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 foundation of mathematics must be built on solid logical principles.
The concept of a ring is a generalization of the concept of integers.
The beauty of mathematics lies in its logical structure.
What is provable is not always true.
I see no reason why the concept of number should be restricted to the rational numbers.
The numbers are free creations of the human mind.
I have often heard that mathematics is the queen of the sciences, but I have never heard that it is the handmaiden of the sciences.
A definition is good if it is useful.
I believe that the true nature of mathematics is to be found in its abstractness.
My work is not for the faint of heart.
I am a mathematician, not a philosopher.
The beauty of mathematics lies in its simplicity.
I have always been fascinated by the concept of infinity.
The foundations of mathematics are not as solid as one might think.
I strive for clarity and rigor in all my work.
Mathematics is a language, and I am trying to speak it fluently.
The joy of discovery is what drives me.
I am not afraid to challenge established ideas.
The real numbers are a continuous domain.
My aim is to make mathematics more accessible.
Contemporaries of Richard Dedekind
Other Mathematicss born within 50 years of Richard Dedekind (1831–1916).