Botany

• John Parkinson
  John Parkinson (botanist)
  John Parkinson was the last of the great English herbalists and one of the first of the great English botanists. He was apothecary to James I and a founding member of the Worshipful Society of Apothecaries in December 1617, and was later Royal Botanist to Charles I...
  
   publishes Theatrum Botanicum:The Theater of Plants, or, An Herbal of a Large Extent.

Exploration

• The Cape Verde Island of Sal is discovered, originally named "Llana" (meaning "flat").

Mathematics

• The 16-year old Blaise Pascal
  Blaise Pascal
  Blaise Pascal , was a French mathematician, physicist, inventor, writer and Catholic philosopher. He was a child prodigy who was educated by his father, a tax collector in Rouen...
  
   demonstrates the properties of the hexagrammum mysticum in his Essai pour les coniques which he sends to Mersenne
  Marin Mersenne
  Marin Mersenne, Marin Mersennus or le Père Mersenne was a French theologian, philosopher, mathematician and music theorist, often referred to as the "father of acoustics"...
  
  .
• October 18 - Fermat states his "little theorem
  Fermat's little theorem
  Fermat's little theorem states that if p is a prime number, then for any integer a, a p − a will be evenly divisible by p...
  
  " in a letter to Frénicle de Bessy
  Bernard Frénicle de Bessy
  Bernard Frénicle de Bessy , was a French mathematician born in Paris, who wrote numerous mathematical papers, mainly in number theory and combinatorics. He is best remembered for Des quarrez ou tables magiques, a treatise on magic squares published posthumously in 1693, in which he described all...
  
  : if p is a prime number
  Prime number
  A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
  
  , then for any integer
  Integer
  The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
  
   a, a ^p − a will be evenly divisible by p.
• December 25 - Fermat claims a proof of the theorem on sums of two squares in a letter to Mersenne ("Fermat's Christmas Theorem"): an odd
  Even and odd numbers
  In mathematics, the parity of an object states whether it is even or odd.This concept begins with integers. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without remainder; an odd number is an integer that is not evenly divisible by 2...
  
   prime
  Prime number
  A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
  
   p is expressible as the sum of two squares.

Technology

• The micrometer
  Micrometer
  A micrometer , sometimes known as a micrometer screw gauge, is a device incorporating a calibrated screw used widely for precise measurement of small distances in mechanical engineering and machining as well as most mechanical trades, along with other metrological instruments such as dial, vernier,...
  
   is developed.
• A form of bayonet
  Bayonet
  A bayonet is a knife, dagger, sword, or spike-shaped weapon designed to fit in, on, over or underneath the muzzle of a rifle, musket or similar weapon, effectively turning the gun into a spear...
  
   is invented; in later years it will gradually replace the pike
  Pike (weapon)
  A pike is a pole weapon, a very long thrusting spear used extensively by infantry both for attacks on enemy foot soldiers and as a counter-measure against cavalry assaults. Unlike many similar weapons, the pike is not intended to be thrown. Pikes were used regularly in European warfare from the...
  
  .
• The reticle telescope is developed and initiates the birth of sharpshooting.

Births

• April 1 - Georg Mohr
  Georg Mohr
  Jørgen Mohr was a Danish mathematician. He travelled in the Netherlands, France, and England.Mohr was born in Copenhagen...
  
  , Danish mathematician
  Mathematician
  A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
  
   (d. 1697
  1697 in science
  The year 1697 in science and technology involved some significant events.-Deaths:* January 26 - Georg Mohr, Danish mathematician...
  
  )
• December 13 (bapt.) - Robert Plot
  Robert Plot
  Robert Plot was an English naturalist, first Professor of Chemistry at the University of Oxford, and the first keeper of the Ashmolean Museum....
  
  , English
  English people
  The English are a nation and ethnic group native to England, who speak English. The English identity is of early mediaeval origin, when they were known in Old English as the Anglecynn. England is now a country of the United Kingdom, and the majority of English people in England are British Citizens...
  
   naturalist
  Naturalist
  Naturalist may refer to:* Practitioner of natural history* Conservationist* Advocate of naturalism * Naturalist , autobiography-See also:* The American Naturalist, periodical* Naturalism...
  
   and chemist
  Chemist
  A chemist is a scientist trained in the study of chemistry. Chemists study the composition of matter and its properties such as density and acidity. Chemists carefully describe the properties they study in terms of quantities, with detail on the level of molecules and their component atoms...
  
   (d. 1696
  1696 in science
  The year 1696 in science and technology involved some significant events.-History of science:* Daniel Le Clerc publishes Histoire de la médecine in Geneva, the first comprehensive work on the subject.-Mathematics:...
  
  )