The Rise of non-Archimedean Mathematics and the Roots of a Misconception I: The Emergence of non-Archimedean Systems of Magnitudes

By Philip Ehrlich. 2006

124 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/db7138b2807b4103f1e7f73728a8484a1b898b9b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Alexandre V. Borovik
2. Mikhail G. Katz
3. Victor Pambuccian
4. Piotr Błaszczyk
5. David Sherry

In Mathematical Physics

1. Mikhail G. Katz
2. David Sherry
3. Piotr Błaszczyk
4. Alexandre V. Borovik
5. Victor Pambuccian

In Theoretical Computer Science

1. Mikhail G. Katz
2. David Sherry
3. Piotr Błaszczyk
4. Alexandre V. Borovik
5. Victor Pambuccian
6. R. Ely

Citations in the corpus

• Ten Misconceptions from the History of Analysis and Their Debunking (2012, background): “Did Weierstrass succeed in eliminating infinitesimals from mathematics? The persistent idea that infinitesimals have been “eliminated” by the great triumvirate of Cantor, Dedekind, and Weierstrass was soundly refuted by Ehrlich [42].”
• Is mathematical history written by the victors (2013, background): “Meanwhile, Stolz was the first modern mathematician to realize the importance of the Archimedean axiom (see entry 2.2) as a separate axiom in its own right (see Ehrlich 2006 [33]), and moreover developed some non-Archimedean systems (Stolz 1885 [113]).”
• Who Gave You the Cauchy–Weierstrass Tale? The Dual History of Rigorous Calculus (2011, background): “Additional such exceptions were published by Seidel and Stokes in the 1840s. Cauchy’s contemporary E. G. Björling anticipated the B-continuum definition in a remarkable passage dating from 1852: when one comes to show that in a series, of which the terms are functions of a quantity x, converges [. ”
• Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond (2012, result): “49Not every hyperreal field can be obtained this way, though a more general construction called limit ultrapower can be used to construct a maximal class hyperreal field (see Ehrlich [35] and Borovik, Jin, and Katz [16]).”
• The axiomatics of ordered geometry: I. Ordered incidence spaces (2011, background): “The modern history of the Archimedean axiom was surveyed in [79,77,78].”