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Annus mirabilis is a Latin phrase that means wonderful year, "year of wonders" or "year of miracles". This term was originally used to refer to the year 1666 (see below), and today is used to refer to several years during which events of major importance are remembered.
The Catholic Monarchs (Isabella I of Castile and Ferdinand II of Aragon) built in 1492 the most powerful monarchy in the Western World by the conquest of Granada (January 2) and the discovery of America (October 12). On March 31 they expelled the Jews from Spain. 1492 is also the year of construction of the first grammar of a modern language: Gramática de la lengua castellana; the author, Antonio de Nebrija (a prominent counselor of the Monarchs) said in it, comparing Spanish with Latin: siempre la lengua fue compañera del imperio ("the language was always the companion of empire").
According to the Oxford English Dictionary, the first known written usage of the Latin phrase "Annus Mirabilis" is as the title of a poem composed by English poet John Dryden about the events of 1666. The phrase "annus mirabilis" translates as "wonderful year" or "year of miracles". In fact, the year was beset by great calamity for England (including the Great Fire of London), but Dryden chose to interpret the absence of greater disaster as miraculous intervention by God, as "666" is the Number of the Beast and the year 1666 was expected by some to be particularly disastrous.
In addition to this, the English fleet defeated a Dutch fleet in the St James' Day Battle, for a great victory at sea. (However, in 1667 the Dutch burned several major warships of the English fleet in the raid on the Medway and Charles II was forced to sue for peace.)
In the year 1666, Isaac Newton made revolutionary inventions and discoveries in calculus, motion, optics and gravitation. As such, it has later been called Isaac Newton's "Annus Mirabilis." It was in this year when Isaac Newton was alleged to have observed an apple falling from a tree, and hit upon the law of universal gravitation (Newton's apple). He was afforded the time to work on his theories due to the closure of Cambridge University by an outbreak of plague.
A series of victories by the British military in 1759 in North America, Europe, India, and in various naval engagements, is occasionally referred to as William Pitt's annus mirabilis, and was the decisive year of the Seven Years' War.
For this year the term annus mirabilis is often used.  David Hume died in August, but could experience the American Declaration of Independence from the British Crown which led to the foundation of the first modern Republic Independence Day and The Wealth of Nations from Adam Smith.
The year 1905 has very much been linked to the term annus mirabilis, as Albert Einstein made important discoveries concerning the photoelectric effect, Brownian motion and the special theory of relativity as well as the famous E = mc2. His articles, collectively known as his Annus Mirabilis papers, were published in Annalen der Physik in 1905.
This phrase has since been used to refer to other years. The examples here are primarily from the English-speaking world.
In the same year  I began to think of gravity extending to the orb of the moon, .... All this was in the two plague years of 1665 and 1666, for in those days I was in the prime of my age for invention, and minded mathematics and philosophy more than at any time since.
In the beginning of the year 1665 I found the Method of approximating series & the Rule for reducing any dignity of any Binomial into such a series. The same year in May I found the method of Tangents of Gregory & Slusius, & in November had the direct method of fluxions & the next year in January had the Theory of Colors & in May following I had entrance into the inverse method of fluxions. And the same year I began to think of gravity extending to the orb of the Moon & (having found out how to estimate the force with which a globe revolving within a sphere presses the surface of the sphere) from Keplers rule of the periodical times of the Planets being in sesquialterate proportion of their distances from the centers of their Orbs, I deduced that the forces which keep the Planets in their Orbs must be reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth ... All this was in the two plague years of 1665 and 1666. For in those days I was in the prime of my age of invention & minded Mathematics & Philosophy more than at any time since.