Errors and Corrections in Mathematics Literature

Grcar, Joseph F.

doi:10.1090/noti988

Cited by 22 publications

(16 citation statements)

References 26 publications

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“…One does not need to trust the author that he or she is correct. While perhaps true in principle, recent philosophical articles and reflections by mathematicians on their practice suggest that such personal verifications on published research articles are often not done (Auslander, 2008;De Millo, Lipton & Perlis, 1979;Geist, Lowe, & Van Kerkhove, 2010;Grcar, 2013).…”

Section: Philosophical Perspectives On Authoritarian Testimony In Matmentioning

confidence: 99%

“…Davis (1972) estimated that half of published proofs contain errors, and Devlin (2003) discussed recent examples of proofs of important theorems that were thought to be valid by the mathematical community before a flaw was discovered. In an empirical study of the number of corrections published in various disciplines, Grcar (2013) found that mathematics papers were not significantly less likely to contain errors than papers from other disciplines. Due to findings such as these, Nathanson (2008) expressed a stronger concern that the mathematics literature was unreliable.…”

Section: Philosophical Perspectives On Deductive Evidence In Mathematicsmentioning

confidence: 99%

“…In short, although deductive evidence is an extremely powerful source of justification in mathematics, a given deductive proof is often insufficient to gain full certainty in the truth of an assertion. Nathanson (2008) and Grcar (2013) (2000) asserted that "all agree that something is either a proof or it isn't and what makes it a proof is that every assertion in it is correct." (p.1).…”

Section: Philosophical Perspectives On Deductive Evidence In Mathematicsmentioning

confidence: 99%

See 2 more Smart Citations

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition

Weber

Inglis

Mejía-Ramos

2014

Educational Psychologist

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Abstract. The received view of mathematical practice is that mathematicians gain certainty in mathematical assertions by deductive evidence rather than empirical or authoritarian evidence. This assumption has influenced mathematics instruction where students are expected to justify assertions with deductive arguments rather than by checking the assertion with specific examples or appealing to authorities. In this paper, we argue that the received view about mathematical practice is too simplistic; some mathematicians sometimes gain high levels of conviction with empirical or authoritarian evidence and sometimes do not gain full conviction from the proofs that they read. We discuss what implications this might have, both for for mathematics instruction and theories of epistemic cognition

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Section: Philosophical Perspectives On Authoritarian Testimony In Matmentioning

confidence: 99%

Section: Philosophical Perspectives On Deductive Evidence In Mathematicsmentioning

confidence: 99%

Section: Philosophical Perspectives On Deductive Evidence In Mathematicsmentioning

confidence: 99%

See 1 more Smart Citation

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition

Weber

Inglis

Mejía-Ramos

2014

Educational Psychologist

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“…The editor weighs the risk of publishing an error against other values and practical considerations, such as the speed of publication, availability of reviewers, and overhead costs of additional reviews. It has been empirically found that published papers in mathematical journals occasionally contain errors (Geist et al 2010;Grcar 2010). Some mathematicians even complain that the rate of published errors is too high (Nathanson 2008).…”

Section: Scientific Theories -Acceptance Versus Beliefmentioning

confidence: 99%

Science, values, and pragmatic encroachment on knowledge

Miller

2014

Euro Jnl Phil Sci

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Philosophers have recently argued, against a prevailing orthodoxy, that standards of knowledge partly depend on a subject's interests; the more is at stake for the subject, the less she is in a position to know. This view, which is dubbed "Pragmatic Encroachment" has historical and conceptual connections to arguments in philosophy of science against the received model of science as value free. I bring the two debates together. I argue that Pragmatic Encroachment and the model of value-laden science reinforce each other. Drawing on Douglas' argument about the indispensability of value judgments in science, and psychological evidence about people's inability to objectively reason about what they care about, I introduce a novel argument for Pragmatic Encroachment.

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“…This, in turn, can hinder the detection of biases and mistakes in earlier studies (Jukola, Forthcoming). Grcar (2013) has discussed the fact that, compared to other areas of investigation, mathematical literature has significantly lower correction rates. However, considering the previous sections, it is hard to maintain that mathematical literature has in fact lower error rates than these other areas of investigation.…”

Section: Mathematical Journalsmentioning

confidence: 99%

Revisiting the reliability of published mathematical proofs: where do we go next?

Frans

Kosolosky

2014

THEORIA

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Mathematics seems to have a special status when compared to other areas of human knowledge. This special status is linked with the role of proof. Mathematicians often believe that this type of argumentation leaves no room for errors and unclarity. Philosophers of mathematics have differentiated between absolutist and fallibilist views on mathematical knowledge, and argued that these views are related to whether one looks at mathematics-in-the-making or finished mathematics. In this paper we take a closer look at mathematical practice, more precisely at the publication process in mathematics. We argue that the apparent view that mathematical literature, given the special status of mathematics, is highly reliable is too naive. We will discuss several problems in the publication process that threaten this view, and give several suggestions on how this could be countered.Keywords: mathematical proof; reliability; publication process; absolutism; fallibilism.RESUMEN: Las matemáticas parecen tener un estatuto especial cuando se las compara con otras áreas del conocimiento humano. Este estatuto especial está conectado con el papel de la demostración. Los matemáticos creen con frecuencia que este tipo de argumentos no deja margen para el error o la falta de claridad. Los filósofos de la matemática han distinguido entre una concepción absolutista y una falibilista del conocimiento matemático, argumentando que estas concepciones están relacionadas con una consideración de las matemáticas-en-proceso o en tanto que matemáticas ya hechas. En este artículo examinamos más de cerca la práctica matemática, más en concreto el proceso de publicación en matemáticas. Argumentaremos que la idea preconcebida de que la literatura matemática, dado el estatuto especial de las matemáticas, es altamente fiable, es demasiado ingenua. Discutiremos algunos problemas del proceso de edición que amenazan esta visión y haremos algunas sugerencias sobre cómo enfrentarlos.Palabras clave: demostración matemática; fiabilidad; proceso de publicación; absolutismo; falibilismo.

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Errors and Corrections in Mathematics Literature

Cited by 22 publications

References 26 publications

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition

Science, values, and pragmatic encroachment on knowledge

Revisiting the reliability of published mathematical proofs: where do we go next?

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