1513 in science

Exploration and cartography

• March 27 – Juan Ponce de León becomes the first European definitely known to sight the modern-day territory of the United States, specifically Florida, mistaking it for another island. His expedition lands on April 2.
• May – Portuguese explorer Jorge Álvares lands on Lintin Island in the Pearl River estuary.
• September 26 – Vasco Núñez de Balboa, "silent upon a peak in Darién", first sees what will become known as the Pacific Ocean.
• Portuguese land on Ambon Island.
• Piri Reis map compiled.
• Publication in Oppenheim of Johannes Stöffler's treatise on the construction and use of astrolabes, Elucidatio fabricae ususque astrolabii.

  Physiology and medicine

• Eucharius Rösslin publishes Der Rosengarten, an obstetrics manual primarily for midwives written in German which will be widely translated and circulated in Europe.

  Births

• Jacques Daléchamps, French physician and botanist

  Deaths

• Ibn Ghazi al-Miknasi, Moroccan scholar and mathematician
• Hua Sui, Chinese pioneer of metal movable type printing