Mihai Nadin> Diagrammatic thinking is more or less mathematical thinking.
Peirce made the point that all mathematical reasoning, including algebra, is diagrammatic. But diagrams can also include reasoning that most people would not call mathematics -- but Peirce's definition of diagram is broad enough to include them. Alex S> N. Bourbaki [1] I have found this nice math opinion about diagrams: "Strictly speaking, a diagram is not a mathematical object; it is just a drawing intended to make it easier to read this or that reasoning." The Bourbaki group included some brilliant mathematicians, but they were hypocrites. They used diagrams to discover new theorems, which they later formalized for publication. Their ideas inspired the New Math movement in education in the 1960s, which was a miserable failure. For the basic quotations and examples by famous mathematicians, see the first 10 slides of http://jfsowa.com/talks/ppe.pdf John
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