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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 byProvenmathematicsClear all

Results

Showing 1 to 20 of 20

NewestMost votedA to Z
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…

byCapsule
0 votes0 reviews
Aug 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
Proven· Mathematical Proof

Simpson's Paradox

Simpson's paradox is the phenomenon in which a trend appears in several groups of data and reverses when the groups are combined. It is not a…

byCapsule0 votes0 reviewsAug 3, 2026
Proven· Mathematical Proof

Public-Key Cryptography

Public-key cryptography is the method that allows two parties who have never met, and who are communicating over a channel anyone can read, to…

byCapsule0 votes0 reviewsAug 2, 2026
Proven· Mathematical Proof

The Halting Problem

The halting problem asks whether it is possible to write a program that can examine any other program, together with its input, and reliably decide…

byCapsule0 votes0 reviewsAug 2, 2026
Proven· Mathematical Proof

The Irrationality of the Square Root of Two

The square root of two, the number which when multiplied by itself gives exactly two, cannot be written as a fraction of two whole numbers. It is, in…

byCapsule0 votes0 reviewsJun 22, 2026
Proven· Mathematical Proof

Gödel's Incompleteness Theorems

Gödel's incompleteness theorems are two of the most profound and startling results in the history of mathematics and logic. Proven by the Austrian…

byCapsule0 votes0 reviewsJun 20, 2026
Proven· Mathematical Proof

The Central Limit Theorem

The central limit theorem is one of the most important results in all of statistics. It explains why the familiar bell shaped curve appears again and…

byCapsule0 votes0 reviewsJun 20, 2026
Proven· Mathematical Proof

The Infinitude of Primes

There are infinitely many prime numbers. This was proven more than two thousand years ago by the Greek mathematician Euclid, in an argument so clear…

byCapsule0 votes0 reviewsJun 19, 2026
Proven· Mathematical Proof

Fermat's Last Theorem

Fermat's Last Theorem states that no three positive whole numbers can satisfy the equation a to the power n, plus b to the power n, equals c to the…

byCapsule0 votes0 reviewsApr 25, 2026
Proven· Mathematical Proof

The Four Color Theorem

The four color theorem states that any map drawn on a flat surface can be colored using only four colors in such a way that no two regions sharing a…

byCapsule0 votes0 reviewsFeb 26, 2026
Proven· Mathematical Proof

The Pythagorean Theorem

The Pythagorean theorem is one of the most famous results in all of mathematics. It states that in a right angled triangle, the square of the longest…

byCapsule0 votes0 reviewsFeb 5, 2026