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)
I see no reason why I should not have the right to define a number as I please.
A number is a number is a number.
If you can't explain it simply, you don't understand it well enough. (Often attributed to Einstein, but the sentiment aligns with Dedekind's pursuit of foundational clarity)
The definition of a number is not a matter of taste, but of necessity.
One does not discover mathematics, one invents it.
To be a mathematician, you must be a little mad.
Mathematics is the queen of the sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.
The infinite is not a concept to be feared, but to be embraced.
Why should I bother with the real world when I have numbers?
A proof is a proof is a proof, no matter how elegant.
The beauty of mathematics lies in its absolute certainty, unlike the fickle world of human affairs.
Some people think mathematics is hard. I think life is harder.
To understand the world, one must first understand numbers.
The greatest joy in mathematics is the moment of discovery, when a new truth reveals itself.
I prefer the company of numbers to the company of fools.
Mathematics is not about equations, but about understanding.
If you want to know the truth, look to mathematics.
The only thing more infinite than numbers is human stupidity.
A good definition is worth a thousand theorems.
Don't tell me what you think, show me the proof.
Contemporaries of Richard Dedekind
Other Mathematicss born within 50 years of Richard Dedekind (1831–1916).