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What a 23-year-old learns

91 topics open up at age 23, across 3 subjects. They are listed in the order they build on each other, not by importance: each one needs the ones above it.

age 22age 24
What should a 23-year-old be learning?

At age 23, 91 topics open up across Science, Mathematics, Computing. Each one has prerequisites that come first, so the order matters more than the list: Controlled Radical Polymerisation and Block Architecture is a typical starting point.

How do I know what a 23-year-old already knows?

LightMySky starts by assuming everything below the learner’s level is already known, then checks the assumption as they practise. What holds up stays lit; what does not comes back for review.

Science

  1. Controlled Radical Polymerisation and Block ArchitectureChemistry
  2. Electron Correlation and Methods Past Hartree-FockChemistry
  3. Excited States by Calculation and Simulated Electronic SpectraChemistry
  4. Functionalising a Carbon-Hydrogen Bond Without a HandleChemistry
  5. Glass Transition, Crystallinity and Entanglement in PolymersChemistry
  6. Molecular Recognition: Preorganisation, Complementarity and Binding ConstantsChemistry
  7. Olefin Metathesis and Ring-Closing StrategyChemistry
  8. Photoredox and Electrochemical Routes to Radical IntermediatesChemistry
  9. Putting the Solvent Into a CalculationChemistry
  10. Molecular Dynamics and Free Energy from SamplingChemistry
  11. Reaction Dynamics: Trajectories Across a Potential Energy SurfaceChemistry
  12. Risk Assessment for a Reaction Nobody Has Run HereChemistry
  13. Self-Assembly: Templates, Reversibility and Error CorrectionChemistry
  14. Taking a Route into Flow and Onto ScaleChemistry
  15. Reading a Total Synthesis as an ArgumentChemistry
  16. Writing a Research Proposal: Question, Feasibility and MilestonesChemistry
  17. Reporting Chemical Data: Statistics, Figures and Data AvailabilityChemistry
  18. Ultrafast Spectroscopy and Watching a Reaction HappenChemistry
  19. Adding Angular Momenta and the Coupled BasisQuantum & Modern Physics
  20. Identical Particles and the Symmetry of a Many-Body StateQuantum & Modern Physics
  21. Degenerate Perturbation Theory and the Variational MethodQuantum & Modern Physics
  22. Density Matrices, Entanglement and the Bell TestQuantum & Modern Physics
  23. Field Quantisation: Creation Operators and Particle NumberQuantum & Modern Physics
  24. The Klein-Gordon and Dirac EquationsQuantum & Modern Physics
  25. The Path Integral and the Sum Over HistoriesQuantum & Modern Physics
  26. Time-Dependent Perturbation Theory and Fermi's Golden RuleQuantum & Modern Physics
  27. Scattering: Cross-Sections and the Born ApproximationQuantum & Modern Physics
  28. Radiation from an Accelerating ChargeElectricity & Magnetism
  29. Crystal Lattices, the Reciprocal Lattice and Bloch's TheoremMatter & Materials
  30. Band Structure: Metals, Insulators and the GapMatter & Materials
  31. Semiconductors, Doping and the p-n JunctionMatter & Materials
  32. Phonons and the Heat Capacity of SolidsMatter & Materials
  33. Superconductivity: the Meissner Effect and Cooper PairsMatter & Materials
  34. The Ising model and the mean-field approximationThermal & Statistical Physics
  35. Critical exponents, scaling and universalityThermal & Statistical Physics
  36. Tensors and the metric on a curved manifoldAstronomy & Astrophysics
  37. Parallel transport, Christoffel symbols and the geodesic equationAstronomy & Astrophysics
  38. Curvature and the Einstein field equationAstronomy & Astrophysics
  39. The Schwarzschild solution: orbits, redshift and the horizonAstronomy & Astrophysics
  40. Linearised gravity and gravitational wavesAstronomy & Astrophysics
  41. Reading a Paper: the Claim, the Evidence and the AssumptionScientific Inquiry
  42. Writing Science: the Figure, the Error Bar and the ClaimScientific Inquiry
  43. Testing thousands of genes at once: false discovery rate and what q meansGenetics & Evolution
  44. From a gene list to biology: enrichment tests and their backgroundsGenetics & Evolution
  45. Single-Cell Analysis: Normalisation, Embedding and Naming Cell StatesGenetics & Evolution
  46. Modelling a Biological System: Rate Equations, Parameters and FitGenetics & Evolution
  47. From Hit to Lead: Structure-Activity RelationshipsChemistry
  48. Drug-Like Properties: Solubility, Permeability and Metabolic FateChemistry
  49. Chemical Biology: Bioconjugation and Reporting on a Molecule in a CellChemistry
  50. Reproducibility in Practice: Data, Code and What Another Lab Can RerunScientific Inquiry
  51. Proteomics: Mass Spectra, Quantification and Interaction MapsBiochemistry & Molecular Biology
  52. Target Validation and Lead Discovery: From a Biological Claim to a MoleculeBiochemistry & Molecular Biology
  53. Engineered Cell Therapy: Receptor Design, Manufacture and ToxicityThe Human Body
  54. Ethics of Emerging Biotechnology: Editing and BiosecurityScientific Inquiry
  55. Pooled Genetic Screens: Library Design, Selection and Reading a Hit ListGenetics & Evolution
  56. Clinical Trials: Phases, Endpoints and Why Most Candidates FailThe Human Body
  57. Synthetic Circuits: Switches, Oscillators and Why They Misbehave in CellsMicrobiology
  58. Metabolic Engineering: Redirecting Flux Through a Production HostMicrobiology
  59. The Host Microbiome: Composition, Causation and InterventionMicrobiology

Mathematics

  1. Conditioning, Stability and Floating-Point ErrorCalculus & Analysis
  2. Iterative Methods for Large Linear SystemsLinear Algebra
  3. Bounded Linear Operators and the Operator NormCalculus & Analysis
  4. Baire Category and the Uniform Boundedness PrincipleCalculus & Analysis
  5. The Hahn-Banach Theorem and the Dual SpaceCalculus & Analysis
  6. Hilbert Spaces and Orthogonal Projection in Infinite DimensionsCalculus & Analysis
  7. Compact Self-Adjoint Operators and the Spectral TheoremCalculus & Analysis
  8. Convolution, Plancherel and Transforming a DerivativeCalculus & Analysis
  9. Numerical Schemes for Evolution EquationsDifferential Equations
  10. Martingales and Optional StoppingProbability
  11. Brownian Motion and Its Defining PropertiesProbability
  12. Characters and the Orthogonality RelationsAbstract Algebra
  13. Decomposing a Representation from Its CharacterAbstract Algebra
  14. Topological Spaces: Continuity Without DistanceTopology
  15. Open Problems as a GenreMathematical Thinking
  16. Compactness and ConnectednessTopology
  17. The Fundamental Group and Loops on a CircleTopology

Computing

  1. Training Across Many Devices: Data, Model and Pipeline ParallelismMachine Learning
  2. Serving a Model: Batching, the Key-Value Cache and QuantisationMachine Learning
  3. Stream Processing: Windows, Watermarks and Late EventsData & Databases
  4. Cloud-Native Architecture: Containers, Schedulers and the Control LoopComputer Systems
  5. Observability and Tail Latency Across ServicesComputer Systems
  6. Model Checking and the State-Space ExplosionSoftware Engineering
  7. Hoare Logic and Proving a Program Meets Its SpecificationSoftware Engineering
  8. Type Soundness: Progress and PreservationComputer Systems
  9. Reproducibility: Seeds, Environments and the AblationSoftware Engineering
  10. Scoping and Writing a Thesis-Scale ProjectSoftware Engineering
  11. Temporal-Difference Learning and Q-LearningMachine Learning
  12. Policy Gradients and the Actor-Critic SplitMachine Learning
  13. Learning from Human Preferences: Reward Models and Policy OptimisationMachine Learning
  14. Cryptographic Security Definitions and Proof by ReductionNetworks & Security
  15. Interpretability: Probes, Features and CircuitsMachine Learning
What a 23-year-old learns · LightMySky