Is Mathematical Rigor Necessary in Physics?

Davey, Kevin

doi:10.1093/bjps/54.3.439

Cited by 18 publications

(15 citation statements)

References 14 publications

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“…Philosophical studies have gone beyond "marveling at the applicability of mathematics to nature in general" [12] to examine scientific argumentation [13]. The highest, or "mathematical", rigor is regarded as an obstacle to investigation [14]. 4 The issue of appropriate rigor cannot be excised from a discussion of mathematics by restricting the literature, because interdisciplinary mathematics largely develops in the allied fields [18], as, for example, the analysis of algorithms.…”

Section: Proclivity For Errorsmentioning

confidence: 99%

“…For rigor in quantum theory see [12], [14], and in engineering see [16], [17]. 5 Perspectives on origins and ramifications of using proofs as evidence are given by [15], [21].…”

Section: Proclivity For Errorsmentioning

confidence: 99%

“…The mathematics subject areas with high rates of (2) comments from readers are all interdisciplinary fields (see Figure 5). Subjects 81 and 83 are heavily published by the Institute of Physics, 14 which invites reader comments in all its journals. Subject 93 is the rare, very large branch of mathematics that publishes comments in theoretical (i.e., mathematical) journals such as Automatica.…”

Section: No Editorial Guidancementioning

confidence: 99%

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Errors and Corrections in Mathematics Literature

Grcar¹

2013

Notices Amer. Math. Soc.

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Section: Proclivity For Errorsmentioning

confidence: 99%

“…For rigor in quantum theory see [12], [14], and in engineering see [16], [17]. 5 Perspectives on origins and ramifications of using proofs as evidence are given by [15], [21].…”

Section: Proclivity For Errorsmentioning

confidence: 99%

Section: No Editorial Guidancementioning

confidence: 99%

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Errors and Corrections in Mathematics Literature

Grcar¹

2013

Notices Amer. Math. Soc.

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“…On the one hand, a model aims to describe or predict the physical situation as accurately as possible. So, a scientific model is usually quantitative, and it borrows mathematics (Suppes, 1960) for the purpose of quantification (Davy, 2003). On the other hand, a model simplifies a physical situation by ignoring details that are thought 14 to be insignificant or unrelated to the inquiry.…”

Section: Scientific Study Elementsmentioning

confidence: 99%

Understanding Scientific Study via Process Modeling

Luk

2010

Found Sci

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This paper argues that scientific studies distinguish themselves from other studies by a combination of their processes, their (knowledge) elements and the roles of these elements. This is supported by constructing a process model. An illustrative example based on Newtonian mechanics shows how scientific knowledge is structured according to the process model. To distinguish scientific studies from research and scientific research, two additional process models are built for such processes. We apply these process models: (1) to argue that scientific progress should emphasize both the process of change and the content of change; (2) to chart the major stages of scientific study development; and (3) to define "science".

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“…ontology (Corfield, 1997(Corfield, , 2003Aberdein, 2003;Davey 2003;Stöltzner, 2002a). A more profound discussion, however, is still lacking.…”

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confidence: 99%

Theoretical Mathematics

Stöltzner¹

The Role of Mathematics in Physical Sciences

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Abstract:Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a 'theoretical' mathematics (alongside 'theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20 th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.

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Is Mathematical Rigor Necessary in Physics?

Cited by 18 publications

References 14 publications

Errors and Corrections in Mathematics Literature

Errors and Corrections in Mathematics Literature

Understanding Scientific Study via Process Modeling

Theoretical Mathematics

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