Britannica Sources used in this answer

Why did Isaac Newton and Gottfried Wilhelm Leibniz disagree about the invention of calculus?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

transformation of a circular region into an approximately rectangular region — analysis \
This suggests that the same constant (π) appears in the formula for the circumference, 2πr, and in the formula for the area, πr². As the number of pieces increases (from left to right), the “rectangle” converges on a πr by r rectangle with area πr²—the same area as that of the circle. This method of approximating a (complex) region by dividing it into simpler regions dates from antiquity and reappears in the calculus.

The disagreement between Isaac Newton and Gottfried Wilhelm Leibniz regarding the invention of calculus was a bitter priority dispute that arose because both men independently discovered the fundamental theorem of calculus around 1670.21

The conflict was fueled by several factors:

Publication Timing: Newton developed his method of "fluxions" in the 1660s but was notoriously slow to publish his work. Leibniz published his own independent research on differential calculus in 1684, which became the first public account of the subject.231
Methodological Differences: Newton’s approach was rooted in kinematics and geometric ratios, while Leibniz developed a more general algorithm using the symbols $d$ and $\int$ , which proved highly influential for its notation.21
Escalation: What began as minor innuendos escalated into public accusations of plagiarism from both sides. Newton, deeply sensitive to these charges, used his position as President of the Royal Society to orchestrate an "impartial" investigation that favored his own claims.3

Ultimately, the dispute caused a long-standing rift in the mathematical community, isolating British mathematics from the more rapid developments occurring on the Continent.1