6 Famous Equations That Changed the World

Tap an equation to see what it means.

Mass–Energy Equivalence

E = mc² — Published by Einstein, this equation shows that mass and energy are fundamentally the same thing and can be converted into one another, forming the theoretical foundation of nuclear energy.

The Pythagorean Theorem

a² + b² = c² — States that in a right triangle, the sum of the squares of the two shorter sides equals the square of the hypotenuse, making it one of the most widely known formulas in geometry.

Euler's Identity

e^(iπ) + 1 = 0 — Links five of the most important constants in mathematics (0, 1, e, i, and π) in a single equation, often called "the most beautiful equation in mathematics."

Newton's Law of Universal Gravitation

F = G(m₁m₂)/r² — States that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them, forming a cornerstone of classical physics.

The Fibonacci Sequence

Fₙ = Fₙ₋₁ + Fₙ₋₂ — A sequence formed by adding the previous two numbers to get the next one, with similar patterns showing up throughout nature, from the spiral arrangement of sunflower seeds to the shape of a nautilus shell.

Schrödinger's Equation

iħ ∂Ψ/∂t = ĤΨ — The core equation of quantum mechanics, describing how the state of a particle changes over time.

The Enormous Meaning Packed Into a Short Formula

Great equations are remarkably concise, yet each contains a profound insight into the fundamental workings of the universe. Even without following the full mathematical derivation, simply grasping the core idea behind each equation can broaden how you see the world.

Famous Experiments Are Worth a Look Too

If famous scientific experiments interest you as well, take a look at our guide to famous psychology and science experiments.

Frequently Asked Questions

Do I need to fully understand these equations mathematically?

Not at all — even without being able to fully derive them mathematically, simply understanding what each equation describes conceptually is genuinely valuable general knowledge.

Does the Fibonacci sequence really show up in nature?

Yes — patterns similar to the Fibonacci sequence have genuinely been observed in places like the spiral arrangement of sunflower seeds, pine cones, and pineapple patterns.