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Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics

Dordrecht, Netherland: Springer (2013)

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  1. The future won’t be pretty: The nature and value of ugly, AI-designed experiments.Michael T. Stuart - 2023 - In Milena Ivanova & Alice Murphy (eds.), The Aesthetics of Scientific Experiments. New York, NY: Routledge.
    Can an ugly experiment be a good experiment? Philosophers have identified many beautiful experiments and explored ways in which their beauty might be connected to their epistemic value. In contrast, the present chapter seeks out (and celebrates) ugly experiments. Among the ugliest are those being designed by AI algorithms. Interestingly, in the contexts where such experiments tend to be deployed, low aesthetic value correlates with high epistemic value. In other words, ugly experiments can be good. Given this, we should conclude (...)
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  • What is a Beautiful Experiment?Milena Ivanova - 2022 - Erkenntnis 88 (8):3419-3437.
    This article starts an engagement on the aesthetics of experiments and offers an account for analysing how aesthetics features in the design, evaluation and reception of experiments. I identify two dimensions of aesthetic evaluation of experiments: design and significance. When it comes to design, a number of qualities, such as simplicity, economy and aptness, are analysed and illustrated with the famous Meselson-Stahl experiment. Beautiful experiments are also regarded to make significant discoveries, but I argue against a narrow construal of experimental (...)
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  • Diversity in proof appraisal.Matthew Inglis & Andrew Aberdein - 2016 - In Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 2012-2014. Springer International Publishing. pp. 163-179.
    We investigated whether mathematicians typically agree about the qualities of mathematical proofs. Between-mathematician consensus in proof appraisals is an implicit assumption of many arguments made by philosophers of mathematics, but to our knowledge the issue has not previously been empirically investigated. We asked a group of mathematicians to assess a specific proof on four dimensions, using the framework identified by Inglis and Aberdein (2015). We found widespread disagreement between our participants about the aesthetics, intricacy, precision and utility of the proof, (...)
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  • Introduction to Special Issue: Aesthetics in Mathematics†.Angela Breitenbach & Davide Rizza - 2018 - Philosophia Mathematica 26 (2):153-160.
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  • Aesthetic values in science.Milena Ivanova - 2017 - Philosophy Compass 12 (10):e12433.
    Scientists often use aesthetic values in the evaluation and choice of theories. Aesthetic values are not only regarded as leading to practically more useful theories but are often taken to stand in a special epistemic relation to the truth of a theory such that the aesthetic merit of a theory is evidence of its truth. This paper explores what aesthetic considerations influence scientists' reasoning, how such aesthetic values relate to the utility of a scientific theory, and how one can justify (...)
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  • Beauty Is Not Simplicity: An Analysis of Mathematicians' Proof Appraisals.Matthew Inglis & Andrew Aberdein - 2015 - Philosophia Mathematica 23 (1):87-109.
    What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, and ‘beautiful’? By applying empirical methods developed by social psychologists, we demonstrate that mathematicians' appraisals of proofs vary on four dimensions: aesthetics, intricacy, utility, and precision. We pay particular attention to mathematical beauty and show that, contrary to the classical view, beauty and simplicity are almost entirely unrelated in mathematics.
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  • Aesthetic Virtues and Theory Acceptance.Milena Ivanova - 2024 - In Claus Beisbart & Michael Frauchiger (eds.), Scientific Theories and Philosophical Stances: Themes from van Fraassen. De Gruyter. pp. 147-164.
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  • Scientific Theories and Philosophical Stances: Themes from van Fraassen.Claus Beisbart & Michael Frauchiger (eds.) - 2024 - De Gruyter.
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  • The aesthetics of scientific experiments.Milena Ivanova - 2021 - Philosophy Compass 16 (3):e12730.
    This article explores the aesthetic dimensions of scientific experimentation, addressing specifically how aesthetic features enter the construction, evaluation and reception of an experiment. I highlight the relationship between experiments and artistic acts in the early years of the Royal Society where experiments do not serve only epistemic aims but also aim to generate feelings of awe and pleasure. I turn to analysing which aspects of experiments are appreciated aesthetically, identifying several contenders, from the ability of an experiment to uncover nature’s (...)
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