Concept

Combinatorics

Overview

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.

Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ad hoc solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is graph theory, which by itself has numerous natural connections to other areas. Combinatorics is used frequently in computer science to obtain formulas and estimates in the analysis of algorithms.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

Possible passages

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1. Aristotle, that it is formed by the fifth body, and by the mixture of extreme heat and cold. CHAPTER XII. INTO HOW MANY CIRCLES IS THE HEAVEN DISTINGUISHED; OR, OF THE DIVISION OF HEAVEN. Thales, Pythagoras, and the followers of Pythagoras do distribute the universal globe of heaven into five circles, which they denominate zones; one of which is called the arctic circle, which is always conspicuous to us, another is…

   Plutarch, Complete Works of Plutarch — Volume 3

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2. In union with itself, it does not by its nature produce anything imperfect or foreign. All its changes are defined; it either produces itself or the Decad, either the homogeneous or the perfect.

   Plutarch, Selected Essays of Plutarch, Vol. II.

   States what Combinatorics is; the author is tied to Combinatorics in the knowledge graph.

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3. This is nothing else than the necessity of abstract logic, which is the presupposition involved in the very fact of interrelated existence as disclosed in each immediate occasion of experience. The key to the pattern means this fact:—that from a select set of those general conditions, exemplified in any one and the same occasion, a pattern involving an infinite variety of other such conditions, also exemplified in…

   Alfred North Whitehead, Science and the modern world

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Philosophers who discussed Combinatorics

• Frank P. Ramsey
• Jerry Fodor

Related ideas

• Automata theory
• Formal language
• Analysis
• Finite set
• Historian
• Abraham ibn Ezra
• India
• Isaac Newton
• Formal grammar
• Archimedes
• Algebra
• Mathematics
• Middle Ages
• Geometry
• Mathematical logic
• Number theory
• Number
• Linguistics
• Probability
• Physics
• Probability theory
• Power set
• Plutarch
• Renaissance

Opposing perspectives

• Probability theory

Place in the tradition

Part of Spanish philosophy.

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