2
$\begingroup$

How was the Fundamental Theorem of Calculus discovered?

The FTC is at once simple enough that Math.SE is full of questions asking "why is it such a big deal" and yet avoided discovery for perhaps centuries. While rigorous proofs took time, simple arguments from velocity and distance are easy.

How was it discovered? What were the obstacles that needed to be solved? Was it done using the simple arguments from velocity that I linked, from geometry, or from some other method?

Or, to put it differently:

What aspects of the FTC are non-obvious such that they eluded discovery for so long? And how were these obstacles to discovery eventually overcome?

One potential source for this: If anyone has access to the original writings introducing the FTC to the world (e.g. by Newton or Leibniz), these might explain the breakthrough.

Note: History of the Fundamental Theorem of Calculus asks what was done before the FTC. I'm asking specifically how the FTC was discovered.

Improve this question
$\endgroup$
3
  • $\begingroup$ It avoided discovery for centuries because in those centuries there was nothing to discover. One had to develop working general conceptions of area and tangency for even geometric formulation of it to make sense. That was done only in the first half of 17th century, and Newton's teacher Barrow discovered it soon after. It appeared in his Lectiones Geometricae X (1666), see Nauenberg for a modern retelling. Once fluxions and infinitesimals were worked out, Newton and Leibniz translated it into them. $\endgroup$
    – Conifold
    Commented Jun 11, 2023 at 23:18
  • $\begingroup$ English translation of Barrow's lectures is available. $\endgroup$
    – Conifold
    Commented Jun 11, 2023 at 23:21
  • $\begingroup$ My first thought when reading your question was that tangent and area problems look nothing alike (when you don’t know calculus), so a big conceptual barrier to discovering FTC is realizing that the two types of problems are even related to each other at all (as a general phenomenon). Before calculus, tangent and area/volume problems were being solved in somewhat individual cases. $\endgroup$
    – KCd
    Commented Jun 14, 2023 at 9:42

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.