1671 in science

Astronomy

• Completion of Paris Observatory, the world's first such national institution.

  Mathematics

• James Gregory develops a series expansion for the inverse tangent function and discovers Taylor's theorem.
• Sawaguchi Kazuyuki publishes Kokin-Sanpo-Ki　, in which he gives the first comprehensive applied account of Chinese algebra in Japan.

  Medicine

• Publication of Les secrets de la medecine des Chinois, the first Western book on traditional Eastern medicine, in Grenoble.

  Physics

• Jacques Rohault publishes Traité de physique in Paris, disseminating Cartesian physics.

  Births

• October 1 – Guido Grandi, Italian mathematician

  Deaths

• June 25 – Giovanni Battista Riccioli, Italian astronomer