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)
Mathematics is not about numbers, but about the relations between them.
The theory of ideals is a natural generalization of the theory of numbers.
The fundamental theorem of arithmetic, that every integer can be uniquely factored into primes, is a cornerstone of number theory.
The concept of a group is one of the most fruitful ideas in modern mathematics.
The true nature of mathematical objects is revealed through their definitions and properties, not their representations.
The development of mathematics is a continuous process of abstraction and generalization.
The beauty of mathematics lies in its logical coherence and internal consistency.
The concept of a module is a powerful tool for studying algebraic structures.
The search for fundamental principles is at the heart of mathematical research.
The rigor of mathematical proof is what distinguishes it from other forms of knowledge.
The concept of an ideal is a generalization of the concept of a number.
The progress of mathematics depends on the clarity and precision of its definitions.
The infinite is not a mere potentiality, but an actual existence in mathematics.
The concept of a ring is a fundamental building block of abstract algebra.
The power of generalization allows us to see connections between seemingly disparate mathematical concepts.
The development of set theory has revolutionized the foundations of mathematics.
The concept of a homomorphism is crucial for understanding the relationships between algebraic structures.
The pursuit of mathematical truth is a noble endeavor.
The elegance of a mathematical proof is a testament to its truth.
The concept of a prime ideal is a powerful tool in algebraic number theory.
Contemporaries of Richard Dedekind
Other Mathematicss born within 50 years of Richard Dedekind (1831–1916).