Calculus' Origins Redefined by Counterexamples
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prominent French mathematicianWired
•Science
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In 1872, Karl Weierstrass published a function that threatened everything mathematicians thought they knew about calculus
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Karl Weierstrass discovered a function that threatened everything mathematicians thought they thought they understood about calculus.
He was met with indifference, anger, and fear, particularly from the mathematical giants of the French school of thought.
The function's derivative does not exist at every point, even though it’s well defined everywhere else.
A function can only zig and zagration: In 1806 , a French mathematician claimed that he’d proved this.
Karl Weierstrass proved beyond doubt that, though his function had no discontinuities, it was never differentiable.
He rewrote the definitions of “continuity” and “differentiability” that had been formulated decades earlier .
The proof demonstrated that calculus could no longer rely on geometric intuition, as its inventors had done.
The work to standardize calculus has since grown into the field known as analysis.
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