Towards a Philosophy of Real Mathematics

Corfield, David

doi:10.1017/cbo9780511487576

Cited by 109 publications

(52 citation statements)

References 173 publications

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“…Sometimes new methods are introduced in the course of a proof; for example, Gauss's sixth proof of the law of quadratic reciprocity introduced the method of Gauss sums, which paves the way to higher-order generalizations; and the Dedekind-Weber proof of the Riemann-Roch theorem was ground-breaking in its introduction of algebraic methods to the study of function spaces (cf. the discussion in Corfield 2003). Sometimes, in contrast, old results are reproved in order to illustrate the benefits of methods that have been introduced in the development of a more general theory.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Method and Proof

Avigad

2006

Synthese

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On a traditional view, the primary role of a mathematical proof is to warrant the truth of the resulting theorem. This view fails to explain why it is very often the case that a new proof of a theorem is deemed important. Three case studies from elementary arithmetic show, informally, that there are many criteria by which ordinary proofs are valued. I argue that at least some of these criteria depend on the methods of inference the proofs employ, and that standard models of formal deduction are not well-equipped to support such evaluations. I discuss a model of proof that is used in the automated deduction community, and show that this model does better in that respect.

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Section: Introductionmentioning

confidence: 99%

Mathematical Method and Proof

Avigad

2006

Synthese

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“…275-281). Corfield (2003) would also appear to reiterate the thoughts elaborated above when he states:…”

Section: Exposition Of Rav's Thesismentioning

confidence: 73%

Proofs as bearers of mathematical knowledge

Hanna

Barbeau

2008

ZDM Mathematics Education

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“…But even then, 23 See problems 18 and 19, respectively. 24 So well-known, in fact, that it has given rise to the title of a recent introduction to the philosophy of mathematics (Corfield 2003). 25 Again, this aspect is also present in Hardy's reflections; World War I is mentioned right after the above quote, in the remainder of Hardy 1940, §21 (see also Hardy 1942).…”

Section: Edmund Landau At Jerusalemmentioning

confidence: 99%

Zionist Internationalism through Number Theory: Edmund Landau at the Opening of the Hebrew University in 1925

Corry

Schappacher

2010

Sci Context

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ArgumentThis article gives the background to a public lecture delivered in Hebrew by Edmund Landau at the opening ceremony of the Hebrew University in Jerusalem in 1925. On the surface, the lecture appears to be a slightly awkward attempt by a distinguished German-Jewish mathematician to popularize a few number-theoretical tidbits. However, quite unexpectedly, what emerges here is Landau's personal blend of Zionism, German nationalism, and the proud ethos of pure, rigorous mathematics – against the backdrop of the situation of Germany after World War I. Landau's Jerusalem lecture thus shows how the Zionist cause was inextricably linked to, and determined by political agendas that were taking place in Europe at that time. The lecture stands in various historical contexts - Landau's biography, the history of Jewish scientists in the German Zionist movement, the founding of the Hebrew University in Jerusalem, and the creation of a modern Hebrew mathematical language. This article provides a broad historical introduction to the English translation, with commentary, of the original Hebrew text.

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Towards a Philosophy of Real Mathematics

Abstract: To speak informatively about bakery you have got to have put your hands in the dough.

Cited by 109 publications

References 173 publications

Mathematical Method and Proof

Mathematical Method and Proof

Proofs as bearers of mathematical knowledge

Zionist Internationalism through Number Theory: Edmund Landau at the Opening of the Hebrew University in 1925

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