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 universe is written in the language of mathematics.
My work is my life, and my life is numbers.
The simpler the concept, the harder it is to define.
I have no need of that hypothesis.
To err is human, to prove divine.
The foundations of mathematics are not built on sand, but on solid logic.
If you want to understand the world, don't ask a philosopher, ask a mathematician.
The only true wisdom is in knowing you know nothing, except in mathematics, where you can know everything.
I don't believe in magic, I believe in theorems.
The more I study mathematics, the more I am convinced that it is the only true religion.
A mathematician's work is never done, there's always another proof to find.
The real world is just a special case of the mathematical world.
Logic is the beginning of wisdom, not the end.
I have never been bored in my life, I always have numbers to keep me company.
The only thing worse than a bad proof is no proof at all.
Mathematics is the language in which God has written the universe.
Why complicate things when you can simplify them with a good definition?
The greatest mathematicians are not those who solve problems, but those who define them.
I find more truth in a theorem than in a sermon.
The infinite is not a quantity, but a quality.
Contemporaries of Richard Dedekind
Other Mathematicss born within 50 years of Richard Dedekind (1831–1916).