Miscellanea analytica…

work by Waring

Also known as: “Meditationes Algebraicae”, “Proprietates algebraicarum Curvarum”(Show More)

Written by

The Information Architects of Encyclopaedia Britannica

Last updated

July 16, 2026

Quick Summary

Edward Waring's Miscellanea analytica (1762) is a significant work in algebra and number theory. This notoriously complex text, later expanded into Meditationes algebraicae, explores topics such as the theory of equations and analytic geometry.1

Within Miscellanea analytica, Waring stated several theorems without proof, including Waring's problem, which conjectures that every positive integer can be expressed as the sum of a fixed number of nth powers. This problem has been a subject of significant mathematical inquiry. The work also introduced concepts that are now recognized as contributions to group theory and presented the Goldbach conjecture for the first time in print.12

Summary created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

6 Britannica Sources

Ask Britannica AI about this topic

Britannica doesn't have a full article on this topic, so we've curated a list of our relevant coverage.

Edward Waring
In 1762 Waring published Miscellanea analytica… (“Miscellany of analysis…”), a notoriously impenetrable work, but the one upon which his fame largely rests. It was enlarged and republished as Meditationes algebraicae (1770, 1782; “Thoughts on Algebra”) and Proprietates algebraicarum Curvarum (1772; “The Properties of Algebraic Curves”). It covers the theory…
Read More
In 1762 Waring published Miscellanea analytica… (“Miscellany of analysis…”), a notoriously impenetrable work, but the one upon which his fame largely rests. It was enlarged and republished as Meditationes algebraicae (1770, 1782; “Thoughts on Algebra”) and Proprietates algebraicarum Curvarum (1772; “The Properties of Algebraic Curves”). It covers the theory…
Read More

Goldbach conjecture
…in English mathematician Edward Waring’s Meditationes algebraicae (1770), which also contained Waring’s problem and what was later known as Vinogradov’s theorem. The latter, which states that every sufficiently large odd integer can be expressed as the sum of three primes, was proved in 1937 by the Russian mathematician Ivan Matveyevich…
Read More
…in English mathematician Edward Waring’s Meditationes algebraicae (1770), which also contained Waring’s problem and what was later known as Vinogradov’s theorem. The latter, which states that every sufficiently large odd integer can be expressed as the sum of three primes, was proved in 1937 by the Russian mathematician Ivan Matveyevich…
Read More

Vinogradov’s theorem
English mathematician Edward Waring’s Meditationes Algebraicae (1770), which contained several other important ideas in number theory, including Waring’s problem, Wilson’s theorem, and the famous Goldbach conjecture.
Read More
English mathematician Edward Waring’s Meditationes Algebraicae (1770), which contained several other important ideas in number theory, including Waring’s problem, Wilson’s theorem, and the famous Goldbach conjecture.
Read More

Waring’s problem
mathematician Edward Waring in Meditationes Algebraicae (1770; “Thoughts on Algebra”), where he speculated that f(2) = 4, f(3) = 9, and f(4) = 19; that is, it takes no more than 4 squares, 9 cubes, or 19 fourth powers to express any integer.
Read More
mathematician Edward Waring in Meditationes Algebraicae (1770; “Thoughts on Algebra”), where he speculated that f(2) = 4, f(3) = 9, and f(4) = 19; that is, it takes no more than 4 squares, 9 cubes, or 19 fourth powers to express any integer.
Read More