Richard Dedekind
A German mathematician who made important contributions to abstract algebra, particularly in algebraic number theory.
Most quoted
"If all points of the straight line fall into two classes such that every point of the first class lies to the left of every point of the second class, then there exists one and only one point which produces this division of all points into two classes, this severing of the straight line into two portions."
— from Stetigkeit und irrationale Zahlen, 1872
"The continuity of the domain of real numbers is the property that if all its elements are divided into two classes, such that every element of the first class is less than every element of the second class, then there exists one and only one number which produces this division."
— from Stetigkeit und irrationale Zahlen, 1872
"The way in which the irrational numbers are usually introduced is based directly upon the conception of extensive magnitudes—which itself is nowhere carefully defined—and explains number as the result of measuring such a magnitude by another of the same kind."
— from Stetigkeit und irrationale Zahlen, 1872
All quotes by Richard Dedekind (399)
The natural numbers are the foundation of all arithmetic.
The concept of infinity is essential for the development of mathematics.
The theory of ideals is a generalization of the theory of numbers.
An ideal is a system of numbers which possesses certain properties.
The concept of a field is fundamental in algebra.
The theory of algebraic numbers is a vast and beautiful field.
The development of mathematics proceeds from the simple to the complex.
The rigor of mathematical proofs is of the utmost importance.
The true nature of numbers is revealed through their abstract properties.
The concept of order is essential for the definition of numbers.
The real numbers form a continuous domain.
The definition of equality for numbers must be precise.
The concept of a system is more general than the concept of a set.
The properties of numbers are independent of their representation.
The theory of numbers is a purely intellectual creation.
The concept of a group is fundamental in algebra and number theory.
The development of mathematics is a continuous process.
The concept of an integer is a generalization of the natural number.
The rational numbers are dense in the real numbers.
The concept of a prime number is central to number theory.
Contemporaries of Richard Dedekind
Other Mathematicss born within 50 years of Richard Dedekind (1831–1916).