Do Mathematicians Agree about Mathematical Beauty?

Sa, Rentuya; Alcock, Lara; Inglis, Matthew; Tanswell, Fenner Stanley

doi:10.1007/s13164-022-00669-3

Cited by 3 publications

(2 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, what about people 4038 who are highly sensitive to non-artistic beauty (ie, natural beauty or, for example, mathematical beauty)? 51,52 At this stage of research, we are not able to answer this question.…”

Section: Discussionmentioning

confidence: 94%

Aesthetic Experience and the Ability to Integrate Beauty: The Mediating Effect of Spirituality

Świątek,

Szcześniak,

Borkowska

et al. 2023

PRBM

View full text Add to dashboard Cite

Background:The ability to integrate beauty (AIB) is the ability to inner transformation including thinking about oneself, perceived phenomena, or the world through exposure to an aesthetic object (or phenomenon). Previous research indicates that the AIB is positively related to aesthetic experience. Still, it is unclear whether spirituality can mediate the relationship between the two variables. Spirituality is understood as an experience of transcendence that relates to the unseen and is "larger than human". The aim of the study was to analyze the relationship between emotional and cognitive experiences related to the reception of art (as the most representative form of beauty) and the ability to connect with spirituality and aesthetic experiences. Methods: The online survey included a sample of N = 195 adults (74% female) between the ages of 18 and 54. The Spirituality Scale (SD-36), the Aesthetic Experience Questionnaire (AEQ) and the Ability to Integrate Beauty Scale (AIBS) were used to test hypotheses. Results: The analysis revealed a statistically significant, moderate relationship between the ability to integrate beauty and both the total aesthetic experience score and the spirituality scale score. The results support the hypothesis that there is a relationship between aesthetic experience in art and spirituality. The study also confirmed the mediating effect of spirituality on the relationship between aesthetic experience and aesthetic intelligence. Conclusion: Individuals with a higher level of spiritual development tend to have a greater ability to integrate beauty and have more intense aesthetic experiences, which in turn may increase their aesthetic intelligence. The results suggest that a deepened spirituality contributes to a greater ability to integrate beauty.

show abstract

Section: Discussionmentioning

confidence: 94%

Aesthetic Experience and the Ability to Integrate Beauty: The Mediating Effect of Spirituality

Świątek,

Szcześniak,

Borkowska

et al. 2023

PRBM

View full text Add to dashboard Cite

show abstract

“…References to Hardy’s thoughts presented in his essay readily appear in the works of philosophers and researchers in mathematics education when investigating, for instance, mathematical problem choice (Ashton 2018 ), whether mathematics can be treated as an art (Tymoczko 1993 ), values in mathematics ((Ernest 1998 ), (Weisgerber 2023 )) and aesthetic considerations in mathematical inquiry more generally (Sinclair 2004 , 2006 , 2011 ) or mathematical beauty ((Dutilh Novaes 2019 ), (Sa et al. 2023 )) and depth (Urquhart 2015 ) in particular.…”

Section: Introductionmentioning

confidence: 99%

Value Judgments in Mathematics: G. H. Hardy and the (Non-)seriousness of Mathematical Theorems

Weisgerber

2024

glob. Philosophy

View full text Add to dashboard Cite

One of the general criteria G. H. Hardy identifies and discusses in his famous essay A Mathematician’s Apology, Cambridge University Press, Cambridge, 1940) by which a mathematician’s patterns must be judged is seriousness. This article focuses on one of Hardy’s examples of a non-serious theorem, namely that 8712 and 9801 are the only numbers below 10000 which are integral multiples of their reversals, in the sense that $$8712=4\cdot 2178$$ 8712 = 4 · 2178 , and $$9801=9\cdot 1089$$ 9801 = 9 · 1089 . In the context of a discussion of generality, which he considers an essential quality of seriousness, he explains that there is nothing in this example which “appeals much to a mathematician” and that it is “not capable of any significant generalization.” Interestingly, since the publication of the Apology, more than a dozen papers—including one by the renowned mathematician Neil Sloane—have been published that discuss generalizations of Hardy’s example. By identifying the most important aspect of Hardy’s notion of generality, it is argued that, contrary to the views of several researchers, Hardy’s claim regarding the non-capability of any significant generalization is still tenable. Furthermore, this case study is presented and discussed as an example of the multifaceted nature of mathematical interest.

show abstract

Comparative judgement for experimental philosophy: A method for assessing ordinary meaning in vehicles in the park cases

Tanswell,

Davies,

Jones

et al. 2023

Philosophical Psychology

View full text Add to dashboard Cite

This paper demonstrates the value to experimental philosophy of an empirical method from the social sciencesthat of comparative judgement. Comparative judgement is a method of assigning scores to (perceptions of) objects using paired comparisons. We use this method to explore the "ordinary meaning" of words, and the classic case of vehicles in the park in particular. We present an empirical study comprising three conditions. Given a pair of potential vehicles, participants were asked to judge either 1) the better example of a vehicle, 2) the worse violation of a sign that reads 'no vehicles in the park', or 3) the bigger nuisance in a park. We find that both the meaning of the wording of the rule and the intention behind it influence participants judgements of ruleviolations, consistent with previous studies. More importantly, comparative judgement provides more fine-grained information about agreement and the weighted rankings of the potential vehicles than other methods, with widespread potential applications in experimental philosophy.

show abstract

Do Mathematicians Agree about Mathematical Beauty?

Cited by 3 publications

References 57 publications

Aesthetic Experience and the Ability to Integrate Beauty: The Mediating Effect of Spirituality

Aesthetic Experience and the Ability to Integrate Beauty: The Mediating Effect of Spirituality

Value Judgments in Mathematics: G. H. Hardy and the (Non-)seriousness of Mathematical Theorems

Comparative judgement for experimental philosophy: A method for assessing ordinary meaning in vehicles in the park cases

Contact Info

Product

Resources

About