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  1. Mathematics and Experience.Carlo Cellucci - forthcoming - Foundations of Science:1-15.
    The question of whether mathematics depends on experience, including experience of the external world, is problematic because, while it is clear that natural sciences depend on experience, it is not clear that mathematics depends on experience. Indeed, several mathematicians and philosophers think that mathematics does not depend on experience, and this is also the view of mainstream philosophy of mathematics. However, this view has had a deleterious effect on the philosophy of mathematics. This article argues that, in fact, the view (...)
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  • Mathematical Beauty, Understanding, and Discovery.Carlo Cellucci - 2015 - Foundations of Science 20 (4):339-355.
    In a very influential paper Rota stresses the relevance of mathematical beauty to mathematical research, and claims that a piece of mathematics is beautiful when it is enlightening. He stops short, however, of explaining what he means by ‘enlightening’. This paper proposes an alternative approach, according to which a mathematical demonstration or theorem is beautiful when it provides understanding. Mathematical beauty thus considered can have a role in mathematical discovery because it can guide the mathematician in selecting which hypothesis to (...)
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