The year 1545 in science and technology involved some significant events.

• Orto botanico di Padova and di Firenze botanical gardens established.

• Gerolamo Cardano publishes his algebra text Ars Magna, including the first published solutions to cubic and quartic equations.

• Pedro de Medina's Arte de navegar is published in Valladolid, the first treatise on the art of navigation to be published in Europe.

• Charles Estienne publishes De dissectione partium corporis humani, libri tres, including a description of the venous valves of the liver.
• Ambroise Paré publishes his first book, a treatise on battlefield medicine, La méthode de traicter les playes faictes par hacquebutes et aultres bastons à feu et de celles qui sont faictes par flèches, dardz et semblables, in Paris.
• Thomas Phaer publishes The Boke of Chyldren, the first book on paediatrics written in English.

• The giant squid (Architeuthis) is first seen.

• January 11 – Guidobaldo del Monte, Italian mathematician (died 1607)^[1]
• March – Gaspare Tagliacozzi, Italian anatomist (died 1599)
• John Gerard, English botanist (died 1612)^[2]

• Christoph Rudolff, Silesian mathematician (born 1499)