Who was the first to prove the fundamental theorem?

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SUMMARY

The fundamental theorem of calculus was first rigorously proven by Augustin-Louis Cauchy, who utilized limits in his proof. Prior to Cauchy, figures such as Isaac Newton and Gottfried Wilhelm Leibniz are credited with the discovery of the theorem, which establishes the relationship between differentiation and integration. Historical contributions to the concepts of tangents and areas can be traced back to Archimedes, while earlier proofs were attributed to James Gregory and Isaac Barrow. The theorem's significance lies in its demonstration that differentiation and integration are inverse processes.

PREREQUISITES
  • Understanding of calculus concepts, specifically differentiation and integration.
  • Familiarity with the historical context of calculus development.
  • Knowledge of limits as a foundational concept in calculus.
  • Awareness of key mathematicians such as Cauchy, Newton, Leibniz, Gregory, and Barrow.
NEXT STEPS
  • Research the historical contributions of Isaac Newton and Gottfried Wilhelm Leibniz to calculus.
  • Study Augustin-Louis Cauchy's proof of the fundamental theorem of calculus.
  • Explore the concept of limits in calculus and their role in rigorous proofs.
  • Investigate the works of James Gregory and Isaac Barrow regarding early calculus concepts.
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Mathematicians, educators, students of calculus, and anyone interested in the historical development of mathematical theories.

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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