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)
My only regret is that I have but one life to give to mathematics.
The more abstract the mathematics, the more applicable it becomes.
Don't trust anything that can't be proven.
The true mathematician is a poet of logic.
If it's not rigorous, it's not mathematics.
The foundations of mathematics are not a matter of opinion, but of absolute truth.
I prefer the certainty of numbers to the uncertainty of human nature.
What is provable in mathematics is not what is true, but what is consistent.
The infinite is not a concept that can be grasped by the senses, but only by the intellect.
The true value of a thing lies not in its immediate utility, but in its potential for further development.
Every theorem in mathematics is a step towards a deeper understanding of the universe.
The human mind, in its quest for knowledge, creates its own objects of study.
The beauty of mathematics is revealed in its logical structure and its profound simplicity.
To understand is to simplify.
The infinite is not a boundary, but a realm to be explored.
The search for truth is an endless journey.
The human spirit finds its highest expression in the creation of abstract concepts.
The power of reason allows us to transcend the limitations of our senses.
Every definition is a step towards clarity.
The true mathematician is an artist of logic.
Contemporaries of Richard Dedekind
Other Mathematicss born within 50 years of Richard Dedekind (1831–1916).