Who was the first to prove the fundamental theorem?

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Discussion Overview

The discussion revolves around the historical attribution of the first proof of the fundamental theorem of calculus, exploring contributions from various mathematicians and the nature of their proofs. It touches on the historical development of calculus, including the roles of Newton, Leibniz, Cauchy, Gregory, and Barrow.

Discussion Character

  • Historical
  • Debate/contested

Main Points Raised

  • One participant inquires about who first proved the fundamental theorem of calculus.
  • Another participant asserts that Cauchy was the first to provide a rigorous proof of the theorem.
  • It is noted that many mathematicians explored concepts related to derivatives and areas before Newton and Leibniz, with Archimedes mentioned as an early contributor.
  • A participant argues that while Cauchy may have proven the theorem rigorously, the theorem itself was "discovered" by Newton and Leibniz, who approached calculus using infinitesimals.
  • Another participant references Wikipedia, claiming that the theorem was known prior to Newton and Leibniz and was first proved by James Gregory and Isaac Barrow.

Areas of Agreement / Disagreement

Participants express differing views on who should be credited with the first proof of the fundamental theorem of calculus, with no consensus reached on the matter. Various historical figures are mentioned, indicating multiple competing perspectives.

Contextual Notes

There are unresolved aspects regarding the definitions of "proof" and "discovery," as well as the historical context of calculus development. The discussion highlights the complexity of attributing mathematical discoveries to specific individuals.

armolinasf
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Just curious who wrote the first proof of the fundamental theorem of calculus. Thanks.
 
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Try google. The theorem was first proven rigorously by Cauchy.
 
There were many people who found different ways of finding tangent lines, and, in particular, the slope of the tangent line (i.e. derivative) before Newton or Leibniz. And finding areas by dividing into smaller and smaller sections goes back to Archimedes. It is the discovery of the "fundamental theorem", that states that these two problems are, in an important sense, "inverse" that make Newton and Leibniz the "creators" of the Calculus. Cauchy may well have been the one to prove the theorem rigorously, using limits (Newton and Leibniz used nebulous appeals to "infinitesmals" rather than limits), but the theorem was "discovered" by Newton and Leibniz.
 

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