Two Perspectives on Proof I: The Baroque Perspective We also prepare the way for continued philosophical discussion in our final section on multicolor, interactive, and animated PWWs 2.0. By the end of the next section, we will conclude that visual proofs often fail to constitute proofs from the Baroque perspective, but that nonetheless, visual proofs are capable of serving many of the same mathematical aims as traditional proof writing-aims that exceed mere pedagogical value. We couch our discussion in this conservative framework because ultimately any defense of the mathematical value of visual proofs will be more persuasive if it is grounded in or at least compatible with a relatively conservative conception of proof in mathematics. We spend much of the rest of this section exploring the doubts raised about the status of visual proofs from the Baroque perspective. Our goal is to encourage readers to take a fresh look at visual proof and the activity of proof writing in mathematics, and this goal will not be served as effectively if we try to situate our discussion in the range of ongoing discussions in the philosophy of mathematics. These terms evoke the notion of a stance, a response pattern, or an approach rather than a specific and developed school of thought. We have chosen to use the terms Baroque and Romantic to characterize these positions partly to avoid any specific allusions to schools of thought in the philosophy of mathematics. We begin in this section by characterizing two somewhat extreme reactions to visual proofs, which we term the Baroque and Romantic reactions to visual proof. Over the next two sections we construct and apply a framework for appraising the mathematical value of visual proofs. Two Perspectives on PWWs as Mathematical Proofs
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