Mathematicians often conduct aesthetic judgements to evaluate mathematical objects such as equations or proofs. But is there a consensus about which mathematical objects are beautiful? We used a comparative judgement technique to measure aesthetic intuitions among British mathematicians, Chinese mathematicians, and British mathematics undergraduates, with the aim of assessing whether judgements of mathematical beauty are influenced by cultural differences or levels of expertise. We found aesthetic agreement both within and across these demographic groups. We conclude that judgements of mathematical beauty (...) are not strongly influenced by cultural difference, levels of expertise, and types of mathematical objects. Our findings contrast with recent studies that found mathematicians often disagree with each other about mathematical beauty. (shrink)

Conviction Narrative Theory (CNT) is a theory of choice underradical uncertainty– situations where outcomes cannot be enumerated and probabilities cannot be assigned. Whereas most theories of choice assume that people rely on (potentially biased) probabilistic judgments, such theories cannot account for adaptive decision-making when probabilities cannot be assigned. CNT proposes that people usenarratives– structured representations of causal, temporal, analogical, and valence relationships – rather than probabilities, as the currency of thought that unifies our sense-making and decision-making faculties. According to CNT, (...) narratives arise from the interplay between individual cognition and the social environment, with reasoners adopting a narrative that feels “right” to explain the available data; using that narrative to imagine plausible futures; and affectively evaluating those imagined futures to make a choice. Evidence from many areas of the cognitive, behavioral, and social sciences supports this basic model, including lab experiments, interview studies, and econometric analyses. We identify 12 propositions to explain how the mental representations (narratives) interact with four inter-related processes (explanation, simulation, affective evaluation, and communication), examining the theoretical and empirical basis for each. We conclude by discussing how CNT can provide a common vocabulary for researchers studying everyday choices across areas of the decision sciences. (shrink)

Many of the methods commonly used to research mathematical practice, such as analyses of historical episodes or individual cases, are particularly well-suited to generating causal hypotheses, but less well-suited to testing causal hypotheses. In this paper we reflect on the contribution that the so-called hypothetico-deductive method, with a particular focus on experimental studies, can make to our understanding of mathematical practice. By way of illustration, we report an experiment that investigated how mathematicians attribute aesthetic properties to mathematical proofs. We demonstrate (...) that perceptions of the aesthetic properties of mathematical proofs are, in some cases at least, subject to social influence. Specifically, we show that mathematicians’ aesthetic judgements tend to conform to the judgements made by others. Pedagogical implications are discussed. (shrink)