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 search for mathematical truth is a deeply human endeavor.
The spiritual dimension of mathematics lies in its ability to inspire awe and wonder.
Mathematics is a journey into the realm of pure thought.
The beauty of mathematical structures is a reflection of the underlying order of the cosmos.
The infinite is a concept that challenges our perception of reality.
The pursuit of mathematical understanding is a path to self-discovery.
Mathematics is a creative act of the human mind.
The truth of mathematics is independent of human opinion.
What are numbers? We must understand by number a free creation of the human mind.
The essence of arithmetic is the concept of number. The concept of number is quite independent of the concepts of space and time.
A system S is infinite if it is similar to a proper part of itself; in the contrary case S is a finite system.
Every infinite system contains a part which is similar to itself.
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.
I see no objection to regarding the number as a pure creation of the human mind.
The real numbers are nothing but cuts in the system of rational numbers.
The definition of the irrational number by means of cuts is the only one which satisfies the requirement of rigor.
The concept of number is not derived from experience, but is a free creation of the human mind.
The natural numbers are a free creation of the human mind, and their properties are not discovered but invented.
The existence of an infinite system is a necessary condition for the existence of numbers.
The concept of a set is fundamental and cannot be reduced to simpler concepts.
Contemporaries of Richard Dedekind
Other Mathematicss born within 50 years of Richard Dedekind (1831–1916).