1736 in science
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- Charles Marie de La Condamine, with François Fresneau Gataudière, makes the first scientific observations of rubber, in Ecuador.
- June 19 – French Academy of Sciences expedition led by Pierre Louis Maupertuis, with Anders Celsius, begins work on measuring a meridian arc in the Torne Valley of Finland.
- June 8 – Leonhard Euler writes to James Stirling describing the Euler–Maclaurin formula, providing a connection between integrals and calculus.
- Euler produces the first published proof of Fermat's "little theorem".
- Sir Isaac Newton's Method of Fluxions (1671), describing his method of differential calculus, is first published (posthumously) and Thomas Bayes publishes a defense of its logical foundations against the criticism of George Berkeley (anonymously).
- c. October – Winchester County Hospital, established by Prebendary Alured Clarke, the first voluntary general hospital in the English provinces, begins to function.
- January 19 – James Watt, Scottish mechanical engineer (died 1819)
- January 25 – Joseph Louis Lagrange, Piedmont-born mathematician (died 1813)
- June 14 – Charles-Augustin de Coulomb, French physicist (died 1806)
- August 19 – Erland Samuel Bring, Swedish mathematician (died 1798)
- November 3 – Christiaan Brunings, Dutch hydraulic engineer (died 1805),n, j
- John Arnold, Cornish-born watchmaker (died 1799)
- Journal du voyage fait par ordre du roi à l'équateur. Paris. 1751.
- Piippola, Takalo. "Maupertuis'n astemittaus Tornionlaaksossa 1736-1737" (in Finnish). Archived from the original on 11 December 2007. Retrieved 2008-03-23.
- Theorematum Quorundam ad Numeros Primos Spectantium Demonstratio.
- An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of the Analyst.