• June 8 –
Leonhard Euler writes to
James Stirling describing the
Euler–Maclaurin formula, providing a connection between
integrals and
calculus. •
Euler produces the first
published proof of
Fermat's "little theorem". • Sir
Isaac Newton's
Method of Fluxions (1671), describing his method of
differential calculus, is first published (posthumously) and
Thomas Bayes publishes a defense of its logical foundations against the criticism of
George Berkeley (anonymously). ==Medicine==