Richard Dedekind

Mathematics German 1831 – 1916 399 quotes

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.

Book 1871

Every theorem is a victory over chaos.

Letter

The real numbers form a complete ordered field.

Book 1872

Friendship with Dirichlet was my greatest inspiration.

Letter 1860

Logic is the thread that weaves mathematical tapestries.

Book 1888

The beauty of math lies in its universality.

Speech

Cuts define the boundaries of rationality.

Book 1872

Aging mathematicians grow wiser with each unsolved problem.

Personal Reflection 1910

Modular arithmetic unlocks the secrets of periodicity.

Book 1877

Truth in math is eternal, unlike fleeting human endeavors.

Letter

The study of primes is an endless quest.

Book 1894

Joy comes from simplifying the complex.

Interview

Set theory provides the foundation for all mathematics.

Book 1888

In reflection, I see the unity of all branches of math.

Personal Reflection 1900

Equations are the language of the cosmos.

Book 1877

Persistence in proof-finding is the mark of genius.

Speech

The irrational permeates the fabric of reality.

Book 1872

My last thoughts were of the infinite continuum.

Deathbed 1916

Humor in math: why did the number go to therapy? It had too many issues!

Witty Remark

Professional insight: Rings are more versatile than fields in algebra.

Book 1894