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 history of mathematics is a history of ideas.
The concept of a lattice is a fundamental structure in order theory.
The clarity of thought is paramount in mathematics.
The concept of a Dedekind domain is central to algebraic number theory.
The true mathematician is a creator, not just a discoverer.
The concept of a field extension is fundamental to Galois theory.
The pursuit of mathematical knowledge is a lifelong journey.
The concept of a unique factorization domain is a generalization of the fundamental theorem of arithmetic.
The power of abstraction allows us to build complex structures from simple foundations.
Mathematics is a language, and its grammar is logic.
The continuum is not a mere collection of points, but a whole whose parts are inseparable.
Mathematics is the art of giving the same name to different things.
Irrational numbers arise naturally from the division of the continuum.
In the theory of numbers, precision is the soul of beauty.
The infinite is not a number, but a mode of being.
Algebraic structures reveal the hidden symmetries of the universe.
To understand the real numbers, one must cut through the illusions of intuition.
Life is like a Dedekind cut: divided yet complete.
The rigor of proof is the foundation of mathematical truth.
Galois theory opens the door to the mysteries of equations.
Contemporaries of Richard Dedekind
Other Mathematicss born within 50 years of Richard Dedekind (1831–1916).