The Birth of Calculus: Towards a More Leibnizian View

TL;DR

This paper re-examines the historical debate over the independent invention of calculus by Leibniz and Newton, arguing for a nuanced understanding of their contributions and the concept of invention in mathematics.

Contribution

It offers a re-evaluation of the Leibniz-Newton calculus debate, supporting the view that their discoveries were more interconnected than traditionally thought.

Findings

Leibniz and Newton's calculus developments were more intertwined than previously believed.

Historical perspectives on calculus invention are reassessed, aligning with modern historians.

The debate over independent invention is nuanced, emphasizing collaborative and incremental contributions.

Abstract

We re-evaluate the great Leibniz-Newton calculus debate, exactly three hundred years after it culminated, in 1712. We reflect upon the concept of invention, and to what extent there were indeed two independent inventors of this new mathematical method. We are to a considerable extent agreeing with the mathematics historians Tom Whiteside in the 20th century and Augustus de Morgan in the 19th. By way of introduction we recall two apposite quotations: "After two and a half centuries the Newton-Leibniz disputes continue to inflame the passions. Only the very learned (or the very foolish) dare to enter this great killing ground of the history of ideas" from Stephen Shapin and "When de l'Hopital, in 1696, published at Paris a treatise so systematic, and so much resembling one of modern times, that it might be used even now, he could find nothing English to quote, except a slight treatise of Craig on quadratures, published in 1693" from Augustus de Morgan.