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 concept of a system is fundamental to understanding mathematical structures.
We must strive for perfect clarity and precision in our mathematical language.
The irrational numbers fill the gaps in the rational number line, creating a continuous whole.
The power of abstraction is what distinguishes mathematics from other sciences.
The notion of a 'cut' allows us to define the continuum without relying on geometric intuition.
Mathematics is the language of the universe.
The concept of an ideal is crucial for understanding the structure of algebraic number fields.
The theory of numbers is a vast and beautiful landscape, full of hidden treasures.
The infinite is not a contradiction, but a profound reality.
My work on cuts was an attempt to provide a purely arithmetical foundation for the theory of real numbers.
Mathematics is a journey into the unknown, guided by logic and intuition.
The concept of a mapping is central to understanding the relationships between mathematical structures.
The beauty of mathematics lies in its simplicity and elegance.
The foundations of mathematics must be built on solid ground, free from ambiguity.
The theory of ideals provides a powerful tool for studying divisibility in algebraic number fields.
Mathematics is a universal language, understood by all who seek truth.
The concept of an infinite set is not paradoxical, but a natural consequence of our definitions.
My aim was to create a purely arithmetical and perfectly rigorous foundation for the science of numbers.
The power of abstract thought allows us to transcend the limitations of our senses.
Numbers are free creations of the human mind.
Contemporaries of Richard Dedekind
Other Mathematicss born within 50 years of Richard Dedekind (1831–1916).