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DebunkedThe PolygraphThe instrument popularly called a lie detector, which records breathing, blood pressure, pulse and skin conductance dur…

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The library

Capsules

1,028 capsules, each one classified by the strength of its evidence.

All1,028Fact599Proven130Theory89Hypothesis71Contested90Debunked48
geography236biology88physics67history54medicine45astronomy33psychology26mathematics26chemistry20engineering20astrophysics19neuroscience19anthropology18art18
Filtered bymathematicsClear all

Results

Showing 1 to 20 of 44

NewestMost votedA to Z
Fact

Probability

The mathematics of uncertainty. It assigns numbers between zero and one to events, and its rules are simple enough to state on a page and produce…

byCapsule
0 votes0 reviews
Aug 5, 2026
Fact

Logic

The study of valid inference: which conclusions follow from which premises, and why. It is the shared foundation of philosophy, mathematics and…

byCapsule0 votes0 reviewsAug 5, 2026
Fact

Numeracy

The ability to understand and work with numbers in practical situations. It is distinct from mathematical education, it is measured internationally,…

byCapsule0 votes0 reviewsAug 5, 2026
Fact

The Normal Distribution

The symmetric bell-shaped probability distribution that arises whenever many small independent influences add together. It is the most important…

byCapsule0 votes0 reviewsAug 5, 2026
Fact

Calculus

The mathematics of continuous change, comprising the differential calculus of rates and the integral calculus of accumulation, and the theorem…

byCapsule0 votes0 reviewsAug 5, 2026
Fact

Zero

The number representing nothing, and the symbol that makes positional notation possible. It arrived late, was resisted, and is the single most…

byCapsule0 votes0 reviewsAug 5, 2026
Theory

Control Theory

The mathematics of making a system behave as intended by measuring what it is doing and acting on the difference from what is wanted. It is the…

byCapsule0 votes0 reviewsAug 4, 2026
Theory

Queueing Theory

The mathematical study of waiting lines, developed to size telephone exchanges and now used wherever demand arrives at random and must be served by…

byCapsule0 votes0 reviewsAug 4, 2026
Proven

The Euclidean Algorithm

A procedure for finding the greatest common divisor of two whole numbers by repeatedly replacing the larger with its remainder on division by the…

byCapsule0 votes0 reviewsAug 4, 2026
Proven

The Monty Hall Problem

A probability puzzle with a counterintuitive answer, made famous when thousands of people including professional mathematicians insisted publicly…

byCapsule0 votes0 reviewsAug 4, 2026
Proven

Cantor's Diagonal Argument

A proof that some infinities are larger than others. It is a few lines long, it requires nothing beyond counting, it was violently rejected when…

byCapsule0 votes0 reviewsAug 4, 2026
Proven

The Four Colour Theorem

Four colours suffice to colour any map so that no two regions sharing a border have the same colour. It was conjectured in 1852, resisted proof for…

byCapsule0 votes0 reviewsAug 3, 2026
Proven

The Nash Equilibrium

A situation in which no participant can do better by changing strategy alone. It is the central solution concept in game theory, it exists in every…

byCapsule0 votes0 reviewsAug 3, 2026
Proven

Non-Euclidean Geometry

For two thousand years one of Euclid's assumptions looked like it should be provable from the others. It is not. Denying it produces consistent…

byCapsule0 votes0 reviewsAug 3, 2026
Proven

Bayes' Theorem

A rule for updating a belief when new evidence arrives. It is a short piece of algebra, it is not in any dispute, and misapplying it produces some of…

byCapsule0 votes0 reviewsAug 3, 2026
Proven

The Fourier Transform

Any signal can be decomposed into a sum of pure sine waves of different frequencies. The claim was disbelieved when made, it is one of the most…

byCapsule0 votes0 reviewsAug 3, 2026
Proven

Error-Correcting Codes

Adding structured redundancy to a message so that errors introduced in storage or transmission can be detected and repaired without asking for a…

byCapsule0 votes0 reviewsAug 3, 2026
Proven

The Hardy-Weinberg Principle

In a large population with random mating and nothing else happening, gene frequencies do not change from one generation to the next. It sounds like a…

byCapsule0 votes0 reviewsAug 3, 2026
Theory

The Basic Reproduction Number

R nought is the average number of people one infectious person infects in a population with no immunity and no countermeasures. It is the single most…

byCapsule0 votes0 reviewsAug 3, 2026
Debunked

The Golden Ratio in Art and Architecture

The golden ratio is a real and interesting number. The claim that it governs the Parthenon, the Great Pyramid, the Mona Lisa and the proportions of…

byCapsule0 votes0 reviewsAug 3, 2026
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