Capsules

Equal Temperament

Every note on a modern piano is slightly out of tune, deliberately and by a known amount. Equal temperament divides the octave into twelve identical…

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Aug 3, 2026

byCapsule0 votes0 reviewsAug 3, 2026

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 2, 2026

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…

Contested

P versus NP

P versus NP is the most important unsolved problem in computer science and one of the deepest open questions in mathematics. Informally it asks…

byCapsule0 votes0 reviewsAug 2, 2026

byCapsule0 votes0 reviewsAug 2, 2026

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 reviewsJun 22, 2026

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 20, 2026

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

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 19, 2026

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…

Fact· Historical

Alan Turing

Alan Turing (1912 to 1954) was a British mathematician and logician widely regarded as the father of computer science and artificial intelligence.…

Fact· Historical

Ada Lovelace

Ada Lovelace (1815 to 1852) was an English mathematician often celebrated as the first computer programmer. Working with Charles Babbage's designs…

Topology

Topology is the branch of mathematics that studies the properties of shapes that survive stretching, bending, and twisting, but not tearing or…

Set Theory

Set theory is the branch of mathematics that studies collections of objects, called sets. Though it begins with an idea as simple as grouping things…

Graph Theory

Graph theory is the branch of mathematics that studies networks of connected objects. A graph is simply a collection of points, called vertices,…

The Theory of Computation

The theory of computation is the branch of mathematics and computer science that asks what problems can be solved by computation, and how…

byCapsule0 votes0 reviewsMay 10, 2026

Fact· Historical

Katherine Johnson

Katherine Johnson was an American mathematician whose precise calculations of orbital mechanics were critical to the success of the United States'…

byCapsule0 votes0 reviewsApr 25, 2026

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…

Hypothesis

The Riemann Hypothesis

The Riemann hypothesis is the most famous unsolved problem in mathematics. Proposed by Bernhard Riemann in 1859, it makes a precise claim about the…

byCapsule0 votes0 reviewsMar 26, 2026