Article ID: CBB253445490

Polygons of Petrović and Fine, algebraic ODEs, and contemporary mathematics (2020)

unapi

In this paper, we study the genesis and evolution of geometric ideas and techniques in investigations of movable singularities of algebraic ordinary differential equations. This leads us to the work of Mihailo Petrović on algebraic differential equations (ODEs) and in particular the geometric ideas expressed in his polygon method from the final years of the nineteenth century, which have been left completely unnoticed by the experts. This concept, also developed independently and in a somewhat different direction by Henry Fine, generalizes the famous Newton–Puiseux polygonal method and applies to algebraic ODEs rather than algebraic equations. Although remarkable, the Petrović legacy has been practically neglected in the modern literature, although the situation is less severe in the case of results of Fine. Therefore, we study the development of the ideas of Petrović and Fine and their places in contemporary mathematics.

...More
Citation URI
https://data.isiscb.org/isis/citation/CBB253445490/

Similar Citations

Article Lukas M. Verburgt; (2018)
Duncan F. Gregory and Robert Leslie Ellis: Second-Generation Reformers of British Mathematics (/isis/citation/CBB954232268/)

Book Charpentier, Éric; Ghys, Étienne; Lesne, Annick; (2010)
The Scientific Legacy of Poincaré (/isis/citation/CBB001023244/)

Article Barbin, Évelyne; Guitart, René; (2001)
Algèbre des fonctions elliptiques et géométrie des ovales cartésiennes (/isis/citation/CBB000770906/)

Article Gandon, Sébastien; (2006)
La réception des Vorlesungen über neuere Geometrie de Pasch par Peano (/isis/citation/CBB000773900/)

Article Nabonnand, Philippe; (2008)
La théorie des Würfe de von Staudt -- Une irruption de l'algèbre dans la géométrie pure (/isis/citation/CBB000850593/)

Article Boucard, Jenny; (2011)
Louis Poinsot et la théorie de l'ordre: un chaînon manquant entre Gauss et Galois? (/isis/citation/CBB001034693/)

Article Sørensen, Henrik Kragh; (2006)
Louis Olivier: A Mathematician Only Known Through his Publications in Crelle's Journal during the 1820s (/isis/citation/CBB000671190/)

Book Flood, Raymond; Rice, Adrian; Wilson, Robin; (2011)
Mathematics in Victorian Britain (/isis/citation/CBB001221196/)

Article Ferraro, Giovanni; Panza, Marco; (2012)
Lagrange's Theory of Analytical Functions and His Ideal of Purity of Method (/isis/citation/CBB001220403/)

Article Leandro Silva Dias; Gerard Emile Grimberg; (2015)
Algebra e Geometria Projectiva Analítica na Inglaterra dos anos 1841-1853 (/isis/citation/CBB920429654/)

Article Parshall, Karen Hunger; (2004)
Defining a Mathematical Research School: The Case of Algebra at The University of Chicago, 1892--1945 (/isis/citation/CBB000470897/)

Article Sheynin, Oscar B.; (2003)
Nekrasov's Work on Probability: The Background (/isis/citation/CBB000340516/)

Article Pedro J. Freitas; (2019)
The Correspondence from Ernesto Cesàro to Francisco Gomes Teixeira (/isis/citation/CBB711366439/)

Article Español González, Luis; (2003)
Avances en la Historia de la Geometría contemporánea española durante el último cuarto de siglo (/isis/citation/CBB000530002/)

Article Nastasi, Tina; (2008)
La storia del pensiero scientifico e il suo significato nell'opera di Federigo Enriques (/isis/citation/CBB001024085/)

Book Gray, Jeremy; Parshall, Karen Hunger; (2007)
Episodes in the History of Modern Algebra (1800--1950) (/isis/citation/CBB000774194/)

Authors & Contributors
Parshall, Karen V. Hunger
Mechthild Koreuber
Freitas, Pedro J.
Gerard Emile Grimberg
Leandro Silva Dias
Wilson, Robin J.
Concepts
Mathematics
Algebra
Geometry
Algebraic geometry
Research schools
Philosophy of mathematics
Time Periods
19th century
20th century, early
18th century
Places
Italy
England
Spain
Russia
Portugal
Rome (Italy)
Institutions
University of Chicago
Comments

Be the first to comment!

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

Log in or register to comment