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)
Gaussian integers are the jewels of number theory.
Every theorem is a victory over chaos.
The real numbers form a complete ordered field.
Friendship with Dirichlet was my greatest inspiration.
Logic is the thread that weaves mathematical tapestries.
The beauty of math lies in its universality.
Cuts define the boundaries of rationality.
Aging mathematicians grow wiser with each unsolved problem.
Modular arithmetic unlocks the secrets of periodicity.
Truth in math is eternal, unlike fleeting human endeavors.
The study of primes is an endless quest.
Joy comes from simplifying the complex.
Set theory provides the foundation for all mathematics.
In reflection, I see the unity of all branches of math.
Equations are the language of the cosmos.
Persistence in proof-finding is the mark of genius.
The irrational permeates the fabric of reality.
My last thoughts were of the infinite continuum.
Humor in math: why did the number go to therapy? It had too many issues!
Professional insight: Rings are more versatile than fields in algebra.
Contemporaries of Richard Dedekind
Other Mathematicss born within 50 years of Richard Dedekind (1831–1916).