Learning paths

From rotating complex numbers to approximating any function and decomposing any signal — the analytic backbone of modern math.

1. 1The Derivative
2. 2The Integral: Adding Up the Infinitely Small
3. 3Logarithms: Taming Huge Numbers
4. 4Infinity: Not All Infinities Are Equal
5. 5Complex Numbers
6. 6Euler's Formula
7. 7Taylor Series
8. 8Newton's Method
9. 9Gradient Descent
10. 10Matrices: Functions That Move Space
11. 11Eigenvectors and Eigenvalues
12. 12The Fourier Transform

How machines search, sort, explore connected data, and sift the primes — the core algorithmic ideas, step by step.

1. 1Logic Gates: How Computers Do Arithmetic
2. 2Compilers: From Source Code to Silicon
3. 3Floating-Point: Why 0.1 + 0.2 ≠ 0.3
4. 4Binary Search
5. 5Recursion: Functions That Call Themselves
6. 6Sorting Algorithms
7. 7Hash Tables
8. 8Caching: The Art of Keeping the Right Things Close
9. 9Dynamic Programming
10. 10Graph Traversal
11. 11Sieve of Eratosthenes
12. 12Error-Correcting Codes: Fixing Bits Without Asking Again
13. 13Data Compression: Saying More With Less
14. 14Public-Key Cryptography
15. 15How Neural Networks Learn
16. 16Distributed Consensus
17. 17Concurrency: When Threads Collide
18. 18P vs NP
19. 19Finite Automata and Regular Expressions
20. 20The Halting Problem

Start with a swinging weight, bend time with relativity, and end where classical physics breaks down entirely.

1. 1The Pendulum
2. 2Resonance and Standing Waves
3. 3Turbulence and the Reynolds Number
4. 4Buoyancy: Why Steel Ships Float
5. 5Momentum: The Quantity Collisions Conserve
6. 6Angular Momentum: Why Skaters Spin Faster
7. 7Kepler's Laws of Planetary Motion
8. 8The Doppler Effect
9. 9Entropy and the Second Law
10. 10Time Dilation
11. 11General Relativity: Gravity as Curved Spacetime
12. 12Electric Circuits and Ohm's Law
13. 13Magnetism: Moving Charges and Aligned Spins
14. 14Maxwell's Equations and the Nature of Light
15. 15Optics: How Light Bends and Focuses
16. 16Wave-Particle Duality
17. 17Nuclear Fission and Fusion
18. 18Superconductivity

What can be said about a system nobody can predict — from a jittering pollen grain to the bell curve, the limits of forecasting, and the arithmetic of uncertainty itself.

1. 1Brownian Motion
2. 2The Central Limit Theorem
3. 3Bayes' Theorem
4. 4Markov Chains
5. 5Chaos and Strange Attractors
6. 6Information Theory
7. 7Game Theory and the Nash Equilibrium

Start with what holds two atoms together, then follow reactions through speed, balance, and the transfer of protons and electrons.

1. 1Atomic Structure and the Periodic Table
2. 2Radioactivity: Random Decay, Predictable Half-Life
3. 3The Periodic Table: Why the Pattern Repeats
4. 4The Mole: Chemistry's Bridge to the Invisible
5. 5Spectroscopy: Reading Matter with Light
6. 6Why Atoms Bond
7. 7Intermolecular Forces and Why Water Is Weird
8. 8Polymers: The Chemistry of Long Chains
9. 9Solutions: Where Does the Sugar Go?
10. 10The Ideal Gas Law and Kinetic Theory
11. 11Phase Transitions
12. 12Reaction Rates and Catalysis
13. 13Free Energy: Why Reactions Happen
14. 14Chemical Equilibrium
15. 15Le Chatelier's Principle: How Equilibrium Pushes Back
16. 16Acids, Bases and pH
17. 17Redox: The Chemistry of Electron Transfer
18. 18Electrochemistry: How Batteries Work

The machinery of a working planet — the rock that moves beneath it, the air and ocean that carry its heat, and the carbon and radiation budgets that set its temperature.

1. 1Plate Tectonics
2. 2The Rock Cycle
3. 3Volcanoes: Why Some Ooze and Some Explode
4. 4Earthquakes and Seismic Waves
5. 5Earth's Magnetic Field
6. 6Auroras: Why the Sky Glows at the Poles
7. 7The Coriolis Effect: Curved Paths on a Spinning World
8. 8The Seasons: It's the Tilt, Not the Distance
9. 9Why Weather Happens
10. 10Clouds and Rain: How Air Makes Water Appear
11. 11Lightning: How a Storm Builds a Spark
12. 12Ocean Circulation
13. 13El Niño: When the Pacific Flips
14. 14Hurricanes: Nature's Heat Engines
15. 15The Water Cycle
16. 16The Ozone Layer
17. 17The Greenhouse Effect
18. 18The Carbon Cycle
19. 19Ice Ages and Milankovitch Cycles

Start with the principle that organises all of biology, then build upward — the code, what it folds into, how energy gets in, and how cells signal and defend.

1. 1Natural Selection
2. 2DNA Replication
3. 3From DNA to Protein
4. 4Epigenetics: The Marks Above the Genes
5. 5CRISPR: Programmable Molecular Scissors
6. 6Heredity and Mendelian Genetics
7. 7Cell Division and the Cell Cycle
8. 8Stem Cells: The Body's Master Cells
9. 9Protein Folding
10. 10Enzymes: The Catalysts That Run Life
11. 11Photosynthesis
12. 12Cellular Respiration
13. 13Cell Membranes and Transport
14. 14Osmosis: Why Water Moves on Its Own
15. 15The Action Potential
16. 16The Synapse: How Neurons Talk
17. 17Viruses: Alive or Not?
18. 18The Microbiome: Your Body's Microbial Partners
19. 19The Adaptive Immune Response

Medicine as measurement and control — reading the heart’s electrical trace, holding glucose in range, tracking a drug through the body, seeing inside it, and losing ground to resistant bacteria.

1. 1The Heart: Two Pumps in One
2. 2How Muscles Work: Pulling, Never Pushing
3. 3How the Heart's Electrical Signal Works
4. 4Blood Pressure and Circulation
5. 5Breathing and Gas Exchange
6. 6Digestion: Breaking Food Down to Its Building Blocks
7. 7Glucose and Insulin: A Feedback Loop
8. 8Hormones: The Body's Chemical Messengers
9. 9The Kidney: The Body's Filter
10. 10How We Hear
11. 11Vision: How the Eye Works
12. 12Anesthesia: Switching Off Pain and Consciousness
13. 13Pharmacokinetics: How Drugs Clear the Body
14. 14Antibiotics and Resistance
15. 15Cancer: When Cell Division Loses Its Brakes
16. 16How MRI Sees Inside You
17. 17Vaccines: Teaching Immunity in Advance
18. 18Epidemic Models and R₀

Outward through the cosmos — from the life and death of a single star to the elements it forges, the worlds around others, the extremes of gravity, and the expansion of everything.

1. 1The Sun: A Nuclear Furnace, Not a Fire
2. 2The Life Cycle of Stars
3. 3The Hertzsprung–Russell Diagram: Mapping the Stars
4. 4Where the Elements Come From
5. 5How the Solar System Formed
6. 6The Moon: Phases, Faces, and Eclipses
7. 7Orbital Mechanics: The Art of Falling Sideways
8. 8Comets and Asteroids: The Solar System's Leftovers
9. 9Tidal Forces: Why the Moon Raises Two Bulges
10. 10How We Find Other Worlds
11. 11Black Holes
12. 12Neutron Stars and Pulsars
13. 13Gravitational Waves
14. 14Galaxies and Dark Matter
15. 15Telescopes: Gathering Light, Resolving Detail
16. 16The Cosmic Distance Ladder
17. 17The Cosmic Microwave Background
18. 18Dark Energy: Why the Universe Speeds Up
19. 19The Expanding Universe

The internet told as a chain of inventions — each one solving the exact limit the last success ran into, from raw packets up to the web you are reading this on.

1. 1Packet Switching
2. 2IP Addresses and Routing
3. 3TCP: Reliability on an Unreliable Network
4. 4DNS: The Internet's Phone Book
5. 5HTTP and the World Wide Web
6. 6NAT: How Billions Share Four Billion Addresses
7. 7TLS: Encrypting the Web
8. 8Certificates and the Chain of Trust
9. 9Load Balancers and Reverse Proxies
10. 10CDNs: Bringing the Web Closer

The layers the first tour skipped and the extensions built on top — how bits reach the wire and the airwaves, how independent networks agree on routes, how the web reinvented its transport, and how private networks span the public internet.

1. 1Ethernet: How Machines Share a Wire
2. 2Wi-Fi: Networking Through the Air
3. 3BGP: How the Internet's Networks Agree on Routes
4. 4HTTP/2 and HTTP/3: Reinventing the Web's Transport
5. 5VPNs and Tunneling

The everyday operation of the network — how a device joins it, the applications and architectures built across it, how to see inside it, and how it is defended.

1. 1DHCP: How Your Device Joins a Network
2. 2Email: The Internet's Oldest Application
3. 3Peer-to-Peer: The Internet Without a Center
4. 4Ping and Traceroute: Seeing the Network
5. 5Firewalls: Filtering the Traffic