- Cataldi finds the sixth and seventh perfect numbers, 216 (217 - 1) =8589869056 and 218 (219 - 1) = 137438691328.
- Accademia dei Lincei founded in Rome.
- Snell makes the first attempt to measure a degree of the meridian arc on the Earth's surface, and so determine the size of the Earth. He publishes Hypomnemata mathematica (Mathematical Memoranda) which is a Latin translation of Stevin's work on mechanics.
- Kepler publishes Astronomia nova (New Astronomy). The work contains Kepler's first and second law on elliptical orbits, but only verified for the planet Mars.
- Galileo publishes Sidereus Nuncius (Message from the stars) which describes the astronomical discoveries he has made with his telescopes. Harriot also observes the moons of Jupiter but does not publish his work.
- Bachet publishes a work on mathematical puzzles and tricks which will form the basis for almost all later books on mathematical recreations. He devises a method of constructing magic squares.
- Cataldi publishes Trattato del modo brevissimo di trovar la radice quadra delli numeri in which he finds square roots using continued fractions.
- Napier publishes his work on logarithms in Mirifici logarithmorum canonis descriptio (Description of the Marvellous Rule of Logarithms).
- Kepler publishes Nova stereometria doliorum vinarorum (Solid Geometry of a Wine Barrel), an investigation of the capacity of casks, surface areas, and conic sections. He first had the idea at his marriage celebrations in 1613. His methods are early uses of the calculus.
- Mersenne encourages mathematicians to study the cycloid. (See this Famous curve.)
- Snell publishes his technique of trigonometrical triangulation which improves the accuracy of cartographic measurements.
- Briggs publishes Logarithmorum chilias prima (Logarithms of Numbers from 1 to 1,000) which introduces logarithms to the base 10.
- Napier invents Napier's bones, consisting of numbered sticks, as a mechanical calculator. He explains their function in Rabdologiae (Study of Divining Rods) published in the year of his death.
- Bürgi publishes Arithmetische und geometrische progress-tabulen which contains his version of logarithms discovered independently of Napier.
- Gunter makes a mechanical device, Gunter's scale, to multiply numbers based on logarithms using a single scale and a pair of dividers.
- Guldin gives Guldin's Centroid Theorem which was already known to Pappus.
- Schickard makes a "mechanical clock", a wooden calculating machine that add and subtract and aid with multiplication and division. He writes to Kepler suggesting using mechanical means to calculate ephemeredes.
- Briggs publishes Arithmetica logarithmica (The Arithmetic of Logarithms) which introduces the terms "mantissa" and "characteristic". It gives the logarithms of the natural numbers from 1 to 20,000 and 90,000 to 100,000 computed to 14 decimal places as well as tables of the sine function to 15 decimal places, and the tangent and secant functions to 10 decimal places.