first principles — the art of breaking everything down to fundamental truths and building up from there

Learn anything by
building it from scratch.

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mathematics · physics · geometry
Advanced Mathematics
★ start here

Mathematics is not about numbers. Not really. Numbers are the surface — the first layer you encounter before you realize the real game is about STRUCTURE, SYMMETRY, and SHAPE. The five ideas in this...

Euler's Identity
Topology
Differential Geometry
chemistry · physics · industry
Benzene

Six carbons. Six hydrogens. C₆H₆. The simplest formula that hides the deepest mystery in organic chemistry. By the 1860s, chemists knew benzene existed. They could measure it, weigh it, burn it, and...

Kekulé's Dream
Aromaticity
Industrial Chemistry
biology · physics · engineering
Dinosaur

66 million years ago, something the size of San Francisco hit the Earth at 20 kilometers per second. Within hours, every animal over 25 kilograms was dead or dying. The sky burned. Then it went dark...

Stand Up
Breathe Enough to Run
Die
physics · cosmology · engineering
Gravity

Your back hurts. Not from bad posture. Not from your chair. Your back hurts because you are a tall column of water and meat fighting a force that has been trying to crush you into a sphere since the...

Make Things Fall
Make Stars Ignite
Shape a Universe
engineering · physics · materials
Stealth Fighter

A radar screen glows green. A sweep arm rotates. Blips appear — commercial airliners at 200 km, a flock of geese at 80 km, a small Cessna at 150 km. The system can detect a bird at 100 km. It tracks...

Make Metal Invisible
See Without Being Seen
Why Only 187?
biology · chemistry · physics
Blood

You got a paper cut. Look at your finger. A thin red line appears — not instantly, but after a beat. A bead forms, swells, and you instinctively put it in your mouth. That red liquid leaking out of...

Make It Carry Oxygen
Make It Flow
Can We Build It?
science · engineering
Rocket

You want to leave. Stand outside tonight. Look up. Every light you see is somewhere you cannot go. The air thins to nothing 100 km above your head. Beyond that — vacuum, radiation, cold so deep it...

Fight the Well
Throw Away the Ship
Leave for Good
how it looks
firstprinciplescroll.com/build-gravity
PHASE 1: Make Things Fall
You need a force. But what does it grab onto?

Options:
├── Color? No — arbitrary
├── Temperature? No — changes constantly
└── Mass? Yes — universal, never cancels
PHASE 2: Make Things Orbit
Everything falls straight down. Your universe will last 20 minutes.

An orbit is FALLING — it just keeps missing.
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Physics
Forces, fields, particles, spacetime. The rules everything else runs on.
gravity · stealth fighter · submarines
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Mathematics
Patterns, proofs, structures. The language underneath every science.
differential geometry · topology · linear algebra
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Biology
Living systems. Molecular machines, evolutionary solutions, emergent complexity.
blood · dinosaurs · immune system
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Engineering
Building things that work. Constraints, tradeoffs, elegant solutions.
stealth fighter · bridges · rockets
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Chemistry
Atoms combining. Bonds, reactions, molecular architecture.
benzene · explosives · materials
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Earth Science
Plate tectonics, weather, the carbon cycle. The planet as a system.
volcanoes · oceans · atmosphere