Infinitesimal calculus
Cálculo infinitesimal (diferencial e integral)
- Date
- 1665-1684 · confidence high
- Place
- Cambridge/Woolsthorpe, England, and Leipzig/Hanover, Germany
- Credited to
- Isaac Newton (fluxions, 1665–66) and Gottfried Wilhelm Leibniz (the dx, ∫ notation, published in 1684)
- People
- 👤 Gottfried Leibniz1646–1716👤 Isaac Newton1642–1727
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What it is
A general method for calculating rates of change (derivatives) and areas or accumulated sums (integrals), unified by the fundamental theorem. It is the mathematical language of modern physics and engineering.
Newton developed it first (1665–66) but did not publish it; Leibniz discovered it independently around 1675 and published in 1684. The Royal Society (with Newton as president) declared Leibniz a plagiarist in 1712; historical consensus recognises independent discovery, and Leibniz's notation prevailed.
What it led to
- Celestial mechanics and universal gravitation (the Principia, 1687)
- 18th-century mathematical physics (Euler, Bernoulli, Lagrange)
- Quantitative machine engineering, hydraulics and ballistics
- A rift between British and Continental mathematics over the priority dispute
Built on
- Symbolic algebra1591
- Analytic geometry1637
- Cavalieri's method of indivisibles
- Infinite series (Wallis, Gregory)
- Fermat's and Barrow's tangents
Made possible
- The number e and the exponential function1683
- Newton's laws of motion1687
- Wave equation1746
- Calculus of variations and Euler-Lagrange equation1755
- Euler method1768-1770
- Jurij Vega's 140-digit calculation of π1789
- Root test1821
- Mean value theorem1691-1823
- Differential equations
- Analytical mechanics
- Theory of steam engines (Carnot, 19th century)