Calculus, created in the 17th century, was initially based on informal reasoning, but faced challenges that led to a rigorous revitalization. French mathematicians embraced its practical applications, while German scholars like Karl Weierstrass critiqued these foundations, revealing inconsistencies through counterexamples. Weierstrass published a groundbreaking function in 1872 that shook the very principles of calculus, stirring controversy among established mathematicians who viewed it as a threat to intuitive understanding. This tension ultimately paved the way for a stricter formalization of calculus, enhancing its credibility as a mathematical discipline.
Weierstrass introduced a monstrous function that challenged traditional understandings of calculus, leading to a re-examination of its foundational principles, which were grounded in intuition.
German mathematicians, unlike their French counterparts, focused on undermining assumptions, using counterexamples to shift calculus from intuition toward precise definitions and robustness.
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