The invention of calculus sparked a fierce rivalry between Newton and Leibniz. Both developed similar ideas independently, but their different notations and publication timelines led to a heated priority dispute that divided the mathematical community.

This controversy had lasting effects on calculus development. While continental Europe embraced Leibniz's notation, British mathematicians stuck with Newton's approach, causing a temporary rift in mathematical progress between the two regions.

Notations and Development

Fluxional and Differential Notations

• Fluxional notation developed by Newton represents rates of change using dots over variables
• Fluxional notation uses $\dot{x}$ to denote the first derivative of x with respect to time
• Higher-order derivatives expressed as $\ddot{x}$, $\dddot{x}$, and so on in fluxional notation
• Differential notation created by Leibniz utilizes dx/dt to represent the derivative of x with respect to t
• Leibniz's notation allows for easier manipulation of higher-order derivatives and partial derivatives
• Differential notation proves more versatile for complex calculations and became widely adopted

Continental vs. British Calculus Development

• Continental Europe primarily followed Leibniz's approach to calculus
• British mathematicians initially adhered to Newton's fluxional calculus
• Continental mathematicians like Bernoulli brothers and Euler advanced calculus using Leibniz's notation
• British development of calculus lagged behind continental progress due to isolation and notation differences
• Continental calculus focused on analytical methods and applications to physics
• British calculus emphasized geometric interpretations and applications to mechanics

Priority Dispute

Newton-Leibniz Controversy Origins

• Dispute arose over who first invented calculus between Isaac Newton and Gottfried Wilhelm Leibniz
• Newton developed calculus concepts in the 1660s but delayed publication
• Leibniz independently developed similar ideas in the 1670s and published first in 1684
• Controversy intensified when Leibniz's work gained popularity in continental Europe
• Accusations of plagiarism emerged from both sides, fueled by nationalist sentiments

Royal Society Investigation

• Royal Society formed a committee in 1712 to investigate the priority dispute
• Committee consisted primarily of Newton's supporters, raising questions of impartiality
• Investigated correspondence and manuscripts from both Newton and Leibniz
• Examined publication dates and development timelines of calculus concepts
• Royal Society's report, known as Commercium Epistolicum, favored Newton's claim to priority
• Report criticized Leibniz for potential plagiarism, damaging his reputation

Publication Timelines and Impact

• Leibniz's publication delay allowed Newton's supporters to question his originality
• Leibniz published his calculus work in Acta Eruditorum in 1684 and 1686
• Newton's ideas appeared in unpublished manuscripts as early as 1669
• Newton's Principia Mathematica, published in 1687, contained calculus concepts without explicit notation
• Principia established Newton's reputation but used geometric methods rather than explicit calculus notation
• Delayed publication of Newton's calculus work complicated the priority dispute resolution