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)
In mathematics, every problem solved begets a thousand more.
The concept of ideal in number theory is a beacon for abstract thought.
Friendship among mathematicians is forged in the fire of shared proofs.
Continuity demands a definition free from the tyranny of the finite.
The real line is constructed, not discovered.
Happiness lies in the pursuit of elegant theorems.
Dedekind cuts sever the bond between rational and irrational.
The essence of mathematics is abstraction from the concrete.
In solitude, the mind wanders to infinite realms.
Fields and rings govern the algebra of numbers.
Proofs are the poetry of logic.
The unknown is the greatest teacher in mathematics.
My work on continuity was born from Riemann's spirit.
Life's divisions are as sharp as a cut in the reals.
Ideals in quadratic fields illuminate the path to generality.
Mathematics demands patience, for truth reveals itself slowly.
The harmony of numbers is a divine symphony.
To teach is to ignite the spark of curiosity.
Abstraction is the ladder to higher mathematics.
In the face of infinity, humility is our greatest virtue.
Contemporaries of Richard Dedekind
Other Mathematicss born within 50 years of Richard Dedekind (1831–1916).