Article ID: CBB066890396

An Okapi Hypothesis: Non-Euclidean Geometry and the Professional Expert in American Mathematics (2022)


Open Court began publishing The Monist in 1890 as a journal “devoted to the philosophy of science” that regularly included mathematics. The audience was understood to be “cultured people who have not a technical mathematical training” but nevertheless “have a mathematical penchant.” With these constraints, the mathematical content varied from recreations to logical foundations, but everyone had something to say about non-Euclidean geometry, in debates that ranged from psychology to semantics. The focus in this essay is on the contested value of mathematical expertise in legitimating what should be considered as mathematics. While some mathematicians urged The Monist to uphold disciplinary standards of geometrical reasoning, authors opposed to non-Euclidean geometry aligned their reasoning with practical applications, universal know-how, and nonhierarchical democracy. As one contributor inquired, “How is the professional expert better fitted to see more lucidly in dealing with the elements of geometry than any other person of good geometric faculty?”

Citation URI

Similar Citations

Article Francesca Biagioli; (2020)
Ernst Cassirer's transcendental account of mathematical reasoning (/isis/citation/CBB961648354/)

Article Kjeldsen, Tinne Hoff; Carter, Jessica; (2012)
The Growth of Mathematical Knowledge---Introduction of Convex Bodies (/isis/citation/CBB001221693/)

Article Ivan Netuka; (2020)
Lebesgue’s criticism of Carl Neumann’s method in potential theory (/isis/citation/CBB941462998/)

Article De Pierris, Graciela; (2012)
Hume on Space, Geometry, and Diagrammatic Reasoning (/isis/citation/CBB001211479/)

Chapter IAN HACKING; (2016)
On the Contingency of What Counts as “Mathematics” (/isis/citation/CBB236243675/)

Book de Ceglia, Francesco Paolo; (1999)
De Natantibus: Una Disputa ai Confini tra Filosofia e Matematica nella Toscana Medicea (1611-1615) (/isis/citation/CBB000100280/)

Article Campos, Daniel G.; (2007)
Peirce on the Role of Poietic Creation in Mathematical Reasoning (/isis/citation/CBB001023426/)

Book Goldenbaum, Ursula; Jesseph, Douglas; (2008)
Infinitesimal Differences: Controversies between Leibniz and His Contemporaries (/isis/citation/CBB000950297/)

Article Vincenzo De Risi; (2021)
Euclid’s Common Notions and the Theory of Equivalence (/isis/citation/CBB348431913/)

Contingency in Mathematics: Two Case Studies (/isis/citation/CBB062227235/)

Book Gray, Jeremy J.; (2004)
János Bolyai, Non-Euclidean Geometry, and the Nature of Space (/isis/citation/CBB000750880/)

Article Abardia, Judit; Reventós, Agustí; Rodríguez, Carlos J.; (2012)
What Did Gauss Read in the Appendix? (/isis/citation/CBB001251202/)

Chapter Giulia Giannini; (2009)
Poincaré, la nozione di gruppo e il Programma di Erlangen di F. Klein (/isis/citation/CBB227666735/)

Book Voelke, Jean-Daniel; (2005)
Renaissance de la géométrie non euclidienne entre 1860 et 1900 (/isis/citation/CBB000830712/)

Book Alberto Cogliati; (2024)
La geometria non euclidea. Una breve storia dall’antichità a Poincaré (/isis/citation/CBB276091257/)

Book Colyvan, Mark; (2001)
Indispensability of Mathematics (/isis/citation/CBB000102198/)

Article Jacy L. Young; (2020)
Thinking in Multitudes: Questionnaires and Composite Cases in Early American Psychology (/isis/citation/CBB385770594/)

Article José Ramón Bertomeu Sánchez; (2021)
Lead Poisoning in France around 1840: Managing Proofs and Uncertainties in Laboratories, Courtrooms, and Workplaces (/isis/citation/CBB619372597/)

Authors & Contributors
De Ceglia, Francesco Paolo
Colyvan, Mark
Gray, Jeremy
Shoji, Kota
Voelke, Jean-Daniel
Bachimont, Bruno
Studies in History and Philosophy of Science
Historia Scientiarum: International Journal of the History of Science Society of Japan
Transactions of the Charles S. Peirce Society
Historia Mathematica
Foundations of Science
Edizioni Giuseppe Laterza
Cambridge University Press
The MIT Press
Walter de Gruyter
Philosophy of mathematics
Controversies and disputes
Non-euclidean geometry
Reasoning in science
Bolyai, Janos (Johann) von
Gauss, Carl Friedrich
Poincaré, Jules Henri
Quine, Willard Van Orman
Putnam, Hilary
Killing, Wilhelm Karl Joseph
Time Periods
19th century
17th century
20th century
20th century, early
18th century
Tuscany (Italy)
United States

Be the first to comment!

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

Log in or register to comment