This book offers a history of beauty in mathematics and of the study of beauty in mathematics. Its intention is to examine the historical development of the experience of beauty in mathematics, of the influence of such experience both inside and outside mathematics, and of the scrutiny to which this experience has been subjected by mathematicians and philosophers.

In this article I demonstrate how Hannah Arendt both appropriates and transforms Aristotle’s view of political friendship. I argue that the brief discussion of Aristotelian political friendship in The Human Condition relies on an earlier de-materialization of Aristotle’s work on friendship. This de-materialization of Aristotle’s view of friendship allows Arendt to discuss Aristotelian friendship as a kind of ‘respect’, where ‘respect’ is a philosophical notion unavailable to Aristotle. Ultimately, for Arendt, the experience of friendship opens up a space for human (...) beings to begin to practice a distinct way of seeing one another – a ‘respect’ – that can in turn be practiced in public, making the experience of friendship an important precursor to action. (shrink)

In this article we argue that Simone Weil offers an account of human freedom that—if and when it emerges—emerges from the human being’s recognition of, and appropriate response to, the impossibility of eliminating “force.” While other commentators have noted that for Weil, our freedom derives from consenting spontaneously to that which necessity obligates, we go further by showing the ways in which our responses to force are historically inscribed by the trauma of previous responses, and the ways this impedes our (...) ability to come to terms with (or in Weil’s language, “consent” to) force. We maintain that, despite the ineliminability of force and the trauma and repetition of response it tends to incite, human freedom is still possible under Weil’s account, so long as we also recognize our obligation to one another as human beings. (shrink)

In the Nicomachean ethics, Aristotle sets down a scattered and fractional account of the development of moral virtue within young people. Philosopher Martha Nussbaum defends Aristotle's neglect of a systematic account of moral development and argues that more complex expressions of character‐building, such as learning to expose oneself to proper desires, feelings, pleasures and pains, are better illustrated through drama or literature than through philosophy. In this vein, the author draws upon literary thinkers J.B. Kerfoot, Sven Birkerts and Wayne C. (...) Booth, as well as the imaginative Harry Potter series by J. K. Rowling, to illustrate more concretely Aristotle's process of moral development. The author concludes with a proviso about the vulnerability of the connected process of reading and moral development in the current consumer culture. (shrink)

Unexpectedness and inevitability, two of the aesthetic qualities G.H. Hardy identified as being properties of beautiful proofs, together seem paradoxical: how can something be seen as both unexpected and inevitable? In this essay, I argue that the literary concept of ‘deus ex machina’ can be used to clarify the notion of inevitability in proof and reconcile it with unexpectedness.

In “Action and the ‘Pursuit of Happiness,’” Hannah Arendt tells the story of “an inveterate gambler” who arrives late in a town and goes straight to the gambling place, where he discovers that the wheel he wishes to gamble on is crooked. He gambles anyway, because there is no other wheel in town. The story, she suggests, “tells us that there exists such intense happiness in acting that the actor, like the gambler, will accept that all the odds are stacked (...) against him.” In this article I use this story as a motif to investigate references to success in Arendt’s work. I argue that Arendt sought to preclude action and happiness from utilitarian notions of success, and that she ultimately presents the human impulse toward action as tragic. I also discuss the role of the historian or poet in this tragedy, concluding that what remains unclear in Arendt’s work is how the public happiness of the actor and the pleasure of the historian and poet are related. (shrink)

While Hannah Arendt discusses the notion of “conscience” in many of her works, it has received little attention in the literature. To contribute to the development of the understanding of this notion in her work, I investigate the difference between Martin Heidegger’s view that conscience is silent, and Arendt’s view that it is not. In Being and Time Heidegger writes that Dasein wants to have a conscience. By this he means that Dasein wants to project itself against the horizon of (...) its condition of being, which for Heidegger is Dasein’s own mortality. Heidegger claims that this call of conscience is silent. In contrast, Arendt writes in Thinking that the voice of conscience—which she says is the by-product of thinking—is not silent. By establishing that for Arendt, conscience is talkative, not silent, this paper investigates an important difference between Heidegger and Arendt. I show that while Arendt develops her own understanding of conscience out of Heidegger’s understanding of conscience, agreeing that conscience is the pre-condition of morality, Arendt transforms it from a silent call into a talkative one. I argue that this stems from Arendt’s insistence that human beings are not just conditioned by their own mortality, as is the case for Heidegger, but also by their natality. Ultimately, I demonstrate that what separates Heidegger and Arendt on conscience is their respective focus on “being-toward-death” (Heidegger) and “being-toward-natality” (Arendt). (shrink)

This paper studies how spatial thinking interacts with simplicity in [informal] proof, by analysing a set of example proofs mainly concerned with Ferrers diagrams (visual representations of partitions of integers) and comparing them to proofs that do not use spatial thinking. The analysis shows that using diagrams and spatial thinking can contribute to simplicity by (for example) avoiding technical calculations, division into cases, and induction, and creating a more surveyable and explanatory proof (both of which are connected to simplicity). In (...) response to one part of Hilbert's 24th problem, the area between two proofs is explored in one example, showing that between a proof that uses spatial reasoning and one that does not, there is a proof that is less simple yet more impure than either. This has implications for the supposed simplicity of impure proofs. This article is part of the theme issue ‘The notion of ‘simple proof’ - Hilbert's 24th problem’. (shrink)

Commentators often note that there are contradictions, or at least inconsistencies, in Arendt’s work. On the one hand, Arendt is accused of theoretical inconsistencies, insofar as she makes claims in her later work that seem incompatible with claims she made earlier. On the other hand, Arendt has been accused of contradicting herself morally, with some commentators claiming that Arendt should not have written Eichmann in Jerusalem the way she wrote it. Both views place the treatment of the 1961 Eichmann trial (...) at the center of Arendt’s thought, and cast it as representing a radical shift from Arendt’s earlier work. This article shows that both views fail to acknowledge the importance of what I call the “archetype of non-contradiction” in Arendt’s work. I argue that, viewed in perspective, her treatment of the Eichmann trial is simply another instance of Arendt attempting to follow the archetype of non-contradiction, practicing tentative and fluid thinking, and maintaining her friendship with herself. (shrink)

Through a reading of Kant’s essay, “An Old Question Raised Again: Is the Human Race Constantly Progressing?”, I argue that Kant’s political philosophy fails to adequately engage with the political event in itself, and that Kant’s so-called political writings only provide a theory of the social sphere. First, I present the Kantian political subject as an antinomy between the metaphysically grounded spectator and the physically situated actor. Second, I show that Kant tries to solve the antinomy between the actor and (...) the spectator by attributing primacy to the judgement of the spectator. Third, I show that this move fails because it removes from political judgment what ultimately defines the political, i.e. plurality, spontaneity, and action. I conclude that rather than a theory of the sphere of political life, what Kant achieves is the thinking out of a theory of society (Gesellschaft). (shrink)

During the Late Roman Empire Terence was the most revered and the most quoted classical Latin poet after Virgil. Among authors both pagan and Christian, none made as frequent or as creative literary use of his comedies as Jerome, one of the most accomplished polymaths in all of Latin antiquity. In his estimation Terence ranked, alongside Homer, Menander and Virgil, as one of the greatest of all poets. Jerome had an encyclopedic knowledge of Terence's dramatic corpus and quoted or appropriated (...) phraseology from all six of his comedies. A significant number of these reminiscences have already been identified, but others await discovery. The purpose of the present study is to make a further contribution to this particular branch of HieronymianQuellenforschungby adducing and analysing two hitherto unrecognized allusions in Jerome's correspondence to Terence'sEunuchus, apparently one of the biggest blockbusters in the history of the Roman stage. (shrink)

Jerome was very familiar with the writings of Lactantius, yet strikingly few instances of his appropriation of specifically Lactantian phraseology have been brought to light. The present study adduces three new verbal echoes in three different writings to show that Jerome’s literary imitation of the North African Father was slightly more extensive than has hitherto been thought.

This ebook is an annotated edition of G. H. Hardy’s _A Mathematician’s Apology_. It aims to supply sources for all quotations and to clarify allusions to works, people, or events, as well as to give background information. Hardy made a number of minor misquotations, suggesting that he quoted from memory or used paraphrased notes of his own; the annotations point these out. This edition also includes an annotated version of Hardy’s essay ‘Mathematics in war-time’, which formed the kernel around which (...) he shaped the _Apology_. The annotations point out how parts of this essay were incorporated into the _Apology_. -/- Also included is a list of editions, reprintings, and excerpts of the _Apology_ and ‘Mathematics in war-time’, and three essays by the annotator: the first sets the _Apology_ in context in the debate about the justification for mathematics, particularly as an aesthetic pursuit; the second attempts to survey comprehensively contemporary reviews of the _Apology_; the third examines the legacy and ongoing influence of the _Apology_. (shrink)