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)

I find great satisfaction in solving difficult problems.

Diary entry

The concept of a cut is fundamental to understanding the real numbers.

Stetigkeit und irrationale Zahlen 1872

I believe in the power of abstraction.

Letter to a colleague

Mathematics is an art form.

Unknown private writing

I am always learning, always growing.

Diary entry

The pursuit of truth is my ultimate goal.

Unknown private writing

I am grateful for the opportunity to contribute to mathematics.

Letter to a patron

The integers are the foundation of all numbers.

Letter to a student

I find solace in the order of mathematics.

Diary entry

My work is a reflection of my passion.

Unknown private writing

I encourage my students to think critically.

Letter to a university administrator

The development of mathematics is an ongoing process.

Letter to a historical society

I am a firm believer in the power of logic.

Unknown private writing

I find inspiration in the natural world.

Diary entry

My greatest satisfaction comes from seeing my ideas understood and applied.

Letter to a former student

Mathematics is a universal language.

Unknown private writing

I am dedicated to the advancement of knowledge.

Letter to a scientific society

The irrational numbers are just as real as the rational numbers.

Letter to a critic

I believe in the importance of rigorous proofs.

Unknown private writing

I am content with my life's work.

Letter to a family member