniendi founds the calculus of variations and gives the equation an extremal curve must satisfy — the tool that turns “least time/action” into a solvable equation [INST·62 The Bead] [INST·63 The Action]
1747 — d'Alembert: solves the vibrating-string wave equation [INST·15 The String]
1750 — Euler: counts vertices, edges and faces of solids in a letter to Goldbach — V − E + F = 2, the number a surface conserves no matter how a drawing on it struggles [INST·91 (Noa Edition) The Utilities]
1760 — Bernoulli: the first mathematical epidemic model — weighing smallpox inoculation against the disease [INST·28 The Contagion]
1763 — Bayes: belief updates as posterior ∝ likelihood × prior — the rule the filter runs [INST·25 The Lens]
1765 — Euler: the equations of torque-free rotation — Theoria motus corporum solidorum, the principal axes and their moments [INST·71 The Racket]
1772 — Lagrange: the equilateral three-body solution and the L-points [INST·17 The Orbit]
1787 — Chladni: bows a sand-strewn metal plate and the grains leap off the moving regions to settle on the still nodal lines — the first images of a vibration’s modes [INST·47 The Drum]
1788 — Lagrange: Mécanique analytique recasts all of mechanics from L = T − V and δ∫L dt = 0 — no forces, no diagrams, one variational principle and the Euler–Lagrange equations [INST·63 The Action]
1796 — Gauss & Legendre: conjecture the prime count grows like x / ln x — Gauss noticed it at fifteen, Legendre put it in print [INST·70 The Prime]
1801 — Young: the original two-slit experiment — light interferes, so light is a wave [INST·11 The Slit]
1809 — Gauss: least squares to track Ceres from a few noisy sightings — estimation is born [INST·25 The Lens]
1810 — Laplace: the Central Limit Theorem in its general form [INST·19 The Walk]
1812 — Gauss: writes Laplace that he knows the invariant measure of the continued-fraction map — the statistics every number’s digits obey, stated a century before ergodic theory existed to prove it [INST·88 (Elias Edition) The Fraction]
1813 — Poncelet: the closure theorem, drafted as a prisoner of war at Saratov — if one orbit riding a caustic closes after n bounces, every orbit on that caustic closes in n [INST·82 (Elias Edition) The Billiard]
1815 — Cauchy: founds the calculus of permutations: every shuffle is even or odd and no sequence of swaps can change which — the coin the fifteen puzzle will be flipping seventy years later [INST·90 (Noa Edition) The Fifteen]
1822 — Fourier: claims any periodic signal is a sum of sines (Théorie analytique de la chaleur) [INST·01 The Spectrum] [INST·15 The String]
1822 — Navier: writes the momentum equation — viscosity and all [INST·03 The Flow]
1831 — Faraday: discovers induction and thinks in lines of force — the first picture of a field filling space, not action at a distance [INST·52 The Field]
1833 — Gauss: writes down the linking integral — a number, computed from two curves, that counts how many times they wind through one another; topology’s first invariant, and the count that makes any two Hopf fibres inseparable [INST·78 The Weave]
1834 — Scott Russell: observes a solitary wave of translation on the Union Canal near Edinburgh — a heap of water that travels a mile without changing shape [INST·40 The Soliton]
1834 — W. R. Hamilton: states the principle of stationary action δS = 0 in its modern form, unifying optics and mechanics under one geometry of extremal paths [INST·63 The Action]
1834 — Poinsot: the geometric picture — the inertia ellipsoid rolling on a fixed plane, tracing the polhode and herpolhode [INST·71 The Racket]
1845 — Stokes: puts it on rigorous footing: the modern Navier–Stokes form [INST·03 The Flow]
1847 — Cauchy: method of steepest descent — follow the negative gradient downhill, the optimiser still in use [INST·27 The Descent]
1848 — Wilbraham: first spots the overshoot at a jump — then it is forgotten for fifty years [INST·01 The Spectrum]
1848 — Villarceau: shows a torus sliced on the right diagonal cuts in perfect circles — the two hidden circles through every point of a ring that the Hopf fibres turn out to trace [INST·78 The Weave]
1850 — Dirichlet: studying quadratic forms, partitions the plane into regions of nearest lattice point — the first “Dirichlet tessellation”, the idea later named after Voronoi [INST·59 The Mosaic]
1852 — Schläfli: classifies the regular polytopes in every dimension — exactly six in 4-D, only three in each dimension above — decades before anyone could draw one [INST·54 The Tesseract]
1859 — Darwin: On the Origin of Species: heritable variation plus differential survival is enough to build endless complexity with no designer — the algorithm before anyone called it one [INST·60 The Strain]
1859 — Riemann: extends ζ to the complex plane and ties π(x) exactly to its zeros — the explicit formula, and the Hypothesis still open [INST·70 The Prime]
1865 — Clausius: names entropy and states the second law of thermodynamics [INST·18 The Arrow]
1865 — Maxwell: unifies electricity, magnetism and light into one set of field equations — and predicts electromagnetic waves at speed c [INST·52 The Field]
1867 — Maxwell: proposes a tiny "demon" that sorts fast from slow molecules — apparently defeating the second law without doing work [INST·39 The Demon]
1867 — Kelvin: proposes atoms are knotted vortex rings in the ether — wrong physics, but it launches the mathematical study of knots [INST·53 The Knot]
1872 — Boltzmann: the H-theorem and S = k ln Ω — irreversibility from counting [INST·18 The Arrow]
1873 — Hierholzer: proves the converse Euler left open: a connected graph with zero or two odd vertices always has an Eulerian trail, built by splicing closed detours — so fixing the parity genuinely opens the walk [INST·92 (Noa Edition) The Bridges]
1876 — Loschmidt: the reversibility objection: symmetric laws, an asymmetric world [INST·18 The Arrow]
1877 — Tait: begins tabulating knots by crossing number — the first knot tables, and the conjectures that drove the field for a century [INST·53 The Knot]
1879 — Cayley: asks which starting points Newton’s method sends to which root — solves the quadratic (a straight border), admits the cubic “presents considerable difficulty”, and stops [INST·80 (Elias Edition) The Basin]
1879 — Johnson & Story: prove in the American Journal of Mathematics that sliding reaches exactly half of all deals — the even half; the 14-15 swap lives on the other island, unreachable by any path [INST·90 (Noa Edition) The Fifteen]
1880 — Stringham: first publishes pictures of the regular 4-polytopes, projected to the page — the figures that made the fourth dimension something you could see [INST·54 The Tesseract]
1883 — Reynolds: his number, and the dye experiment that catches laminar flow breaking up [INST·03 The Flow]
1887 — Michelson–Morley: find no aether — light's speed refuses to add up [INST·22 The Cone]
1888 — Hinton: coins the word "tesseract" for the 4-cube and popularises seeing the fourth dimension through its 3-D shadows and cross-sections [INST·54 The Tesseract]
1890 — Poincaré: no closed form for three bodies — the first sight of chaos [INST·05 The Divergence] [INST·17 The Orbit] [INST·89 (Elias Edition) The Last Torus]
1890 — Poincaré: recurrence: a closed system must eventually return near its start [INST·18 The Arrow] [INST·81 (Elias Edition) The Cat]
1891 — Hurwitz: every irrational is approached within 1/(√5·q²) by infinitely many fractions p/q — and √5 is sharp, because the golden ratio can be served no better: the worst-approximable number, identified and convicted [INST·88 (Elias Edition) The Fraction]
c. 1891 — Loyd: claims the fifteen-puzzle craze and hangs $1000 on the 14-15 swap — a prize designed to be safe, twelve years after the proof that it could never be paid [INST·90 (Noa Edition) The Fifteen]
1892 — Lyapunov: his stability theory gives the exponent λ that measures the stretch [INST·05 The Divergence]
1895 — Korteweg & de Vries: derive the KdV equation for shallow water waves and find its exact soliton solution, vindicating Scott Russell 60 years later [INST·40 The Soliton]
1895 — Lorentz: the force on a moving charge, F = q(E + v×B) — the law that bends every trajectory in this instrument [INST·52 The Field]
1896 — Hadamard & de la Vallée Poussin: independently prove the Prime Number Theorem, from ζ having no zeros on the line Re(s) = 1 [INST·70 The Prime]
1897 — Pareto: measures incomes across Europe and finds the same heavy power-law tail everywhere — the 80/20 law, the first quantitative law of inequality [INST·72 The Ledger]
1899 — Gibbs: explains it: the ripple narrows but homes in on ≈8.95%, never vanishing [INST·01 The Spectrum]
1900 — Bachelier: models market prices as a random walk — finance meets diffusion, the first time-series [INST·19 The Walk] [INST·24 The Oracle]
1904 — von Koch: draws the Koch curve — a continuous line with no tangent anywhere, built by one recursive rule that replaces each segment with four — an early fractal decades before the word existed [INST·58 The Seed]
1905 — Einstein: Brownian motion ties the walk to atoms and Avogadro's number [INST·19 The Walk] [INST·43 The Bloom]
1905 — Einstein: special relativity: c is invariant, and space and time mix [INST·22 The Cone]
1906 — Markov: the Markov chain — a process whose next step depends only on the present, with a long-run equilibrium [INST·32 The Rank] [INST·45 The Regime]
1908 — Minkowski: spacetime — the geometry in which the light cone is absolute [INST·22 The Cone]
1908 — Langevin: the Langevin equation — Newton plus a random force; the stochastic differential equation that underlies every diffusion here [INST·43 The Bloom]
1908 — Voronoi: generalises the nearest-point partition to any dimension and gives it rigour; the cells now carry his name and turn up across physics, biology and computer science [INST·59 The Mosaic]
1909 — Haar: the first wavelet — a square step that splits a signal by scale [INST·37 The Loom]
1911 — Weyl: Weyl’s law — the count of eigenfrequencies below a bound grows with the drum’s area, so the spectrum does betray the size, if not the shape [INST·47 The Drum]
1912 — Perron & Frobenius: a positive matrix has one largest eigenvalue with an all-positive eigenvector — the unique, well-defined rank [INST·32 The Rank]
1912 — Smoluchowski: the one-way-valve gedankenexperiment — a passive trapdoor cannot rectify thermal fluctuations into work, because at one temperature the door jiggles exactly as hard as the molecules it is meant to sort [INST·87 (Elias Edition) The Ratchet]
1913 — Bohr: quantises the hydrogen atom — electrons sit on fixed energy rungs E_n = −13.6 eV/n², explaining its spectral lines a decade before wave mechanics justified the ladder [INST·51 The Orbital]
1913 — Dudeney: prints gas–water–electricity in The Strand Magazine, calling the puzzle "as old as the hills" — three houses, three utilities, nine wires, no crossings; already known to have no answer [INST·91 (Noa Edition) The Utilities]
1915 — Einstein: general relativity: matter curves spacetime, and light follows the curve [INST·07 The Well] [INST·48 The Horizon]
1915 — Whittaker: the interpolation formula that rebuilds a signal from its samples [INST·08 The Strobe]
1916 — Schwarzschild: the first exact solution — and with it, the event horizon [INST·07 The Well] [INST·48 The Horizon]
1918 — Julia & Fatou: the dynamics of z² + c — decades before anyone could see it [INST·21 The Set] [INST·80 (Elias Edition) The Basin]
1919 — Eddington: the eclipse measures the bending at twice Newton's value — Einstein, famous overnight [INST·07 The Well]
1924 — Bose: new statistics for light quanta — particles that bunch together [INST·14 The Condensate]
1924 — de Broglie: matter has a wavelength too — so particles can interfere [INST·11 The Slit] [INST·51 The Orbital]
1925 — Einstein: extends Bose statistics to atoms and predicts the condensate [INST·14 The Condensate]
1925 — Ising: solves the 1D chain — and finds no phase transition (the model nearly dies here) [INST·04 The Threshold] [INST·36 The Engram]
1925 — Lotka: derives the oscillating predator–prey equations in Elements of Physical Biology — a population read as a chemical-style dynamical system [INST·44 The Tide]
1925 — Yule: a growth process for biological genera in which the already-large grow fastest — the first “rich get richer” mechanism behind a power law [INST·74 The Hub]
1926 — Schrödinger: the wave equation — the whole future of ψ [INST·12 The Wavefunction] [INST·51 The Orbital]
1926 — Born: |ψ|² is probability: the cloud itself (Nobel 1954) [INST·12 The Wavefunction] [INST·51 The Orbital] [INST·67 The Qubit]
1926 — Volterra: explains why the WWI pause in Adriatic fishing raised the shark fraction — the same equations, from his son-in-law fish-market data [INST·44 The Tide]
1927 — Hund: first spots tunnelling, in the splitting of molecular spectra [INST·13 The Tunnel]
1927 — Madelung: rewrites ψ as a fluid — a density and a flowing phase [INST·12 The Wavefunction]
1927 — Kermack & McKendrick: the SIR model and the epidemic threshold: an outbreak needs R₀ > 1 to take off [INST·28 The Contagion]
1927 — Reidemeister: proves that any two diagrams of the same knot differ by three local moves — so a knot invariant is anything those moves leave unchanged [INST·53 The Knot]
1927 — Birkhoff: makes the billiard the model dynamical system — the flight between walls compressed into the area-preserving bounce map (s, sin θ), the whole table read two numbers at a time [INST·82 (Elias Edition) The Billiard]
1928 — Gamow: explains alpha decay by tunnelling — radioactivity as a quantum leak [INST·13 The Tunnel]
1928 — Nyquist: fixes the rate: sample above twice the top frequency [INST·08 The Strobe]
1929 — Hubble: galaxies recede at a speed proportional to their distance — the universe is expanding [INST·50 The Web]
1929 — Szilárd: resolves the demon with a one-molecule engine: one measurement yields kT ln 2 of work — and costs one bit of memory [INST·39 The Demon]
1930 — Kuratowski: characterizes every graph that can be drawn flat: planar exactly when it hides no K₅ and no K₃,₃ — the utilities board convicted by name, and made one of only two minimal culprits [INST·91 (Noa Edition) The Utilities]
1931 — Gibrat: the law of proportionate effect — sizes that grow by random percentages drift into a log-normal spread, an early mechanism for the fat tail [INST·72 The Ledger]
1931 — Hopf: fibres the 3-sphere into linked circles, one over each point of the 2-sphere — the first map proven impossible to unwind (π₃(S²) ≠ 0), and the shape hiding under every qubit [INST·78 The Weave]
1933 — Kotelnikov: proves the sampling theorem in full [INST·08 The Strobe]
1933 — Zwicky: the Coma cluster moves far too fast for its visible mass — most of the gravitating matter is unseen [INST·50 The Web]
1933 — Thompson: the first bandit algorithm — to choose between two medical treatments, draw each one’s success rate from its Bayesian posterior and play the winner; posterior sampling, forgotten for sixty years then found to be near-optimal [INST·76 The Bandit]
1934 — Gause: tests predator–prey in test tubes of Paramecium and Didinium — the predator eats all prey then starves; coexistence needs a refuge [INST·44 The Tide]
1934 — Delaunay: defines the dual triangulation — connect seeds whose cells touch — that maximises the smallest angle and avoids thin slivers, the default mesh of computational geometry [INST·59 The Mosaic]
1935 — Einstein, Podolsky & Rosen: argue QM must be incomplete — "spooky action at a distance" can't be real [INST·38 The Pact]
1935 — Greenshields: measures the first speed–density relation from photographs of real traffic — the fundamental diagram, where flow rises, peaks at a critical density, then falls as the road clogs [INST·55 The Jam]
1936 — Whitney: the embedding theorem — any smooth d-manifold sits faithfully inside ℝ^(2d+1) [INST·31 The Shadow]
1936 — Church: defines the λ-calculus and shows it captures all effective computation — the same class Turing’s machine reaches, the two halves of the Church–Turing thesis [INST·64 The Tape]
1936 — Turing: On Computable Numbers defines the machine, builds a universal one that runs any other, and proves the halting problem has no algorithm — the birth of computer science [INST·64 The Tape]
1937 — Landau: the general theory of phase transitions and the order parameter [INST·04 The Threshold]
1938 — London: ties superfluid helium to Bose–Einstein condensation [INST·14 The Condensate]
1942 — Alfvén: magnetohydrodynamics and the guiding-centre drift — why a plasma follows field lines and slips sideways as E×B (Nobel 1970) [INST·52 The Field]
1944 — Onsager: solves the 2D Ising model exactly — T_c and the critical exponents, by hand [INST·04 The Threshold]
1944 — Gutenberg & Richter: earthquake magnitudes follow a power law — no characteristic size, decades before anyone could say why [INST·29 The Sandpile]
1944 — Itô: stochastic calculus: the lemma that integrates dS exactly into a log-normal [INST·24 The Oracle]
1944 — von Neumann & Morgenstern: Theory of Games and Economic Behavior founds game theory — rational players, payoff matrices and the minimax theorem [INST·33 The Tournament]
1946 — Gabor: tiles time–frequency into "logons" and finds the joint-resolution limit [INST·37 The Loom]
1946 — Bloch: introduces the Bloch vector for nuclear magnetic resonance — the unit sphere it sweeps out becomes, decades later, the geometry of every single qubit [INST·67 The Qubit] [INST·78 The Weave]
1946 — Black: poses the mutilated chessboard in Critical Thinking — cut two opposite corners and no thirty-one dominoes can tile the sixty-two squares, because every domino covers one black and one white and the lost corners share a colour [INST·93 (Noa Edition) The Tiling]
1948 — Shannon: 'A Mathematical Theory of Communication' — entropy, capacity, the whole field [INST·20 The Code]
1948 — von Neumann & Ulam: invent cellular automata — a self-reproducing machine on a grid [INST·09 The Rule] [INST·35 The Garden] [INST·79 The Broth]
1948 — Coxeter: publishes Regular Polytopes — the modern synthesis of Schläfli symbols, reflection groups and projections the field still works from [INST·54 The Tesseract]
1948 — Feynman: recasts quantum mechanics as a sum over all paths weighted by e^(iS/ℏ) — and shows the classical least-action path is simply where the phases stop cancelling [INST·63 The Action]
1949 — Onsager: circulation is quantised: vortices carry integer charge [INST·12 The Wavefunction]
1949 — Shannon: makes the sampling theorem a cornerstone of digital signal processing [INST·08 The Strobe]
1949 — Ulam · Metropolis: the Monte Carlo method — answer by sampling when the formula is hard [INST·24 The Oracle] [INST·34 The Anneal]
1949 — Hebb: 'neurons that fire together wire together' — memory as the strengthening of a connection [INST·36 The Engram]
1949 — Flood: poses the “fiancée problem” — choosing when to stop among candidates seen one at a time in random order; the first statement of what would become the secretary problem, from a co-author of the Prisoner’s Dilemma [INST·77 The Secretary]
1950 — Hamming: the first error-correcting code — parity that names the flipped bit [INST·20 The Code]
1950 — Nash: the Nash equilibrium — every finite game has a stable strategy profile no player can beat by deviating alone [INST·33 The Tournament]
1951 — Belousov: discovers a chemical reaction that oscillates in colour instead of settling to equilibrium — rejected as impossible by the journals, and ignored for a decade [INST·46 The Spiral]
1952 — Turing: 'The Chemical Basis of Morphogenesis' — diffusion can make pattern, not just smooth it [INST·06 The Skin]
1952 — Robbins: Some aspects of the sequential design of experiments — names and formalises the multi-armed bandit, the clean statement of the explore-versus-exploit dilemma [INST·76 The Bandit]
1953 — Metropolis, Rosenbluth & Teller: the Metropolis algorithm — sample a Boltzmann distribution by accepting moves with probability min(1, e^−ΔE/T) [INST·34 The Anneal]
1954–63 — Kolmogorov, Arnold & Moser: the KAM theorem — under a small perturbation the invariant tori that survive are exactly the ones whose winding numbers are hardest to approximate by rationals: order persists where arithmetic is worst [INST·89 (Elias Edition) The Last Torus]
1955–56 — Lighthill, Whitham & Richards: model traffic as a compressible fluid: density obeys a conservation law, and a jam is a shock wave — a moving discontinuity that travels backward through the stream of cars [INST·55 The Jam]
1956 — Kelly: A New Interpretation of Information Rate — a gambler with a private wire should stake the fraction of his bankroll that maximises expected log-wealth, and his growth rate then equals the Shannon capacity of the channel [INST·75 The Wager] [INST·86 (Elias Edition) The Ensemble]
1957 — Esaki: the tunnel diode puts the effect to work (Nobel 1973) [INST·13 The Tunnel]
1957 — Broadbent & Hammersley: founding paper on percolation — originally motivated by fluid flow through random media [INST·26 The Percolation]
1957 — Bellman: dynamic programming and the principle of optimality — the value of a state is its best reward plus the discounted value of where you land; also names the curse of dimensionality [INST·42 The Maze]
1958 — Rosenblatt: the perceptron: a learning machine of weighted neurons — but a single layer cannot solve XOR [INST·27 The Descent]
1959 — Holling: the functional response — a predator saturates because prey take time to handle (type II); the realism that lets the model cycle and crash [INST·44 The Tide]
1959 — Erdős & Rényi: the theory of random graphs — wire N nodes with independent edges and a giant component snaps in abruptly; the null model every real network is measured against [INST·74 The Hub]
1960 — Reed & Solomon: codes that armour CDs, QR codes and deep-space links [INST·20 The Code]
1960 — Kalman: the recursive filter: optimal estimation of a linear system, one step at a time [INST·25 The Lens]
1960 — Gardner: popularises the puzzle as the “sultan’s dowry” / secretary problem in Scientific American, and the surprising 1/e answer reaches a wide audience [INST·77 The Secretary]
1961 — Jönsson: runs the double slit with single electrons, one at a time [INST·11 The Slit]
1961 — Landauer: shows that erasing one bit of information dissipates at least kT ln 2 as heat — information is physical [INST·39 The Demon]
1961 — FitzHugh & Nagumo: reduce the Hodgkin–Huxley nerve impulse to two variables — a fast excitable voltage and a slow recovery — the minimal model of a firing, refractory medium [INST·46 The Spiral]
1961 — Wang: proposes edge-matching tiles and conjectures that any set able to tile the plane can also tile it periodically — turning geometry into a decision problem [INST·66 The Tile]
1961 — Breiman: proves the log-optimal (Kelly) strategy is asymptotically best two ways at once — it maximises the long-run growth rate and minimises the expected time to reach any wealth goal, almost surely beating every other rule [INST·75 The Wager]
1961 — Lindley: gives the dynamic-programming solution — reject a fixed early block, then take the first candidate better than all before it — and shows the optimal cutoff is the fraction 1/e [INST·77 The Secretary]
1962 — Radó: introduces the busy beaver game — a perfectly well-defined function that no program can compute, the halting problem wearing a number [INST·64 The Tape]
1962 — Thorp: Beat the Dealer — takes Kelly from card-counting blackjack to Wall Street, running the first quantitative hedge fund on the growth-optimal bet; the criterion crosses from the casino to the market [INST·75 The Wager]
1963 — Lorenz: three equations for convection — the butterfly effect, chaos found by accident from a rounded printout [INST·05 The Divergence] [INST·16 The Attractor] [INST·31 The Shadow]
1963 — Rosenzweig & MacArthur: a graphical predator–prey model with logistic prey and saturating predation — isoclines that predict a stable point or a limit cycle [INST·44 The Tide]
1963 — Ulam: doodling through a dull talk, coils the integers on a grid and the primes fall onto unmistakable diagonal lines [INST·70 The Prime]
1963 — Dynkin: sets optimal stopping on rigorous ground as a theory of Markov processes, proving the secretary problem’s cutoff fraction and win probability both tend to exactly 1/e as the field grows [INST·77 The Secretary]
1963 — Feynman: the ratchet-and-pawl lecture — works Smoluchowski’s verdict to the numbers: in a single heat bath the pawl bounces just often enough to undo its own rectifying, and the wheel only turns when two temperatures differ [INST·87 (Elias Edition) The Ratchet]
1964 — Sharkovskii: orders the periods: a map with a 3-cycle must have cycles of every length [INST·02 The Cascade]
1964 — Bell: turns "is the world local?" into an inequality you can actually measure [INST·38 The Pact]
1964 — Zhabotinsky: revives Belousov’s reaction and finds it makes travelling and rotating waves in a dish — chemistry that propagates like a nerve impulse or a heartbeat [INST·46 The Spiral]
1964 — McCarthy: files the mutilated chessboard as a "tough nut" for automated reasoning — a proof a child finds by counting colours that a resolution prover grinds at exponentially; the cycle’s wink across at the halting wall [INST·93 (Noa Edition) The Tiling]
1965 — Penrose: collapse to a singularity is inevitable — black holes are a robust prediction of relativity, not a fluke (Nobel 2020) [INST·48 The Horizon]
1965 — Cooley & Tukey: the FFT makes the transform cheap — now inside MP3, JPEG, every analyser [INST·01 The Spectrum]
1960s — Kirkpatrick et al.: Monte Carlo computation of p_c for the square lattice ≈ 0.5927 [INST·26 The Percolation]
1965 — Samuelson: geometric (not arithmetic) Brownian motion for prices — they can never go negative [INST·24 The Oracle]
1965 — Zabusky & Kruskal: rediscover solitons on a computer, observe that two pulses pass through each other unchanged — and coin the name "soliton" [INST·40 The Soliton]
1966 — Kac: “Can one hear the shape of a drum?” — asks whether two differently-shaped membranes could ever share an identical spectrum of tones [INST·47 The Drum]
1966 — Berger: disproves Wang — the domino problem is undecidable — and in the proof exhibits the first aperiodic tile set: 20,426 tiles that cover the plane but never repeat [INST·66 The Tile]
1967 — Winfree: biological oscillators sync once the coupling beats the spread [INST·23 The Chorus]
1967 — Mandelbrot: 'How Long Is the Coast of Britain?' — fractional dimension enters science: the length depends on the ruler [INST·30 The Dendrite]
1967 — Viterbi: the Viterbi algorithm — dynamic programming recovers the single most-likely hidden path through a noisy sequence, exactly, in one backward sweep [INST·45 The Regime]
1968 — Veneziano: his amplitude for the strong force secretly describes a string [INST·15 The String]
1968 — Lindenmayer: a botanist invents L-systems to model how plants develop: a grammar that rewrites every symbol in parallel each step, so a one-line rule grows into a branching organism [INST·58 The Seed]
1968 — Arnold & Avez: stretches a picture of a cat over the torus as the model chaotic map — area exactly preserved, every detail shredded along the golden-ratio directions [INST·81 (Elias Edition) The Cat]
1969 — Clauser, Horne, Shimony & Holt: the experimentally testable form of Bell's bound, S ≤ 2 [INST·38 The Pact]
1969 — Apollo: the Kalman filter flies the guidance computer to the Moon and back [INST·25 The Lens]
1969 — Chirikov: distills every kicked rotor into one area-preserving map and one knob k — the standard map, chaos’s hydrogen atom, with a resonance-overlap criterion for when the last order breaks [INST·89 (Elias Edition) The Last Torus]
1970 — Nambu, Nielsen & Susskind: read it literally: the constituents are vibrating strings [INST·15 The String]
1970 — Conway: the Game of Life makes cellular automata famous [INST·09 The Rule] [INST·35 The Garden] [INST·79 The Broth]
1970 — Gosper: finds the glider gun — Life grows without bound, so it can store and move information [INST·35 The Garden]
1970 — Zel'dovich: the approximation that lets gravity be run by hand — matter collapses first into sheets (pancakes), then filaments, then knots [INST·50 The Web]
1970 — Baum, Petrie, Soules & Weiss: the hidden Markov model with forward–backward and Baum–Welch — infer the hidden states, and the chain itself, from the observations alone [INST·45 The Regime]
1970 — Sinai: proves the dispersing billiard — a square with a disc cut out — is ergodic and hyperbolic: the first mechanical system where Boltzmann’s ergodic hypothesis actually holds [INST·82 (Elias Edition) The Billiard]
1971 — Wilson: the renormalisation group explains universality (Nobel 1982) [INST·04 The Threshold]
1971 — Hafele–Keating: flying atomic clocks confirm time dilation directly [INST·22 The Cone]
1971 — Rosenzweig: the paradox of enrichment — raising the prey carrying capacity destabilises the equilibrium into ever-wider cycles that can drive extinction [INST·44 The Tide]
1971 — Sakoda: the checkerboard model of social interaction — agents on a grid move by attraction and aversion, the first cellular model of self-sorting [INST·73 The Enclave]
1971 — Schelling: Dynamic Models of Segregation — a mild preference not to be a small local minority tips a mixed city into near-total segregation; micromotives ≠ macrobehavior [INST·73 The Enclave]
1972 — Gierer & Meinhardt: name the design rule: short-range activation, long-range inhibition [INST·06 The Skin]
1972 — May: asks whether a large complex system is stable and finds it usually is not — richly connected ecosystems tend to be less stable, not more [INST·44 The Tide]
1972 — Winfree: shows the rotating chemical spiral turns about a phase singularity — a point where phase is undefined — and ties the same geometry to cardiac fibrillation [INST·46 The Spiral]
1973 — Black · Scholes · Merton: the same log-normal, priced: option value as a discounted forecast [INST·24 The Oracle]
1973 — Maynard Smith & Price: the evolutionarily stable strategy — game theory carried into biology, where fitness rather than reason selects the move [INST·33 The Tournament]
1973 — Rechenberg: evolution strategies: mutate and select real-valued design parameters to optimise wings and nozzles in a wind tunnel — the parallel European root of evolutionary computation [INST·60 The Strain]
c. 1973 — Gomory: removes any one black and any one white square and shows a domino tiling always survives — the board’s Hamiltonian rook circuit splits into two even arcs, each trivially tiled; the exact door to Black’s wall [INST·93 (Noa Edition) The Tiling]
1974 — Little: casts a neural network as a spin system — persistent firing states are the stored memories [INST·36 The Engram]
1974 — Penrose: finds an aperiodic set of just two tiles — kite and dart — with five-fold symmetry and golden-ratio statistics, beauty falling out of impossibility [INST·66 The Tile]
1974 — Bunimovich: the stadium — chaos out of focusing walls: pull a circle apart by any nonzero amount, splice in two straight edges, and the billiard turns fully chaotic [INST·82 (Elias Edition) The Billiard]
1975 — Li & Yorke: coin the word — “Period Three Implies Chaos” [INST·02 The Cascade]
1975 — Kuramoto: the exactly solvable synchronization model — order parameter r and the critical K_c [INST·23 The Chorus]
1975 — Holland: Adaptation in Natural and Artificial Systems formalises the genetic algorithm — selection, crossover and mutation on bit-strings — and proves the schema theorem that says why it works [INST·60 The Strain]
1976 — Robert May: the logistic map as a toy ecology (Nature) — a simple law, an uncomputable fate [INST·02 The Cascade]
1976 — Price: cumulative advantage in citation networks — papers are cited in proportion to the citations they already have, deriving the power-law tail decades before it was rediscovered [INST·74 The Hub]
1978 — Feigenbaum: finds the doubling ratio δ ≈ 4.6692 is universal — on a pocket calculator [INST·02 The Cascade]
1978 — Granovetter: threshold models of collective behavior — each person acts once enough others have, so a crowd tips on the distribution of thresholds, not the average [INST·73 The Enclave]
1979 — Kaplan–Yorke: conjecture links the Lyapunov exponents to the attractor's fractal dimension [INST·16 The Attractor]
1979 — Gittins: collapses the intractable Bayesian bandit to a single number per arm — the Gittins index — and playing the highest index is exactly optimal; a landmark that was optimal but too costly to compute in practice [INST·76 The Bandit]
1979 — Greene: prices the death of the standard map’s last invariant circle: the golden torus breaks at k ≈ 0.971635, located by watching the residues of its Fibonacci-convergent orbits cross ¼ [INST·89 (Elias Edition) The Last Torus]
1980 — Benettin: an algorithm to measure λ from a shadow orbit — the method the rack uses live [INST·05 The Divergence] [INST·16 The Attractor] [INST·85 (Elias Edition) The Tangle]
1980 — Tsirelson: proves quantum mechanics can violate CHSH only up to 2√2 [INST·38 The Pact]
1980 — Mandelbrot: computes the set at IBM and reveals the shape [INST·21 The Set] [INST·49 The Bulb]
1980 — Peebles: the gravitational theory of how faint early-universe ripples grow into the cosmic web (Nobel 2019) [INST·50 The Web]
1980 — Packard, Crutchfield, Farmer & Shaw: “Geometry from a Time Series” — reconstruct an attractor from a single signal’s own delayed copies [INST·31 The Shadow]
1980 — Benioff: builds the first quantum-mechanical model of a Turing machine, showing computation can run on quantum hardware — the field’s opening move [INST·67 The Qubit]
1981 — Binnig & Rohrer: the scanning tunnelling microscope feels single atoms (Nobel 1986) [INST·13 The Tunnel]
1981 — Witten & Sander: diffusion-limited aggregation — random walkers stick on contact into a branching fractal of dimension ≈ 1.71 [INST·30 The Dendrite]
1981 — Takens: proves it: delay-coordinate embedding is generically diffeomorphic to the true attractor — same invariants [INST·31 The Shadow]
1981 — Axelrod & Hamilton: the iterated tournament — Tit-for-Tat beats every cleverer rule; cooperation evolves among selfish agents that meet again [INST·33 The Tournament]
1981 — Benzi, Sutera & Vulpiani: introduce stochastic resonance to explain the 100,000-year ice-age cycle: orbital forcing alone is too weak — noise from climate fluctuations makes it detectable [INST·41 The Noise]
1982 — Sparrow: the definitive study of the Lorenz equations [INST·16 The Attractor]
1982 — Aspect: switches the analysers in flight — closes the locality loophole, S ≈ 2.7 [INST·38 The Pact]
1982 — Nienhuis: exact critical exponents β = 5/36, ν = 4/3 via Coulomb gas / conformal field theory [INST·26 The Percolation]
1982 — Hopfield: a recurrent net whose energy only falls, so memories are the basins of attraction it rolls into [INST·36 The Engram]
1982 — Berlekamp, Conway & Guy: 'Winning Ways' proves Life is Turing-complete — a universal computer built from one rule [INST·35 The Garden]
1982 — Douady & Hubbard: prove M is connected, and give it his name [INST·21 The Set]
1982 — Bennett: proves the demon cannot violate the second law: the erasure of its memory ledger, not the measurement, is the thermodynamic cost [INST·39 The Demon]
1982 — Anderson: the reverse-time SDE — a diffusion run backward is itself a diffusion, driven by the score of the density; the theorem generative models would later stand on [INST·43 The Bloom]
1957 / 1982 — Lloyd: his 1957 least-squares quantization method, finally published in 1982, iterates seed → cell centroid to minimise error — the algorithm behind centroidal Voronoi tessellations and k-means [INST·59 The Mosaic]
1982 — Shechtman: discovers quasicrystals — real matter with Penrose-like aperiodic order and forbidden symmetry, ridiculed for years, then the Nobel in Chemistry, 2011 [INST·66 The Tile]
1982 — Feynman: “Simulating Physics with Computers” — argues no classical machine can efficiently simulate quantum systems, and proposes a computer built of quantum parts to do it [INST·68 The Circuit]
1983 — Gray & Scott: the autocatalytic reaction–diffusion model this engine runs [INST·06 The Skin]
1983 — Wolfram: sorts the 256 elementary rules into four behaviours [INST·09 The Rule] [INST·35 The Garden]
1983 — Grassberger & Procaccia: the correlation dimension — read a strange attractor’s fractal dimension straight off the reconstructed cloud [INST·31 The Shadow]
1983 — Kirkpatrick, Gelatt & Vecchi: Optimization by Simulated Annealing — melt a hard problem, then cool it slowly through Metropolis moves into its best state [INST·34 The Anneal]
1984 — Morlet & Grossmann: formalise the continuous wavelet transform, out of seismic traces [INST·37 The Loom]
1984 — Brady & Ball: copper electrodeposits grow as DLA fractals — the model caught in the lab, the same dimension measured in metal [INST·30 The Dendrite]
1984 — Jones: discovers a new knot polynomial out of operator algebras — distinguishing knots that had resisted for decades (Fields Medal 1990) [INST·53 The Knot]
1985 — Amit, Gutfreund & Sompolinsky: the spin-glass calculation: the net stores ≈0.138N patterns before the basins dissolve [INST·36 The Engram]
1985 — Černý: independently applies thermodynamic annealing to the travelling-salesman problem — the method arrives twice at once [INST·34 The Anneal]
1985 — Deutsch: defines the universal quantum computer and the quantum Turing machine, and gives the first problem a quantum computer answers in fewer queries than any classical one [INST·67 The Qubit] [INST·68 The Circuit]
1985 — Dzhanibekov: a cosmonaut spins a wing-nut off a bolt aboard Salyut-7 and films it flipping end over end, unbidden, in free fall [INST·71 The Racket]
1985 — Lai & Robbins: proves the hard floor — no policy can do better than regret growing as the logarithm of time, and gives index rules that achieve it; the benchmark every bandit algorithm is now measured against [INST·76 The Bandit]
1986 — Rumelhart, Hinton & Williams: backpropagation trains hidden layers efficiently — the multilayer network finally learns [INST·27 The Descent]
1986 — Reynolds: Boids: three local rules — align, cohere, separate [INST·10 The Flock]
1986 — Langton: describes the ant: a two-rule automaton that wanders chaotically for about ten thousand steps and then, unbidden, builds a periodic “highway” and follows it forever [INST·65 The Ant]
1987 — Bak, Tang & Wiesenfeld: self-organized criticality: a sandpile tunes itself to the critical point and emits 1/f noise — no parameter set by hand [INST·29 The Sandpile]
1988 — Daubechies: compactly-supported orthonormal wavelets — the basis inside JPEG 2000 [INST·37 The Loom]
1988 — Sutton: temporal-difference learning — update a prediction from a later, better prediction, with no model of the world; the bracket that becomes Q-learning [INST·42 The Maze]
1989 — Laskar: the inner Solar System is chaotic, with a ~5-million-year horizon [INST·17 The Orbit]
1989 — Mallat: multiresolution analysis + the fast wavelet transform [INST·37 The Loom]
1989 — Hart, Sandin & Kauffman: distance-estimated ray tracing — march a ray by a safe lower bound on the distance to the surface, which is what makes a 3D escape-time fractal renderable at all [INST·49 The Bulb]
1989 — Watkins: Q-learning — a model-free, off-policy rule that provably converges to the optimal action-values just by trying, watching and updating [INST·42 The Maze]
1989 — Hamilton: the Markov-switching model carries hidden-state inference into economics — reading booms and recessions as latent regimes behind the noise of GDP and returns [INST·45 The Regime]
1989 — Goldberg: Genetic Algorithms in Search, Optimization, and Machine Learning carries the method out of Holland’s lab into mainstream engineering and optimization [INST·60 The Strain]
1990 — De Kepper: first chemical Turing patterns seen in the lab (the CIMA reaction) [INST·06 The Skin]
1990 — Dhar: the abelian sandpile: topplings commute, the recurrent states form a group, and the identity is a fractal [INST·29 The Sandpile]
1990 — Prusinkiewicz & Lindenmayer: The Algorithmic Beauty of Plants gives L-systems a turtle to draw with, plus brackets, randomness and parameters — and lifelike ferns, trees and flowers fall straight out of the strings [INST·58 The Seed]
1991 — Shishikura: proves the Mandelbrot boundary has Hausdorff dimension 2 [INST·21 The Set]
1991 — Ashbaugh, Chicone & Cushman: a rigorous account of the half-turn — the “tennis-racket theorem”, why the middle-axis flip is exactly periodic [INST·71 The Racket]
1992 — Nowak & May: spatial games — cooperators and defectors on a grid form ever-shifting fractal patterns; structure alone sustains cooperation [INST·33 The Tournament]
1992 — Tesauro: TD-Gammon reaches near-expert backgammon by playing millions of games against itself — temporal-difference learning, scaled up, beats hand-tuned programs [INST·42 The Maze]
1992 — Gordon, Webb & Wolpert: answers Kac — no: they build two different polygonal drums with exactly the same spectrum. You can hear the area and perimeter, but not the shape [INST·47 The Drum]
1992 — Nagel & Schreckenberg: reduce traffic to four cellular-automaton rules — accelerate, brake, dawdle, move — and a phantom jam condenses out of nothing above a critical density, with no accident or bottleneck to cause it [INST·55 The Jam]
1992 — Bunimovich & Troubetzkoy: prove the ant’s path is always unbounded from any finite start — so the highway must eventually emerge, though no shortcut says when [INST·65 The Ant]
1992 — Deutsch & Jozsa: turn that into the first exponential separation — decide in a single query whether a function is constant or balanced, where every classical method needs many [INST·68 The Circuit] [INST·69 The Search]
1992 — Dyson & Falk: the period of the discrete cat map — a scrambled N-pixel picture must return exactly, in at most 3N steps, on a schedule no smooth formula predicts [INST·81 (Elias Edition) The Cat]
1992 — Shinbrot, Grebogi, Wisdom & Yorke: run a real double pendulum on a bench and measure its trajectories diverging at λ ≈ 7.5 s⁻¹ — the textbook clock, hinged once more, certified chaotic in the laboratory [INST·85 (Elias Edition) The Tangle]
1992 — Ajdari & Prost: the flashing ratchet — switch an asymmetric sawtooth potential on and off and diffusing particles are pumped one way with no net force applied: a rectified fluctuation, running as a machine [INST·87 (Elias Edition) The Ratchet]
1993 — Berrou: turbo codes reach within a whisker of the Shannon limit [INST·20 The Code]
1994 — Watts & Strogatz · Barabási: percolation transitions in real-world networks: internet, epidemics, markets [INST·26 The Percolation] [INST·32 The Rank]
1994 — Moss, Pierson & O'Gorman: demonstrate stochastic resonance in biological neurons — sensory systems appear to operate near the optimal noise level for signal detection [INST·41 The Noise]
1994 — Shor: finds a quantum algorithm that factors large integers in polynomial time — breaking RSA in principle and turning a curiosity into a field with stakes [INST·69 The Search]
1995 — Englert–Greenberger–Yasin: pin down the exact duality relation V² + D² ≤ 1 [INST·11 The Slit]
1995 — Cornell, Wieman & Ketterle: the first gaseous BEC, at JILA and MIT (Nobel 2001) [INST·14 The Condensate]
1995 — Vicsek: the minimal model — collective motion as a true phase transition [INST·10 The Flock]
1996 — Grover: shows a quantum computer can find a marked item in an unsorted list of N in about √N steps — a provably optimal quadratic speedup [INST·69 The Search]
1996 — Parrondo: two games of chance, each losing on its own, alternate into a steady winner — devised as the game-theoretic shadow of the flashing ratchet (christened “Parrondo’s paradox” by Harmer & Abbott, 1999) [INST·87 (Elias Edition) The Ratchet]
1998 — Watts & Strogatz: small-world networks — a few long-range links collapse the distance a contagion must travel [INST·28 The Contagion]
1998 — Page & Brin: PageRank — rank the web by its link structure alone; a random surfer’s equilibrium, and the founding of Google [INST·32 The Rank]
1998 — Gammaitoni, Hänggi, Jung & Marchesoni: publish the landmark review of stochastic resonance, establishing it as a universal phenomenon in nonlinear noisy systems [INST·41 The Noise]
1999 — Jos Stam: “Stable Fluids” — an unconditionally stable solver; real-time fluids in a browser [INST·03 The Flow]
1999 — Barabási & Albert: Emergence of scaling in random networks — growth plus preferential attachment breeds a scale-free degree distribution P(k) ~ k⁻³, the hubs of the web made inevitable [INST·74 The Hub]
2000 — Nakagaki, Yamada & Tóth: a brainless slime mould (Physarum polycephalum) finds the shortest path through a maze between two food sources — solving a problem with its body, not a nervous system (Ig Nobel, 2008) [INST·56 The Mold]
2000 — Drăgulescu & Yakovenko: the statistical mechanics of money — if agents conserve and randomly swap it, wealth relaxes to the exponential Boltzmann–Gibbs law, money as energy [INST·72 The Ledger]
2000 — Chakraborti & Chakrabarti: let each agent save a fixed fraction before trading and the exponential becomes a peaked Gamma distribution — a self-organised middle class [INST·72 The Ledger]
2000 — Bouchaud & Mézard: a wealth model where multiplicative luck plus exchange can condense almost all the money onto a vanishing fraction of agents — economic oligarchy as a phase [INST·72 The Ledger]
2000 — Bruss: the odds theorem — a single one-line rule for a whole class of stopping problems: sum the odds of the remaining trials and stop the moment that sum passes one; the 1/e law falls out as a special case [INST·77 The Secretary]
2001 — Pastor-Satorras & Vespignani: on scale-free networks the epidemic threshold can vanish — hubs change everything [INST·28 The Contagion] [INST·74 The Hub]
2001 — Jaeger: introduces the Echo State Network: leave a large random recurrent net fixed and train only a linear readout off its activity — turning recurrent learning into one cheap regression [INST·57 The Echo]
2001 — Hubbard, Schleicher & Sutherland: how to find all roots of a polynomial by Newton’s method — a universal grid of starting points that cannot miss, Cayley’s question finally engineered [INST·80 (Elias Edition) The Basin]
2002 — Couzin: maps the switch between swarm, torus and aligned flock [INST·10 The Flock]
2002 — Maass, Natschläger & Markram: arrives at the same idea from neuroscience — the Liquid State Machine: a spiking cortical microcircuit as a fixed “liquid” whose ripples a simple readout decodes [INST·57 The Echo]
2002 — Wolfram: A New Kind of Science argues computational irreducibility is generic — that for most simple programs the only way to know the outcome is to run them [INST·65 The Ant]
2002 — Auer, Cesa-Bianchi & Fischer: UCB1 — act on the upper confidence bound of each arm, optimism in the face of uncertainty, and achieve logarithmic regret with a simple, finite-time, distribution-free rule [INST·76 The Bandit]
2003 — Galperin: “playing pool with π” — two blocks and a wall count their own collisions to 3, 31, 314, 3141…: a mass ratio of 100^(d−1) spells the first d digits of π [INST·83 (Elias Edition) The Clack]
2004 — Cook: proves Rule 110 is Turing-complete — a universal computer [INST·09 The Rule]
2005 — Strogatz: the Millennium Bridge wobble: pedestrians lock step with the sway [INST·23 The Chorus]
2005 — Nobel — Schelling: the Sveriges Riksbank Prize to Schelling (with Aumann) for game-theoretic analysis of conflict and cooperation — the segregation model among its legacy [INST·73 The Enclave]
2008 — Ballerini: real murmurations: each bird tracks ~7 neighbours, by rank not distance [INST·10 The Flock]
2008 — Sugiyama et al.: drives 22 cars around a single-lane ring told only to hold a steady speed — and a stop-and-go jam forms on its own and crawls backward, proving the model right on a real circular track [INST·55 The Jam]
2009 — White & Nylander: the Mandelbulb — take the nth power of a point in spherical coordinates and z → zⁿ + c becomes a 3D fractal with genuine surface detail [INST·49 The Bulb]
2009 — Lukoševičius & Jaeger: unify the two strands under one name — reservoir computing — and set the practical recipe: tune the spectral radius, leak rate and input scaling, then fit the readout [INST·57 The Echo]
2010 — Jones: reproduces Physarum as a multi-agent model: thousands of particles that sense, steer toward, and deposit a chemoattractant trail — from which transport networks emerge with no central control [INST·56 The Mold]
2010 — Tero et al.: fed oat flakes at the 36 cities around Tokyo, the slime grows a network rivalling the real rail map on cost, efficiency and fault-tolerance — and they distil it to an adaptive-conductivity rule [INST·56 The Mold]
2012 — Krizhevsky, Sutskever & Hinton: AlexNet: the same gradient descent, scaled to GPUs, wins ImageNet and ignites deep learning [INST·27 The Descent]
2012 — Sugihara et al.: convergent cross mapping — “shadow manifolds” turn reconstruction into a test for causation between time series [INST·31 The Shadow]
2015 — DeepMind: the Deep Q-Network learns to play 49 Atari games from raw pixels and the score alone, at human level — Q-learning with a deep net as the value function [INST·42 The Maze]
2015 — Sohl-Dickstein et al.: deep unsupervised learning by nonequilibrium thermodynamics — destroy data with a slow diffusion, then train a network to reverse each step [INST·43 The Bloom]
2016 — DeepMind: AlphaGo defeats Lee Sedol at Go — self-play reinforcement learning plus tree search solves a game long thought a decade away [INST·42 The Maze]
2016 — Gumin: releases Wave Function Collapse — a constraint-propagation tiler that learns adjacencies from one sample image — and procedural generation never looks back [INST·66 The Tile]
2018 — Pathak, Ott et al.: a reservoir trained only on data forecasts a chaotic system for several Lyapunov times and even recovers its attractor — model-free prediction right up to the horizon chaos allows [INST·57 The Echo]
2019 — Event Horizon Telescope: photographs a black hole's shadow for the first time [INST·07 The Well] [INST·48 The Horizon]
2019 — Song & Ermon: score-based generative modelling — learn the gradient of the log-density and sample by following it with Langevin dynamics [INST·43 The Bloom]
2019 — Google Quantum AI: Sycamore (53 qubits) samples a random circuit in 200 seconds that they estimate would take a classical supercomputer millennia — the first claimed quantum advantage [INST·68 The Circuit]
2019 — Chan: Lenia — Conway’s Life let go of its grid: continuous in space, time and state, one differential update grows a whole zoo of smooth, self-propelled organisms [INST·79 The Broth]
2019 — Brown: shows the bouncing blocks are Grover’s quantum search in disguise — the same 2θ rotation per step, the same ⌊π/θ⌋ count, one run in wood and one in amplitude [INST·83 (Elias Edition) The Clack]
2019 — Peters: the ergodicity problem in economics — for multiplicative wealth the time average is not the ensemble average, so a gamble can enrich the average while ruining almost everyone: a century of utility puzzles reread as one confusion of averages [INST·86 (Elias Edition) The Ensemble]
2020 — Ho, Jain & Abbeel: denoising diffusion probabilistic models — the clean recipe that made diffusion the engine behind modern image generators [INST·43 The Bloom]
2021 — Song et al.: unifies diffusion as a reverse-time SDE with a deterministic probability-flow ODE twin — one framework for every sampler [INST·43 The Bloom]
2022 — Aspect, Clauser & Zeilinger: the Nobel for the experiments proving the world is not locally real [INST·38 The Pact]
2023 — Smith, Myers, Kaplan & Goodman-Strauss: find the “hat”, a single tile — an einstein — that tiles the plane only aperiodically, ending a sixty-year search for one stone that never repeats [INST·66 The Tile]
2024 — Hopfield & Hinton: the Nobel Prize in Physics for the physics of memory and learning in neural networks [INST·36 The Engram]
2024 — bbchallenge: a distributed, machine-verified proof settles S(5) = 47,176,870 — every 5-state machine now known to halt or run forever, sixty years after the question was posed [INST·64 The Tape]

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