When Richard Dedekind ‘invented’ real numbers at ETH Zurich
What is the nature and meaning of numbers? Mathematician Richard Dedekind asked these questions 159 years ago at ETH Zurich, and became the first person to define real numbers. To mark this occasion, the Israeli science historian Leo Corry will give a public lecture on the unity of Dedekind’s number theoretic concepts.
“Numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things,” wrote mathematician and temporary ETH professor Richard Dedekind (1831-1916) in his work The Nature and Meaning of Numbers (variously translated as What Are Numbers and What Should They be?). Published in 1888, it provided the first precise axiomatic foundation for natural numbers. In the essay Continuity and Irrational Numbers, published in 1872, Dedekind also defined real numbers for the first time. His inspiration came in 1858 while lecturing as a professor at what was then called the Polytechnikum in Zurich.
Unity of concepts
To be able to establish a system of real numbers, Dedekind introduced the term “cut”, thereby laying the groundwork for modern analysis. His work on algebraic numbers is based on the concept of the ideal, and his foundation of natural numbers on that of the chain.
Israeli science historian Leo Corry, author of A Brief History of Numbers (2015), will give a public lecture to students, researchers and mathematics enthusiasts at ETH Zurich on Thursday 23 November. He will discuss the extent to which Dedekind’s entire body of work was based on a methodological unity.
The lecture is being held as part of the Dedekind Lectures series by the Department of Mathematics (D-MATH).
Dedekind Lectures 2017
The Nature and Meaning of Dedekind’s Numbers:
Ideals, Cuts and Chains in a Unified World of Numbers
Public lecture by Leo Corry, Professor at the Cohn Institute for the History and Philosophy of Science and Ideas at Tel Aviv University,
as part of the Dedekind Lectures on the foundations of arithmetic
ETH Zurich, Main Building
Lecture hall HG G3
23 November 2017
5.15–6.30 p.m.
With refreshments to follow.