Ways of Abstraction. Artistic Vision and the "Ideality" of Mathematics

When I run into the Needham’s question – “What was it that happened in Renaissance Europe when mathematics and science joined in a combination that was qualitatively new and destined to transform the world?” – I could not help thinking of Brunelleschi and Leonardo. The “exact fantasy” of the design for the cupola of Santa Maria del Fiore together with the grace that emanates from The Virgin and Child with Saint Anne immediately came to my mind. Is there an answer here? Cassirer’s philosophical reflection helped me focus on the issue of abstraction, whereas Hilbert’s vision of geometry helped me grasp the ideality of mathematics and art.