- Vander Hoecke uses the + and - signs.
- Tunstall publishes De arte supputandi libri quattuor (On the Art of Computation), an arithmetic book based on Pacioli's Summa.
- Rudolff introduces a symbol resembling √ for square roots in his Die Coss the first German algebra book. He understands that .
- Dürer publishes Unterweisung der Messung mit dem Zirkel und Richtscheit, the first mathematics book published in German. It is a work on geometric constructions.
- Frisius publishes a method for accurate surveying using trigonometry. He is the first to propose the triangulation method.
- Hudalrichus Regius finds the fifth perfect number. The number 212 (213 - 1) = 33550336 is the first perfect number to be discovered since ancient times. (See this History Topic.)
- Rheticus publishes his trigonometric tables and the trigonometrical parts of Copernicus's work.
- Copernicus publishes De revolutionibus orbium coelestium (On the revolutions of the heavenly spheres). It gives a full account of the Copernican theory, namely that the Sun (not the Earth) is at rest in the centre of the Universe.
- Ries publishes his famous arithmetic book Rechenung nach der lenge, auff den Linihen vnd Feder. It taught arithmetic both by the old abacus method and the new Indian method.
- Recorde translates and abridges the ancient Greek mathematician Euclid's Elements as The Pathewaie to Knowledge.
- Recorde publishes The Whetstone of Witte which introduces = (the equals sign) into mathematics. He uses the symbol "bicause noe 2 thynges can be moare equalle".
- Cardan writes his book Liber de Ludo Aleae on games of chance but it would not be published until 1663.
- Viète begins publishing the Canon Mathematicus which he intends as a mathematical introduction to his astronomy treatise. It covers trigonometry, containing trigonometric tables and the theory behind their construction.
- Bombelli publishes the first three parts of his Algebra. He is the first to gives the rules for calculating with complex numbers.
- Maurolico publishes Arithmeticorum libri duo which contains examples of inductive proofs.
- Stevin publishes De Thiende in which he presents an elementary and thorough account of decimal fractions.
- Stevin publishes De Beghinselen der Weeghconst containing the theorem of the triangle of forces.
- Viète writes In artem analyticam isagoge (Introduction to the analytical art), using letters as symbols for quantities, both known and unknown. He uses vowels for the unknowns and consonants for known quantities. Descartes, later, introduces the use of letters at the end of the alphabet for unknowns.
- Pitiscus becomes the first to employ the term trigonometry in a printed publication.
- Clavius writes Novi calendarii romani apologia justifying calendar reforms.