1734 in science
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- George Berkeley publishes The Analyst, an empiricist critique of the foundations of infinitesimal calculus, influential in the development of mathematics.
- Leonhard Euler introduces the integrating factor technique for solving first-order ordinary differential equations.
- René Antoine Ferchault de Réaumur begins publication of Mémoires pour servir à l'histoire des insectes in Amsterdam.
- January 23 – Wolfgang von Kempelen, Hungarian inventor (died 1804)
- April 18 – Elsa Beata Bunge, Swedish botanist (died 1819)
- May 23 – Franz Mesmer, German physician (died 1815)
- September 3 – Joseph Wright, English painter of scientific subjects (died 1797)
- February 1 – John Floyer, English physician (born 1649)
- April 25 – Johann Conrad Dippel, German theologian, alchemist and physician (born 1673)