| I meant "Formalization" in the larger sense of the word. The Definition/Theorem/Proof (DTP) emphasis (to the exclusion of everything else) for axiomatization in mathematics arose in the late-19th century and solidified in the 20th century. Prior to this, while mathematicians always practiced rigour, they valued insight/intuition more for understanding. An attempt was made to teach "Modern Math" in a "New Math" manner which though withdrawn, has left its detrimental mark on mathematics education to this day. See the "Reception" and "Legacy" sections at https://en.wikipedia.org/wiki/New_Math Excerpts: Physicist Richard Feynman argued, "first there must be freedom of thought; second, we do not want to teach just words; and third, subjects should not be introduced without explaining the purpose or reason, or without giving any way in which the material could be really used to discover something interesting. I don't think it is worthwhile teaching such material." In a 1971 article, mathematician René Thom rejected the New Math as "a test of memory that poisons intelligence" because of its complete neglect of intuition. Mathematician and historian of mathematics Morris Kline observed that it was "practically impossible" to learn new mathematical creations without first understanding the old ones, and that "abstraction is not the first stage, but the last stage, in a mathematical development." Mathematician and author George F. Simmons wrote in the algebra section of his textbook Precalculus Mathematics in a Nutshell (1981) that by focusing on form rather than substance, the New Math produced students who had "heard of the commutative law, but did not know the multiplication table." Mathematician Laurent Schwartz described the new reforms as "very poor" pedagogy. For him, "The goal of mathematics is not to prove rigorously things that everyone knows. Instead, the goal is to find rich results and then, in order to make sure they are true, to prove them." See also; Against mathematical proof - https://mathwithbaddrawings.com/2021/05/12/against-mathemati... Proof and Understanding in Mathematical Practice by Danielle Macbeth - https://journals.openedition.org/philosophiascientiae/712?la... |