1631 in science

Geology

• December 16 – Volcanic eruption of Mount Vesuvius for the only time this century.

  Mathematics

• William Oughtred publishes Clavis Mathematicae, introducing the multiplication sign and proportion sign.
• Some of Thomas Harriot's writings on algebra are published posthumously as Artis Analyticae Praxis.

  Technology

• Earliest known bentside spinet, made by Hieronymus de Zentis.

  Births

• Richard Lower, English physician who performed the first direct blood transfusion
• approx. date – William Ball, English astronomer

  Deaths

• October 20 – Michael Maestlin, German astronomer and mathematician
• 26 October - Catherine de Parthenay, French noblewoman and mathematician
• December 10 – Sir Hugh Myddelton, Welsh-born goldsmith and hydraulic engineer