Article ID: CBB986120792

On the Development of a Complex Number Interpretation from the 16th to the End of the 19th century (2023)


We will look at the development of geometric concepts of complex and negative numbers during the period from the 16th to the 20th century. For a long time, these numbers, being obtained analytically, could not find their interpretation; they were called false and imaginary. In 1544, M. Stifel expressed the idea that negative numbers are numbers less than zero. It was a seditious thought because zero meant “nothing” and there could be nothing less than “nothing.” At the turn of the 16th and 17th centuries, this interpretation of negative numbers was embodied in chronology (countdown, before and after the birth of Christ), and in the 18th century, it began to be used in the temperature scale. Attempts at a geometric interpretation of imaginary numbers were undertaken by J. Wallis, G. Leibniz, I. Bernoulli, A. Moivre. L. Euler advanced further than others, who began to depict complex numbers as points on a plane, introduced trigonometric and exponential forms, almost simultaneously with d’Alembert introduced the condition for the analyticity of a function, noticed the symmetry of the function of the conjugate argument, introduced the symbol of an imaginary number. K. Wessel, K. Gauss, and then Argand introduced the complex plane and the geometric interpretation of complex numbers as directed segments, and operations on them. This led W. Hamilton to the concept of quaternion, and his followers to the creation of vector calculus. How much easier the presentation of physics, geodesy, theory of electrical networks, and other applications thanks to complex numbers and vectors!

Citation URI

This citation is part of the Isis database.

Similar Citations

Book Koetsier, Teun; Bergmans, Luc; (2005)
Mathematics and the Divine: A Historical Study (/p/isis/citation/CBB000500288/) unapi

Book Beeley, Philip; Scriba, Christoph J.; (2012)
Correspondence of John Wallis (1616--1703). Vol. III, October 1668--December 1673 (/p/isis/citation/CBB001200116/) unapi

Article O'Neill, John; (1986)
Formalism, Hamilton and complex numbers (/p/isis/citation/CBB000041051/) unapi

Article Heeffer, Albrecht; (2012)
The Genesis of the Algebra Textbook: From Pacioli to Euler (/p/isis/citation/CBB001320800/) unapi

Book Nahin, Paul J.; (2006)
Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills (/p/isis/citation/CBB000772751/) unapi

Article Simmons, Charlotte; (2008)
William Rowan Hamilton and George Boole (/p/isis/citation/CBB000931920/) unapi

Article Anne van Weerden; Steven Wepster; (2018)
A Most Gossiped About Genius: Sir William Rowan Hamilton (/p/isis/citation/CBB864123041/) unapi

Article Bruno, Giuseppe; Genovese, Andrea; Improta, Gennaro; (2011)
Routing Problems: A Historical Perspective (/p/isis/citation/CBB001034720/) unapi

Book Féry, Suzanne; (2012)
Aventures de l'analyse de Fermat à Borel: Mélanges en l'honneur de Christian Gilain (/p/isis/citation/CBB001550745/) unapi

Article Eberhard Knobloch; (2018)
Euler and d’Alembert — Brothers Only in Mind (/p/isis/citation/CBB669654030/) unapi

Article Maria Teresa Borgato; (2013)
Lagrange et les fonds de pension pour les veuves (/p/isis/citation/CBB017117785/) unapi

Article Nakata, Ryoichi; (2002)
The General Principle for Resolving Mechanical Problems in d'Almbert, Clairaut and Euler (/p/isis/citation/CBB000330337/) unapi

Article Pepe, Luigi; (1996)
Condorcet et l'Italie: La vie de Voltaire et les éloges d'Euler and de d'Alembert (/p/isis/citation/CBB000073839/) unapi

Article Ferlin, Fabrice; (2008)
Les lunettes achromatiques: un enjeu européen dans la deuxième moitié du 18e siècle (/p/isis/citation/CBB000933177/) unapi

Article Demidov, Serge S.; (2008)
D'Alembert et la notion de solution des équations différentielles aux dérivées partielles (/p/isis/citation/CBB000933173/) unapi

Article Raman, Varadaraja V.; (1985)
The D'Alembert-Euler rivalry (/p/isis/citation/CBB000033446/) unapi

Article Ferraro, Giovanni; (2008)
D'Alembert visto da Eulero (/p/isis/citation/CBB000933180/) unapi

Authors & Contributors
Beeley, Philip
Bergmans, Luc
Borgato, Maria Teresa
Bruno, Giuseppe
Demidov, Serghei S.
Euler, Leonhard
Bollettino di Storia delle Scienze Matematiche
British Society for the History of Mathematics Bulletin
Acta Baltica historiae et philosophiae scientiarum
Centaurus: International Magazine of the History of Mathematics, Science, and Technology
Historia Scientiarum: International Journal of the History of Science Society of Japan
Oxford University Press
Presses Universitaires de Nancy
Princeton University Press
Correspondence and corresponding
Science and society
Complex numbers
Euler, Leonhard
Alembert, Jean le Rond d'
Hamilton, William Rowan
Lagrange, Joseph Louis
Clairaut, Alexis Claude
Condorcet, Jean Antoine Nicolas Caritat, Marquis de
Time Periods
18th century
19th century
17th century
Early modern
Great Britain
Berlin (Germany)
Deutsche Akademie der Wissenschaften, Berlin
Oxford University
Royal Society of London
Rossiiskaia Akademiia Nauk

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment