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Architecture, training, and evaluation, for a research scientist
Full routeSystems, performance, and failure, for technical staff
Full routePricing, risk, and signal, for a systematic trading seat
Full routeCost, supply, and regulation, for advising a decision
Full routeDirectory
Introduction
Defines the scope, fixes the notation, names the terms of reuse.4 pages
Fundamentals
States what is true by construction, derives the machinery, writes the notation the field uses.20 pages
MathematicsVectors, matrices, derivatives, and probability, in the notation papers actually useTopology and GeometryDistance, shape, curvature, and why high-dimensional space stops being picturableStatisticsEstimation, inference, regression, and causality, plus how uncertain each number isStochastic ProcessesMarkov chains, state space models, volatility, and the behavior of tailsEconomicsSupply, demand, and cost curves, plus the incentive problems of asymmetric informationMacroeconomicsOutput, inflation, and cycles, and the schools that disagree about whySoftwareInterfaces, serialization, protocols, and the relational model every other page assumesData StructuresThe containers and their costs, what each makes cheap and quietly expensiveCompilers and RuntimesBetween the source you write and the instructions that actually runCryptographyGuarantees that hold against a deliberate adversary, and the assumptions beneathHardwareDies, memory hierarchies, interconnect, and why machine shape decides what is cheapOperating SystemsWhat the kernel does for you, and what it chargesDistributed SystemsMany machines presenting as one, and the consistency you trade for availabilityDatabasesHow data survives a crash, and what a query costsData EngineeringMoving data and keeping it trustworthy, through lineage, licensing, and schema contractsTraining DataThe training corpus, how it is filtered, and what synthetic data changesMachine LearningRegression, decision trees, gradient boosting, clustering, and Bayesian inferenceModelsHow a network is assembled, from token through embedding to attention blockTrainingHow a model acquires weights, by pretraining, fine-tuning, and preference optimizationInferenceWhat executes on a request, including the forward pass and decoding
Theory
Proves the results, carries the hypotheses each one needs, marks where they fail.12 pages
OptimizationMinimizing under constraint, the rates convexity buys, and what survives without itOperations ResearchLinear programming, duality, network flows, queues, and scheduling scarce resourcesInformation TheoryEntropy, mutual information, channel capacity, and why compression is what models optimizeLearning TheoryWhy fitting a finite sample predicts the next, and how much dataDecision TheorySingle choices without dynamics, covering utility axioms, information value, and regretReinforcement LearningLearning a policy from interaction, with value, policy gradient, and reward specificationControl TheorySteering a system you cannot fully model, and proving it stableGame TheoryPayoffs depending on everyone else, the resulting equilibria, and where they failAsset PricingWhat an uncertain future claim is worth, and the no-arbitrage assumptions beneathLogicWhat follows from what, the incompleteness and undecidability results, and machine-checked proofComputability and ComplexityWhat a machine can compute, what it computes cheaply, and what cannotQuantum ComputingAlgorithms proved to win, the error correction required, and the remaining distance
Application
Records what was built, prices what it cost, dates every claim.19 pages
RetrievalGiving a model facts it never trained on, by search and rerankingAgentsSystems choosing their next action, the tools they use, and recoverability boundsDiscoveryUsing models to prove theorems, and telling genuine results from plausible onesQuantitative TradingTurning a statistical edge into a position that survives transaction costsInterpretabilityReading what a trained network computes, and how much evidence holds upAlignmentMaking a system behave as intended, with measurable targets rather than hopeSimulationAnswering questions by running a system, when the mathematics will not closeRoboticsLearned control meeting contact, friction, and the cost of being wrongEngineering PracticeVersion control, testing, review, and release, which keep software changeableDeploymentServing a model to real traffic, with capacity, autoscaling, rollout, and failuresPerformance EngineeringMeasuring where time actually goes, and what optimization can possibly returnEvaluationKnowing whether a system works, through benchmarks, contamination, and statistical powerJudgment and Failed BetsHow the field decides under uncertainty, and what research taste actually isSecurityHow these systems are attacked, by prompt injection, poisoning, and extractionOpen SourceLicenses, stewardship, and dependency risk, including what open weights withholdGovernanceCopyright, regulation, and liability, plus the safety commitments labs actually signedSupply ChainThe physical path from sand to serving rack, and where it breaksCompute EconomyWho supplies compute, who buys it, and where the margin landsWhere the Field StandsCapability, compute, power, and economics as of September 2026
Appendix: General
Collects the terms, credits the work, indexes the named results.9 pages
GlossaryEvery term defined once and alphabetized, each linked to its full treatmentPapersResearch results, methods, surveys, and system reports, with their recorded contributionsPeopleWho produced these results, each entry naming the specific contributionOrganizationsFirms, labs, funds, and agencies, each entry naming what it controlsLandmark ResultsTuring awards, Nobels, Fields medals, and Abel prizes, tied to their pagesLaws, Theorems, and ParadoxesNamed results the field reasons with, grouped by what each one constrainsBiases and FallaciesHow reasoning fails predictably, and which corrections have evidence behind themThought ExperimentsConstructed cases that isolate one variable, and what each settlesLanguages and FormatsHow code and data are written down, and what each notation decides
Appendix: Interviews
Asks what the hard interviews test, shows the expected answer, times the work.6 pages
Interview TipsWhat the hard interviews actually test, and how each firm tests itLeetCode PatternsEvery LeetCode topic in twenty solution families, with tested templatesFermi ProblemsEstimating an unknown quantity from what you already know, with worked examplesCase StudiesWorked decisions naming which principle applies, and why not anotherData StorytellingTurning a number into an argument, with encodings, chart types, and librariesResume FeedbackWhat a technical resume must show, and what gets it cut
Appendix: Tangential Topics
Surveys the neighboring fields, preserves each vocabulary, connects them to the core.10 pages
LawHow rules are made, applied, and contested, and where liability landsAccountingHow a firm reports what it owns, owes, and earnedCorporate FinanceHow firms raise capital, value assets, and choose what to fundPhysicsConservation, scale, and the limits no amount of engineering movesDesignSpacing, hierarchy, color, and what a layout decides for the readerIndustrial DesignHow manufactured objects are shaped by the body, the tool, and volumePhilosophyKnowledge, meaning, agency, and what a fair distribution isPublic PolicyHow policy is actually made, by parties, coalitions, voters, and captured regulatorsApplied EthicsThe decisions a working researcher faces, past the moral frameworksCryptocurrencyPermissionless ledgers, the consensus beneath them, and the throughput actually measured
Appendix: Whimsical Fun
Wagers on a probability estimate, settles it in cash, counts the cost of being wrong.8 pages
Odds and PricesHow a quoted price becomes a probability, and the margin inside itBankroll and RuinSizing a stake so a losing run does not end the sequenceSports BettingHow a line is set and moved, and what a book sellsCasino GamesHouse edge by game, why it is fixed, and when it brokePokerIncomplete information, solved equilibria, and where the money comes fromHorse RacingPari-mutuel pools, the takeout, and the biases measured inside themPrediction MarketsPrices read as forecasts, their accuracy, and the frictions that bend themGames of SkillSeparating skill from chance, how that is measured, and why it matters