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Number Theory
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Number theory is the branch of mathematics concerned with the properties of whole numbers, including divisibility, prime numbers and the solutions of equations in integers. Euclid's Elements already contains early results in the subject in its books seven through nine, among them the Euclidean algorithm for finding the greatest common divisor of two numbers and a proof that the prime numbers are infinite in quantity. Carl Friedrich Gauss's 1801 Disquisitiones Arithmeticae unified centuries of earlier, scattered results from Fermat, Euler, Lagrange and Legendre into one rigorous, systematic framework and is widely regarded as having founded modern number theory as a coherent discipline. In the twentieth century Srinivasa Ramanujan made major further contributions to the field, particularly on the partition function counting the ways a whole number can be written as a sum of smaller whole numbers.
Facts
Proposed YearSourced to the subject's own account Proposed BySourced to the subject's own accountGauss's Disquisitiones Arithmeticae (1801) gathered the field's earlier isolated theorems and conjectures (Euclid's Elements among them, already cited on this entity) into the first systematic framework; this is the founding of number theory as a coherent modern discipline, not a claim that no earlier results existed. Cross-Tradition Connections
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1. Disquisitiones Arithmeticae (Wikipedia)
WikipediaImportance sectionQuote, Importance section
Before the Disquisitiones was published, number theory consisted of a collection of isolated theorems and conjectures. Gauss brought the work of his predecessors together with his own original work into a systematic framework, filled in gaps, corrected unsound proofs, and extended the subject in numerous ways.
Disquisitiones Arithmeticae (1801)
Carl Friedrich Gauss, Gerh. Fleischer (Leipzig), 1801
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