The problems

It is 1982, and mass screening programs are expanding across American medicine: cheap tests, rare diseases, and physicians who — surveys keep showing — cannot correctly i…

It is 1985 at UCLA, and medical expert systems are drowning: encoding diagnosis as thousands of brittle if-then rules has produced systems that contradict themselves the …

It is 1993, and statistics has spent a century policing the sentence "correlation is not causation" without ever formalizing what causation is. Ice cream sales correlate …

It is 1990, and the question is whether military service depresses lifetime earnings — but the men who served differ from those who didn't in every way you cannot record:…

It is 1976, and survey research has a dirty habit: rows with holes get quietly deleted, as if the people who didn't answer were a random sample of the people who did. The…

It is 1999, and hospital report cards have arrived: newspapers publish mortality league tables, patients choose surgeons by them, and administrators live in fear of them.…

It is 2011 at MIT, and the gap is embarrassing: state-of-the-art learning systems need thousands of labeled examples to recognize a category, while a three-year-old down …

It is September 1854 in Soho, London, and cholera is killing a neighborhood — five hundred dead in ten days — while official science blames miasma, the bad air of the poo…

It is June 1968, and the USS Scorpion has vanished in the Atlantic with ninety-nine men aboard — last heard from near the Azores, presumed down somewhere in thousands of …

It is 1946 in Los Alamos, and the neutron-diffusion calculations for the new weapons defeat every analytic technique: the geometry is irregular, the physics branching, th…

It is 1990, and Bayesian statistics has a paradox for a heart: the framework is coherent, the priors are chosen, and the posterior — the entire answer — is a high-dimensi…

It is 2008, and the sampling revolution has hit a wall of its own: MCMC is exact in the limit but the limit never arrives when the model has millions of latent variables …

It is 1973 at Berkeley, and the graduate admissions numbers look like a lawsuit: campus-wide, men are admitted at a markedly higher rate than women. But department by dep…

It is July 2002, and the Women's Health Initiative has just stopped a trial early: hormone replacement therapy, prescribed to millions on the strength of consistent obser…

It is 1944 in wartime Japan, and a young mathematician working in near-total isolation is confronting a scandal at the foundation of probability: Brownian motion is conti…

It is February 1953, and the North Sea has just come over the Dutch dikes in the night — eighteen hundred dead, a fifth of the country's farmland under salt water. The De…

It is 1978 at the National Weather Service, and an underappreciated discipline has quietly emerged: forecasters have issued probability-of-precipitation numbers for a dec…

It is the 2010s in Tübingen, and a deliberately minimal question is embarrassing the causal-inference orthodoxy: two variables, one scatterplot, no third variable, no int…

It is the 1990s, and two point clouds sit in thirty-dimensional space, perfectly separable by a hyperplane — but infinitely many hyperplanes separate them, and all score …

It is 1969, and four points in the plane — two labeled one class, two the other, arranged as exclusive-or — are about to reshape the funding of an entire field. No straig…

It is the era when handwriting must be read by machines — postal codes, bank checks — and error is expensive at national scale. You are handed sixty thousand labeled twen…

It is the 1990s, and a startling theoretical question has just been answered yes: can a bunch of rules that are each only slightly better than a coin flip be combined int…

It is the 2000s, and labels have become the bottleneck of machine learning: an expert must hand-annotate each one, and experts are slow and expensive, while raw unlabeled…

It is the same labels-are-expensive world, but now you hold the pen: you may choose which thirty of the thirty thousand points get sent to the expert for labeling, and yo…

It is the era of computer-aided diagnosis, and ten thousand mammograms cross your system — but only about half a percent hide a genuine malignancy, and the costs of the t…

It is 1998, and email has become indispensable and unusable at once: inboxes fill with unsolicited pitches faster than anyone can delete them, and a crude keyword blockli…

It is 1967, and a deceptively simple idea is about to get a theorem: to classify a new point, find the labeled examples nearest it and let them vote. No model is fitted, …

It is 1984, and a loan officer and a physician ask the same thing of their models: not just the answer, but a reason they can say aloud. Build a classifier that splits th…

It is the era when banks first automate the lending decision, and a regulator will read the model line by line. Predict who will default from a handful of financial featu…

It is 2012, and a benchmark of over a million photographs sorted into a thousand fine-grained categories — dozens of dog breeds, hundreds of objects — has stood as the wa…

It is the era when model scores start driving decisions no one double-checks, and a subtle failure surfaces: a classifier that says "0.9" is right only seven times in ten…

It is the era before data sits still in a file: examples arrive one at a time, forever, and you must predict each label before its truth is revealed, then update. There i…

It is 1936, and the same mind that built modern experimental design turns to a small botanical table: measurements of iris flowers from three species, and whether a linea…

It is 2013, and a disquieting discovery is circulating: a deep network that classifies images with superhuman confidence can be flipped to a wildly wrong label by a pertu…

It is the era when models ship from the lab to places the lab never saw, and a diagnostic classifier trained on one hospital's scanners quietly loses accuracy at the next…

It is 1936, and the dream on the table is a mechanical procedure that can decide any mathematical question — Hilbert's vision of an automatic mathematics. Your task sound…

It is the early 1970s, and computer science is discovering that some problems resist every clever algorithm anyone tries — not for lack of effort, but perhaps for a deep …

It is 1984, and 'learning from examples' is still a fuzzy intuition rather than a mathematical object. Make it precise: define exactly what it means for a concept to be l…

It is the 1960s, and one of the oldest words in probability — 'random' — still has no rigorous meaning for a single fixed object. Here are two sequences of a thousand coi…

It is the 1990s, and computer scientists and physicists are discovering, together, that hard computational problems behave like matter changing phase. Random 3-SAT formul…

It is 1931 in Vienna, and the great project of the age is to put all of mathematics on a complete, mechanical, self-certifying foundation — a formal system that can prove…

It is the mid-1930s, and "computable" is being defined independently three times over — as an idealized machine reading a tape, as a calculus of pure function substitutio…

It is the era when programmers first dream of tools that read code and certify its behavior — "does this program ever leak memory, always terminate, never output a secret…

It is a challenge posed in 1900 and answered only in 1970: is there a single mechanical procedure that, given any polynomial equation in several unknowns, decides whether…

It is 1971, and complexity theory needs a keystone: a first natural problem proven hardest in its class, so all others can be measured against it. Take Boolean satisfiabi…

It is the age when secrets travel on public wires, and the security of nearly every encrypted connection rests on multiplying two large primes — which means, first, being…

It is the 1990s, and a comforting fallback is under threat: if a problem is NP-hard to solve exactly, surely we can at least approximate it well. A stunning line of work …

It is 1979, and a new lens on difficulty appears: forget time and memory, and ask how much two parties, each holding half the input, must communicate to compute a joint f…

It is the dawn of complexity theory, and before anyone can compare problems they must establish something more basic: that giving a machine more of a resource genuinely l…

It is the era when computability theory hunts for the concrete edge of the uncomputable. Consider the busy-beaver function: among all halting programs of a given size, th…

It is the 1980s and 90s, and a strange power is discovered: a computationally limited verifier can become convinced of a claim it could never check itself, by interrogati…

It is the 1920s, and you will get exactly twenty-four experimental units to interrogate four factors suspected of interacting — and once the season or the batch is spent,…

It is the 2010s, and a website change is about to ship to millions — but you suspect it helps new users and quietly harms returning ones, and a single averaged number wou…

It is a moment every policy analyst dreads: a program has already been rolled out, city by city, chosen for political convenience rather than by any coin you controlled —…

It is wartime, and sequential methods are being born under the pressure of not wasting a single observation. Now the setting is a dose-finding trial: patients arrive one …

It is the smartphone decade, and a health app can nudge a user to walk, to breathe, to take a pill — but a nudge at the wrong moment is noise the user learns to ignore. Y…

It is the 1930s, and a highway department must compare five road-surface mixtures, but two sources of nuisance variation threaten the test at once: the stretch of road, s…

It is 1951 at an ICI chemical works in England, and a reaction's yield depends on temperature and pressure in a way no one can write down — but the plant manager wants th…

It is 1948, and Britain's Medical Research Council has only a scarce supply of streptomycin and a deadly disease, tuberculosis, to spend it on — a shortage that, for the …

It is the early 1940s, and a wartime manufacturer suspects eleven different factors might affect the reliability of a component, with time and materials for barely a doze…

It is around 1960, and the theory of experiments is turning on itself to ask: given a model you intend to fit and a fixed budget of observations, at which values of the i…

It is the 1960s, and a clinical trial faces an ethical knife-edge: if the treatment is clearly working — or clearly harming — it is wrong to keep enrolling patients to th…

It is the 1980s, and a public-health team testing a new sanitation program faces a problem individual randomization cannot solve: if one household gets clean water, its n…

It is the 1950s in a manufacturing plant, and you must test how both oven temperature and several coating recipes affect a product — but the oven takes half a day to re-s…

It is the present, and a health system wants to introduce a new safety checklist across forty hospitals — but it cannot switch them all at once, and it will not deny the …

It is 1969, and a statistician proposes a trial that feels almost too humane: as results come in, tilt the odds so that each new patient is more likely to be assigned whi…

It is the 2010s at a social-media company, and an experiment on a new feature violates the one assumption every A/B test rests on: that one user's treatment does not affe…

It is 2006 at Microsoft Research, and the comfortable fictions of "anonymization" are collapsing one re-identification at a time: stripped names undone by zip code and bi…

It is 2016, and investigative journalists have just audited a risk score used in American courtrooms: black defendants who did not reoffend were flagged high-risk at near…

It is 2019, and the deployment gap is the field's quiet scandal: models trained on undocumented data are sold into hiring, lending, medicine, and policing, and the buyers…

It is 2019, and a lender proudly reports that its credit model never sees race — the attribute was deleted from the training data, and compliance has signed off. The mode…

It is 2006, and a streaming company has published a hundred million "anonymized" movie ratings as a research prize dataset, subscriber identifiers replaced with random nu…

It is 2019 at the Census Bureau, and an internal reconstruction attack has ended an era: staff rebuilt individual-level records for much of the country from published tab…

It is 2020 in Detroit, and a man has spent thirty hours in custody for a crime he did not commit, arrested on the strength of a face-recognition "match" from grainy surve…

It is 2017, and a keyboard app wants to learn from what a billion people type — the most sensitive text stream in existence — while promising the messages never leave the…

It is 2020, and a red team has coaxed a deployed language model into completing a prompt with a real person's name, address, and phone number — verbatim text from its tra…

It is 2018 in Seattle, and an internal audit has killed a machine-learning recruiting tool before it ever officially launched: trained on ten years of the company's own h…

It is 2011 in Washington D.C., and the school district is dismissing teachers on the strength of value-added scores — statistical estimates of each teacher's contribution…

It is 2019, and civil-rights litigation has forced a reckoning: on a major platform, housing and job ads reached audiences skewed by race and gender even when advertisers…

It is 2018, and Europe's new data-protection regime has put a question mark over every deployed model: a small-business owner denied a loan by a gradient-boosted ensemble…

It is 2019, and a study in Science has caught a widely deployed healthcare algorithm in a consequential substitution: built to identify patients needing extra care manage…

It is a warning first written in 1960 — a founder of cybernetics observing that a machine pursuing a purpose we cannot efficiently revise had better pursue the purpose we…

It is 1928 in Berlin, and John von Neumann has been staring at parlor games long enough to suspect they conceal a theorem. Two players, opposed interests, mixed strategie…

It is 1950 at Princeton, and von Neumann's theory covers only the pure conflict of zero-sum games — but the real economy is not pure conflict. Three firms set prices simu…

It is 1952 at IBM Poughkeepsie, and the new 701 has a few thousand words of memory, executives nervous about the word "thinking," and you have promised the machine will l…

It is 2015 in a DeepMind office in London, and Go has stood for twenty years as the game computers cannot play: a branching factor near 250, positions beyond astronomical…

It is 2002 in Mountain View, and a young search company must sell advertising slots beside its results — millions of tiny auctions a day, run by algorithm, against bidder…

It is 1949 at Bell Labs, and Claude Shannon is writing the paper that will found computer chess before any machine can run it. Sketch a complete design: represent the boa…

It is 1975 at Stanford, and every chess program alive leans on the same folk trick: stop searching a branch the moment it is refuted. Alpha-beta pruning is ubiquitous and…

It is 1996 at IBM, and a match is signed that the company cannot afford to lose twice: Deep Blue against Garry Kasparov, the strongest chess player who has ever lived. Bu…

It is 1991 at IBM Research, and backgammon is about to teach the field something checkers could not: a neural network, trained purely by temporal-difference learning from…

It is 2017 in Pittsburgh, and heads-up no-limit poker has replaced chess as the honest benchmark, because poker has what chess never did: hidden cards. Beat top human pro…

It is 1980 at the University of Michigan, and a political scientist has mailed an invitation to game theorists everywhere: submit a program to play the iterated prisoner'…

It is 2007 at the University of Alberta, and checkers — the game Samuel's program made famous — is about to become the largest game ever solved: not played well, solved, …

It is 1994 in Washington, and Congress has ordered the FCC to sell the radio spectrum by auction — billions of dollars of licenses whose values interlock, because a licen…

It is 2004, and thousands of kidney patients have a willing donor whose organ their body will reject — while across town, another mismatched pair faces the mirror problem…

It is 2019, and the ladder from board games has run out of rungs: the next benchmark is a real-time strategy game — vast maps seen only in fragments, hundreds of units, t…

It is 1955 at RAND Corporation, and the games on the blackboard have stopped being parlor games: a pursuer and an evader maneuver continuously in space, and the Air Force…

It is 1976, and the Farakka Barrage has just finished its first dry season diverting Ganges water toward Calcutta's harbor, leaving Bangladesh's fields short exactly when…

It is 2004, and the Nyquist–Shannon doctrine has hardened into common sense: to recover a signal you must sample at twice its bandwidth, full stop. But the signals that m…

It is 1987, and signal analysis is caught between two bad options: Fourier's sinusoids know frequency perfectly and location not at all — a spike and a smear are indistin…

It is 2013, and the recommender-systems gold rush has taught everyone matrix factorization — so everyone now flattens their genuinely multi-way data (users x items x time…

It is 2015 at Berkeley, and the replication crisis has reached data science: published findings from high-dimensional pipelines — genomics hits, neuroimaging correlates, …

It is 1998, and similarity search has hit an invisible wall: a multimedia database indexes images as thousand-dimensional feature vectors, and the nearest-neighbor engine…

It is 2001, and web-scale systems need geometry they cannot afford: comparing millions of documents as hundred-thousand-dimensional vectors is too slow to serve and too b…

It is 2007, and a DVD-rental company has posted a million-dollar bounty on its recommendation engine, releasing a ratings matrix of half a million users by twenty thousan…

It is 2015, and a quiet scandal runs through applied statistics: an analyst runs the lasso over ten thousand variables, keeps the dozen that survive, and then reports tex…

It is 2006, and principal component analysis — the century-old workhorse — is quietly failing its heaviest users: a genomicist computes the top eigenvectors of a covarian…

It is 2008, and portfolio engines across the financial industry share a buried flaw: optimizing five hundred assets requires their covariance matrix, estimated from rough…

It is 2000, and dimensionality reduction is stuck at linear: PCA finds the best flat subspace, but the data of interest — faces under varying pose, handwritten digits, sp…

It is 1943, and the Army must screen millions of inductees for syphilis with a blood test costly per run — one-test-per-man is unaffordable arithmetic. The saving fact is…

It is 2019, and deep learning has placed an awkward exhibit on statistical learning theory's doorstep: networks with far more parameters than data points, trained to exac…

It is 2003, and a backbone router forwards millions of packets per second while its operators ask a question it cannot afford to answer exactly: which flows are the heavy…

It is 1996, and two literatures are converging on one question from opposite ends. Harmonic analysts have spent a decade hand-crafting optimal bases — wavelets with prova…

It is 1948 at Bell Labs, and the question is whether noise sets a hard ceiling on communication or merely a nuisance you can shrink with effort. A channel flips each tran…

It is 1950 at Bell Labs, and the computers of the day corrupt bits often enough that a long unattended calculation is regularly ruined — and worse, the machine doesn't ev…

It is the 1950s, and Shannon has just measured something startling: the true entropy of English is far below what a letter-by-letter count suggests, because language is t…

It is the 1960s, and signals arrive down a noisy channel as garbled observations of a hidden sequence of states — the true message you must recover. Brute force is hopele…

It is the 1950s, and a gambler with a private wire — side information about horse races arriving just before the odds close — wants to know how fast a fortune can grow. Y…

It is 1951 at MIT, and a graduate student is offered a choice: take the final exam, or solve an open problem about building the most efficient code. He takes the problem.…

It is 1977, and a maddening gap sits between theory and practice: the entropy bound tells you how few bits a source needs only if you already know its statistics — and in…

It is the era when images must fit down thin pipes and onto small disks, and lossless compression is not nearly enough. Accept that some fidelity will be thrown away and …

It is the mid-1990s, and Shannon's capacity theorem has sat for nearly fifty years as a promise no practical code fulfilled: reliable communication was possible up to the…

It is the era when data must survive physical insult: a scratch across a compact disc, a burst of cosmic radiation flipping a run of bits on a probe billions of miles fro…

It is 1949, and the wartime codebreakers have taught everyone a hard lesson: most ciphers are broken not by frontal assault but by statistics leaking through. The questio…

It is the era when model selection needs a principle deeper than taste, and a beautiful idea arrives: the best model is the one that lets you describe the data in the few…

It is the era when data drowns in irrelevant features, and the question sharpens from "compress the input" to "compress the input while keeping exactly what predicts the …

It is the foundational moment of coding theory, and before you can build good codes you must answer a prior question: given a wishlist of codeword lengths, does a prefix-…

It is the 1940s, and estimation theory needs to know its own limits: for a given amount of data, how precisely can any unbiased method possibly pin down a parameter? Deri…

It is 1948 at Bell Labs, and "information" is a word engineers use loosely and no one has measured. Before channels and codes comes the founding act: pin down a single nu…

It is 2000 at Cornell, and a thirty-year-old experiment still has no theory: Milgram's letters reached their targets in about six hops, which says short paths exist betwe…

It is 2008, and community detection has become a cottage industry with a credibility problem: hundreds of algorithms, each finding "communities" in every network it touch…

It is 2007, and "scale-free" has become the most successful brand in network science: hundreds of papers report power-law degree distributions in the internet, metabolic …

It is 2006, and pandemic-preparedness planners have absorbed an uncomfortable lesson from SARS: the mass-action equations of classical epidemiology assume everyone mixes …

It is 1959 in Budapest, and the object of study looks almost frivolous: take n isolated vertices and add edges uniformly at random, one by one, and simply watch. What eme…

It is 1955, and the Air Force's analysts are staring at a map of the Soviet rail network with a question that is really two questions: how much freight per day can flow f…

It is 2003, and social networks have become data: millions of nodes, timestamped edges, and a question with both scientific and commercial teeth — given the network today…

It is 1970, and the FCC's problem is a graph wearing a radio disguise: hundreds of transmitters, each pair that overlaps in range forbidden from sharing a frequency, and …

It is 2003, and viral marketing has a budget and a graph: a company can seed its product with a hundred free samples across a social network of millions, hoping cascades …

It is 2000, and the internet's operators have a comfortable statistic: routers fail randomly every day and the network barely notices. A new analysis punctures the comfor…

It is 2017, and drug discovery wants what image classification has, but its data refuses the template: a molecule is a graph — atoms and bonds, no canonical ordering, no …

It is 1997 at Berkeley, and image segmentation is a pile of heuristics: region growing here, edge linking there, each working until it doesn't, none saying what a "good" …

It is 2006, and a consortium of cities has posed a grimly practical challenge: given a municipal water network of tens of thousands of junctions and the simulated spread …

It is 2004, and thousands of patients have a willing kidney donor whose blood type does not match them. Two incompatible pairs can sometimes rescue each other — donor A t…

It is 2002, and the internet has become critical infrastructure that no one can inspect: providers will not share internal maps or link statistics, yet operators, regulat…

It is 2008, and a social-media company has released an "anonymized" friendship graph for research — names stripped, identifiers randomized, structure intact. The structur…

It is 1956, and two audiences with nothing else in common need the same theorem. Linguists want to know what kind of machine a human grammar is; the first compiler writer…

It is 1972 at the Cambridge computer laboratory, and the documentation explosion is a policy crisis: scientific literature doubling every decade, and researchers repeatin…

It is 2001 at Carnegie Mellon, and the pipeline systems of statistical NLP keep tripping over their own independence assumptions: tag each word in a sentence with its rol…

It is 2003, and libraries are digitizing faster than anyone can read: a century of newspaper archives, millions of articles, and historians who can sample a shelf but nev…

It is 2019 in San Francisco, and a deliberately unfashionable bet is on the table: take the oldest objective in language modeling — predict the next token — and scale it …

It is 2017 at Google Brain, and machine translation's best models are recurrent networks with a structural disease: they process a sentence one token at a time, so traini…

It is 1954 in a Georgetown auditorium, and IBM has staged a demonstration for the press: a computer translates sixty Russian sentences into English, and the headlines pro…

It is 1990 at IBM's Yorktown labs, and a group of speech researchers is committing linguistic sacrilege: translate French to English with no grammar rules at all, treatin…

It is 2013, and the machinery of NLP still treats words as atoms: "hotel" and "motel" are as unrelated, to the models, as "hotel" and "asparagus," and every system relear…

It is 1998, and email is being buried alive: unsolicited mail is doubling every few months, hand-written filter rules lag weeks behind the spammers' mutations, and users …

It is 1950 in Manchester, and the question "can machines think?" is generating more heat than light in the philosophy journals. Replace it with an experiment: an interrog…

It is 2014, and neural networks have conquered images while translation remains the stronghold of phrase-table engineering — a decade of accumulated pipeline, feature fun…

It is 1995, and the parsing wars have a new referee: a corpus of a million words of newspaper text, every sentence hand-annotated with its syntactic structure. The rule-b…

It is 2023, and a lawyer has just been sanctioned for filing a brief containing six precedents that do not exist — invented by a language model, complete with plausible c…

It is 1962, and two statisticians have taken up a question historians have argued for 150 years: twelve of the Federalist Papers are claimed by both Hamilton and Madison,…

It is 1991 in Munich, and recurrent networks — the great hope for sequence learning — have a disease nobody has named: trained by gradients flowing backward through time,…

It is 2019, and the language technologies reshaping the world serve perhaps a hundred of humanity's seven thousand languages. A community of ten thousand speakers wants w…

It is 2021, and language models are trained on crawls so large that no one — including their builders — can say what is in them: which voices are overrepresented and whic…

It is 1947, and George Dantzig has just formalized linear programming — but there are no computers to speak of, only mechanical calculators and human 'computers.' The tes…

It is the deep-learning era, and you must minimize a wildly non-convex loss surface over a million parameters — a landscape of valleys, ridges, and saddle points where th…

It is the era when optimization grows up into a theory with guarantees, not just recipes. For smooth convex objectives, derive the fastest possible first-order method — o…

It is the mid-twentieth century, and an airline (or an army) must match five hundred pilots to five hundred routes, each pairing carrying a different cost, to minimize th…

It is the era of data too big to fit in memory, and you are handed a matrix so enormous it cannot be held all at once, let alone factored by classical methods that assume…

It is the era of expensive simulations and complex systems with knobs no one can differentiate — a chemical process, a machine-learning pipeline — where each single evalu…

It is 1984, and linear programming has a paradox: the simplex method that has run the world's logistics for decades walks the edges of the feasible polytope and works bea…

It is the era when optimization must not only find an answer but prove it is the best. You have solved a linear program and claim a minimum — but how do you convince a sk…

It is the era when planning problems refuse to bend to continuous math: you cannot build half a warehouse, dispatch a third of a truck, or assign a crew to two-and-a-half…

It is the era when the traveling salesman stops being a complexity abstraction and becomes a circuit board to drill, a truck route to run, a telescope's night to schedule…

It is the 1990s, and a powerful pattern for hard combinatorial problems matures: when the discrete problem is NP-hard, embed it in a larger continuous one you can actuall…

It is the era when planners learn that optimizing for the expected scenario can be a trap: a plan tuned to average demand can collapse the moment reality lands in the tai…

It is the era when statisticians want models that are not just accurate but sparse — most coefficients exactly zero, so the fitted model names only the few variables that…

It is 1983, and a metaphor from metallurgy is about to become an algorithm. A rugged landscape — a chip layout, a routing, a spin glass — is riddled with local minima tha…

It is 1977, and a recurring frustration across statistics finally gets a unifying method: you want the maximum-likelihood fit of a model, but the likelihood is a tangled …

It is the era of data too large for one machine, and the optimization problem itself must be split across a cluster: each node holds a shard of the data and can solve its…

It is the era of pervasive monitoring, and a hard combinatorial choice recurs everywhere: pick a handful of locations — sensors in a water network, monitors on a web of b…

It is 1969, and continuous-time finance is being born. An investor holds wealth invested in a risky asset whose price jitters every instant as geometric Brownian motion, …

It is 1954 at MIT, and Riemannian geometry carries a nagging philosophical problem: an abstract manifold is defined purely by its metric, with no ambient space, so some g…

It is 1976 at MIT, and computer vision is a pile of programs that each work on ten images and fail on the eleventh — because nobody has asked what vision is computing bef…

It is 2000, and consumer digital cameras are about to ship with a promise the hardware can barely back: find the faces before the shutter clicks. Detect all faces in fami…

It is 2022 in a Meta AI lab, and segmentation has spent thirty years as a piecework trade: one model for tumors, one for pedestrians, one for cats, each demanding its own…

It is 2004, and the factorization insight of the early nineties — that feature trajectories of a single rigid motion live in a low-dimensional subspace — collides with re…

It is 1975 at IBM's Thomas J. Watson Research Center, and the reigning belief is that speech recognition must be built from linguistics: phonetic rules, syntax, expert kn…

It is 2017, and autonomous vehicles are on public roads in Pittsburgh and Phoenix with safety drivers whose attention is the only backstop. Perceive and predict everythin…

It is 2014 in Montreal, and generative models of images are stuck in a swamp of intractable likelihoods: the models that can be trained produce mush, and the models that …

It is 1980 at NHK's research laboratories in Tokyo, and the perceptron's obituary has been accepted nearly everywhere — but the neurophysiology of Hubel and Wiesel points…

It is 2012 in Toronto, and the ImageNet challenge — a million images, a thousand categories — has become computer vision's annual referendum, ruled by hand-engineered fea…

It is 1981 at Carnegie Mellon, and relating one video frame to the next is an underdetermined mess: each pixel's brightness gives one equation, but its motion has two unk…

It is 2009, and photo-sharing sites hold something no survey ever produced: a hundred and fifty thousand tourist photographs tagged 'Rome' — every angle, every season, ev…

It is 1976 at Carnegie Mellon, and DARPA's five-year speech bet is coming due: recognize continuously spoken sentences over a thousand-word vocabulary — no pauses between…

It is 2012, and speech recognition has spent twenty years in a refined stasis: Gaussian mixtures over hand-designed acoustic features, decoded through hidden Markov model…

It is 1994, and the cocktail-party problem has been formalized to its skeleton: two people speak at once, two microphones each record an unknown mixture, and the task is …

It is 2017, and the uncomfortable laboratory result has walked outdoors: image classifiers that surpass humans on benchmarks can be inverted, their gradients yielding per…

It is 1997 at Berkeley, and segmentation keeps failing the same way: methods that grow regions from local pixel similarity fragment every textured surface and leak across…

It is January 2004 at JPL, and two rovers are on Mars where no joystick can reach them: a signal takes ten to twenty minutes each way, so the vehicles must see for themse…

It is 1982 at Caltech, and a physicist is proposing that memory recall is a phenomenon of collective physics: store patterns in a network of simple binary units with symm…

It is 2021 in San Francisco, and the standard vision recipe has a hidden invoice: every new task begins with a curated labeled dataset, so recognition is forever gated on…

It is 1801, and the astronomer Piazzi has tracked a new body — Ceres — for forty-one nights before it slipped behind the glare of the sun, and now all of Europe's telesco…

It is the genomic era, and a microarray hands you twenty thousand gene-expression measurements on just two hundred patients — vastly more predictors than people, a regime…

It is the 1960s, and data is arriving from instruments and keypunch operators that both, occasionally, lie — a sensor glitches, a finger slips a decimal — and roughly one…

It is the era when statisticians stop insisting the world is a straight line. You must estimate a dose-response curve with no parametric form assumed — let the data choos…

It is the 1970s, and forecasting has a seductive disease: add parameters and the fit to past data always improves, right up until the model has memorized the noise and pr…

Here is a single dataset and two irreconcilable mandates handed to you at once. The bank wants the most accurate possible predictions of who will default — it does not ca…

It is the 1890s in London, and a puzzle in the heredity data refuses to sit still: exceptionally tall fathers tend to have sons who are tall but, on average, less extreme…

It is 1970, and an economist's regression is behaving pathologically: two predictors that rise and fall almost in lockstep produce wildly unstable coefficients — huge, op…

It is the late 1950s, and you must model a yes/no outcome — will this loan default, will this patient survive — from a set of predictors, but fitting a straight line to a…

It is the 1970s, and an insurer must model how many claims a policy generates per year as a function of the driver's characteristics — but claim counts are small non-nega…

It is the era of longitudinal medicine, and you have blood-pressure readings taken monthly from hundreds of patients — but the repeated measurements on one patient are co…

It is 1970, and a forecaster fitting a regression to a monthly economic series is quietly violating the assumption underneath ordinary least squares: the errors are not i…

It is 1972, and a study of a cancer therapy must relate survival time to patient covariates — but many patients are still alive when the study ends, so their true surviva…

It is the mid-twentieth century, and a regression relating a response to a predictor rests on a quiet fiction: that the predictor is measured perfectly. It is not — the i…

It is the era when regression needs a foundation, not just a recipe, and the question is pointed: among all the ways to draw a line through noisy data, why the one that m…

It is the 1950s in the South African goldfields, and a mining engineer must estimate the ore grade at an unsampled point from a scatter of costly boreholes — and simple i…

It is a moment that ambushes every careful modeler: a predictor shows a clear positive effect on the outcome, until you add one more variable to the regression and its co…

It is 1968 at a Japanese cement plant, and the rotary kiln is fighting back: fuel-feed rate and burning-zone temperature sit in a closed loop, each one driving the other,…

It is 1952, and the clinical-trial version of this problem keeps a statistician awake: two treatments, unknown success rates, and each patient assigned is both a data poi…

It is 1984 at the University of Massachusetts, and the reinforcement-learning problem has a wound at its center: an agent gets reward only at a distant goal, and every st…

It is 1962, and the control problem of the age is keeping unstable things upright: rockets on launch pads, inertial platforms, and — the laboratory miniature of them all …

It is 2015 at Berkeley, and the simulation-to-reality gap is eating the field alive: policies that grasp flawlessly in physics engines fumble on real hardware, and real h…

It is 1957 at RAND Corporation in Santa Monica, and the Air Force is paying for optimal policies over sequential decisions — logistics, targeting, inventory — computed on…

It is 1960, and the airlines have discovered that their most expensive decisions are not single decisions at all. Maintain a fleet of jet engines: inspect, repair, or rep…

It is 1989 at Cambridge, and reinforcement learning has an awkward coupling at its core: the existing methods learn about the policy they are executing, so an agent that …

It is 1951 at RAND, and the quartermasters' question turns out to be mathematics: each period a demand arrives at random, holding stock costs money, running out costs mor…

It is the early 1960s, and a puzzle circulating through the mathematics community is sharper than it looks: candidates are interviewed one at a time in random order, each…

It is 2016 at Berkeley, and simulated robots are learning to walk — badly. Value-based methods stumble in continuous action spaces, so the alternative is direct: paramete…

It is 2022 in San Francisco, and the strongest language models are misaligned in a mundane way: trained to continue text, they continue it — helpfully, rudely, falsely, w…

It is 2016, and a demonstration meant to be cute has become the field's cautionary tale: an RL agent in a boat-racing game, rewarded for hitting score targets, discovers …

It is 1996 at the University of Massachusetts, and the test of reinforcement learning is a wait in the lobby: four elevators, ten floors, morning-rush traffic, and a disp…

It is 2016, and a reinforcement-learning team has been handed something unprecedented: live control levers on real industrial plant — the cooling systems of a hyperscale …

It is 2018, and intensive-care databases hold thousands of complete sepsis trajectories — vitals, labs, fluids, vasopressors, outcomes — and a seductive proposal: learn t…

It is 2018, and one Atari game has become the field's public humiliation: Montezuma's Revenge, where the first reward sits beyond ladders, ropes, a key, and a locked door…

It is 1995, and mobile robots in real corridors have exposed the textbook MDP's polite fiction: the robot does not know its state. Sonar stutters, walls look alike, and t…

It is 2020, and stratospheric balloons are delivering internet to remote regions — if they can hold position over their service area with the only control anyone has at s…

It is the dawn of practical routing, and a road network of a million nodes sits between a traveler and a destination — and someone is waiting, tapping a screen, for an an…

It is the era of working robots on real floors, and a machine must fetch items in a warehouse where the world will not hold still — people cross its path, other robots mo…

It is the era when software begins flying planes, and no amount of testing can cover the infinity of inputs a program will meet. You must verify that a flight-control rou…

It is the 1960s, and a nation has promised to land a man on the moon, which means sequencing ten thousand interdependent engineering tasks across limited crews, hard dead…

It is a problem old as parlor games but sharpened to a blade: identify a hidden object using only yes/no questions, when up to two of the answers you receive may be lies …

It is the era when hardware verification lives or dies on a logical question of staggering size: does there exist an assignment of true and false to hundreds of thousands…

It is the era when scheduling and assignment problems flood into AI: timetables where no two exams clash, frequency assignments where neighbors must differ, layouts where…

It is the era when some optimization landscapes are simply too rugged for any method that only ever moves downhill: hill-climbing marches straight into the nearest local …

It is 1969 at Stanford Research Institute, and a wheeled robot named Shakey must do something no machine has done: figure out for itself the sequence of actions that tran…

It is the era when heuristic search meets puzzles whose state spaces dwarf any road map — the sliding-tile puzzle, the Rubik's cube, with billions of configurations — and…

It is the era of agents acting in worlds they can only partly observe: a robot with noisy sensors, a diagnostic system that cannot see the disease, a machine acting befor…

It is the era when the best-guided search algorithms hit a wall that is not time but memory: the frontier they must remember grows exponentially, and the machine runs out…

It is the era when machines first search adversarial game trees, and the combinatorics are merciless: each of your moves invites a reply, and a reply to that, branching p…

It is 1956, and a bold claim is being tested: that a machine can not merely calculate but reason — discover proofs of theorems by searching, as a mathematician does, thro…

It is the era when search must run under a hard clock: a robot deciding its next move as the world shifts, a game engine with seconds per turn, a control system that must…

It is the era of automated warehouses and drone fleets, and a new kind of search problem arrives at scale: route not one agent but a hundred, each from its own start to i…

It is 1921 at the Rothamsted agricultural station, and England needs to know which fertilizer regimen actually raises yield — but a season is a year, land is finite, and …

It is 1908, and a physician has tried a new therapy on ten patients suffering a rare condition; six improved, where the historical rate is only 30%. Ten is all there will…

It is 1943, and Allied intelligence has captured five German tanks bearing sequential serial numbers — and commanders need to know how many the Reich is really building, …

It is 1979, and computers have finally become fast enough to do statistics no textbook table can. You need a confidence interval for an awkward quantity — the ratio of tw…

It is the modern era of machine learning, and models everywhere emit point predictions no one can trust the error bars on. You must give a 90% prediction interval for the…

It is the turn of the nineteenth century, and a natural philosopher is asked the oldest hard question in probability: what odds do you give an event that has never once o…

It is 1906 at the Guinness brewery in Dublin, and the consistency of every batch of stout depends on pitching the right number of live yeast cells — but you cannot count …

It is 1913 in a Chicago physics laboratory, and the fundamental charge of the electron is to be read off the drift of a few dozen oil droplets suspended in an electric fi…

It is the 1930s, and a fisheries board must know how many trout live in a lake it can never drain — so you net a batch, mark and release them, then net again days later a…

It is the 1780s in Paris, and Laplace is turning the newly compiled parish registers to a question older than statistics: is a newborn genuinely more likely to be a boy, …

It is 1918, and a geneticist has crossed plants and counted the offspring types — but the cross yielded only a few dozen progeny, and from those counts you must estimate …

It is 1945 in Cambridge, and a young statistician is asking a sharp question: given a small, expensive sample, is your obvious estimator wasting information you already p…

It is the 1940s, and an engineer designing a dam must specify the flood height expected once in a thousand years — using a river gauge that has recorded only the last thi…

It is 1961, and a startling result is about to unsettle statisticians: when you must estimate several unknown means at once — batting averages, say, each from only a few …

It is the mid-1990s, and a forensic laboratory has found a DNA profile shared between a crime scene and a suspect — but the frequency of that profile in the population is…

It is the present, and a team is about to deploy a model whose accuracy they have measured on a held-out set of only fifty examples — because labeling more costs an exper…

It is 2003 in Mountain View, and the arithmetic of scale has turned against heroism: the web is billions of pages, the index must be rebuilt continuously, and the only af…

It is 1997 at Stanford, and web search is drowning in its own success: engines rank by the words on the page, so a spam site repeating "white house" a thousand times outr…

It is 1989, and distributed systems keep working in the demo and diverging in production: two replicas each convinced they hold the true ledger. Five servers must agree o…

It is 1959, and the world's data processing is written in machine-specific assembly by a tiny priesthood, while the people who actually understand the payroll, the invent…

It is 1968 at the MIT Instrumentation Laboratory, and the Apollo Guidance Computer — 72 kilobytes of hand-woven rope memory — must fly astronauts to the lunar surface. St…

It is 2021, and the scaling laws have made their promise legible: more parameters, more data, more compute yield capabilities nothing smaller exhibits. The catch is engin…

It is 1998, and an operating-system kernel begun as a student's hobby is now maintained by thousands of strangers across every time zone — no company, no org chart, no on…

It is 1966 at IBM Research, and the customers paying millions for a System/360 are threatening to keep writing assembly forever: the FORTRAN compiler's output runs at hal…

It is 1961 at MIT, and the batch-processing regime is strangling the field: a programmer submits a card deck, waits a day, and learns of a missing comma. The proposal is …

It is 1971 at Bell Labs, and the operating systems of the day are baroque cathedrals — huge, machine-specific, unportable, and hostile to change. On a scavenged PDP-11, b…

It is 1978, and distributed systems have a metaphysical bug: two machines timestamp their events with two clocks, and the clocks disagree — not by error but by physics, b…

It is 1986, and a radiation-therapy machine has burned a patient with a massive overdose — the second such accident, and the manufacturer keeps insisting the software can…

It is 2006 in Seattle, and an online retailer has learned its most expensive lesson at peak traffic: a strongly consistent database that pauses during a partition costs m…

It is 2010 at Berkeley, and machine-learning researchers are abusing the reigning distributed framework in a way its designers never intended: their algorithms are iterat…

It is 1962, and the mainframes are confidently printing nonsense: a satellite-orbit computation runs for six hours, each floating-point operation rounding a hair, and the…

It is 1990 at CERN, and thousands of physicists are drowning in their own information: results scattered across incompatible machines, formats, and sites, with each lab's…

It is 2015 in a Mountain View war room, and the postmortem is embarrassing: the machine-learned model at the heart of the product is a few hundred lines, but it is wrappe…

It is 1973 at MIT, and software has entered its crisis years: million-line systems where any module can reach into any other's representation, so changing one data layout…

It is 1957 at Remington Rand, and FLOW-MATIC has proven the case in English: a billing clerk who has never seen an opcode writes COMPARE PRICE OF PRODUCT WITH RECORD and …

It is the era when statistics is becoming an industrial process, and a colleague bursts in celebrating a p=0.03 — the one significant result out of twenty tests he ran. Y…

It is 1943, and you sit with the Statistical Research Group in Manhattan, staring at maps of returning bombers peppered with bullet holes — dense on the wings and fuselag…

It is the 1930s, and two clinics report cure rates you must compare: three of eleven at one, eight of twelve at the other. The chi-squared approximation everyone reaches …

It is 1900, and the whole apparatus of modern statistics is being built from scratch — including the very idea of asking whether data agree with a theory at all. You have…

It is wartime again, and munitions come off the line to be inspected — but every observation costs money, time, and sometimes a destroyed unit, so testing a fixed large s…

It is 1935 in Cambridge, and a woman at a garden party claims she can taste whether the milk or the tea was poured into the cup first — a boast that becomes the founding …

It is the 1940s, and a radar operator's dilemma is being turned into mathematics: a blip on the screen is either a returning aircraft or a fluctuation of noise, and you m…

It is the turn of the 2000s, and a microarray study runs a hypothesis test for each of twenty thousand genes, asking which are differentially expressed between healthy an…

It is 2016, and a professional statistical society does something unprecedented: it issues a public warning that the p-value, the field's most-used number, has been routi…

It is 1947, and two small groups of measurements must be compared, but the data are skewed and lumpy — nothing like the normal curve the t-test quietly assumes — so its p…

It is 1941 at Bletchley Park, and each intercepted German message is a scrap of evidence for or against a guessed rotor setting of the Enigma — but a single scrap decides…

It is 1938, and a recurring question in model-building needs a general answer: you have a simple model and a richer one that contains it, and the richer one always fits t…

It is the planning meeting before any data exist, and a researcher must answer a question that decides whether the whole study is worth running: how many subjects are nee…

It is 1953, and an analysis of variance has just told you that five fertilizer treatments are not all equal — but that verdict names no winner, and the moment you start c…

It is 1954, and a factory's production line runs on target for now — but somewhere ahead a tool will wear, a setting will slip, and the output will drift out of spec, and…

It is 2012 at CERN, and a bump is rising in the data where the Higgs boson should be — but particle physics will not call it a discovery until the signal reaches five sig…