Bubonic plague devastates Vienna: 76,000 dead. It originates from the marshy lands of the Ottoman Empire in the east.

Robert Hooke: in “De poentia restitutiva or of a spring” he discovers that the deformation of a material allows it to exert a reaction force (“ut tensio, sic vis”, as much as the deformation as much as the force)

Gottfried Leibniz introduces binary arithmetic

Pierre de Fermat in De Tangentibus Linearum Curvarum illustrates a method for drawing straight lines tangent to any curved line.

England. Maria Beatrice d’Este and James Stuart, Duke of York, leave England just before the opening of Parliament, which is hostile to the Catholic regency. They then set out for Brussels, arriving on March 27th with three ships of the Prince of Orange. In May, Parliament will introduce the Exclusion Bill, which aims to exclude James Stuart, Duke of York from the succession to the throne, as he is Catholic. The bill is passed with 207 votes in favor and 128 against.

Isaac Newton suffers a severe nervous breakdown

The philosopher Baruch Spinoza dies of tuberculosis, a disease caused by inhaling glass dust from his work grinding lenses. That same year, several of his works are published pseudonymously, only to be banned by the Dutch government within twelve months. He argues that the human mind and body do not belong to two different worlds. He also identifies God and Nature.

Jubilee celebrated by Innocent X

Netherlands. The painter Johannes Vermeer dies in Delft, where he spent his entire life, producing several dozen works but failing to sell a single one. His wife will sell some of them after his death to pay off debts, including one to the baker.

Modena. Maria Beatrice d’Este married James Stuart, represented by proxy from Peterborough. On October 5, she left Modena with her mother, Laura Martinozzi, and an entourage of about sixty people, and—passing through Voghera, Mont Cenis, Chambéry, and Lyon—arrived in Paris on November 2, where she was festively welcomed by Louis XIV. After overcoming a slight illness, Maria Beatrice d’Este, still with her mother at her side, left Paris on November 23 to embark for Calais. On December 1, she met her husband in Dover, where the Anglican Bishop of Oxford publicly read the marriage contract and the consummation of the marriage took place. Sailing up the Thames, the couple reached London and on December 6th took up residence at St. James’s Palace, the residence of the Duke of York. Staying with Maria Beatrice d’Este were the chaplain Ronchi, the Jesuits Antonio Maria Giudici and Gottardo Belluomo, a miniaturist, two painters, a page, two valets, two cooks, and five ladies, all from Modena. The English servants also joined them, around sixty people directly dependent on Maria Beatrice d’Este; Edward Coleman, destined to be executed for his involvement in papist plots, was chosen as secretary. Maria Beatrice d’Este adapted to the married state. She found consolation in the fact that the duke—of whose private conduct Maria Beatrice d’Este was to a certain extent aware, and over time, not without suffering, she came to terms with his systematic infidelity—had religious sentiments. On this point, the ducal couple remained steadfast, even though James Stuart’s religious intransigence would prove politically unsuccessful. Maria Beatrice carried five pregnancies to term within a few years, though they were marred by the early deaths of the children: Catherine Laura (21 January – 13 October 1675); Isabella (1676-81); Charles, Duke of Cambridge (7 November – 12 December 1677); her baby, born in early March 1681, died almost immediately, and Carla, born just three days after, in August 1682. Among the unfortunate births, the couple also experienced forced exile from London for a period of exile in Brussels, from 1679 to 1684, followed by an obligatory stay in Edinburgh. Charles II died a Catholic on 6 February 1685, and was succeeded by James II, with Mary Beatrice at his side as Queen of England.

Modena. The Este court of Modena receives a letter addressed to the young Maria Beatrice from Pope Clement X, urging her to accept the marriage proposal of James Stuart, Duke of York, in England (obviously to establish a Catholic king and queen in England). The English court must choose a second wife for James Stuart, Duke of York, who had been widowed the previous March. His first wife, Catherine of Braganza, was sterile. The English court is considering Maria Beatrice d’Este, of the Duchy of Modena. In the spring of 1673, Lord Peterborough, who had been charged with finding his future wife, had spoken in Paris with the Jesuit Father Alexander Conn, who had introduced him to the Modenese abbot Gaspare Rizzini, from whom he had learned about Laura Martinozzi’s daughter: very young, beautiful, lively, highly cultured, a brilliant conversationalist, and a lover of art and music. Unfortunately, Maria Beatrice isn’t entirely on board: she would like to become a nun instead. Initially the answer is therefore negative, but after several pressures, crucially the letter from the Pope, Maria Beatrice accepts.

John Wallis proposed thinking of the complex number x + iy as a point on a plane. The idea was ignored by almost everyone, or worse, harshly criticized. It was taken up and expanded upon by Gauss in 1811.

Giovanni Domenico Cassini discovers Iapetus, a satellite of Saturn.

Gian Domenico Cassini, in Paris, discovers the rotation of Mars, Jupiter and 4 satellites of Saturn and the separation in Saturn’s rings

Isaac Barrow leaves his Lucasian Chair at Cambridge to Isaac Newton

Cretan War. Francesco Morosini concludes the agreement for the surrender of Candia to the Turks. He allows Venice to withdraw with honors and maintain small naval bases of commercial importance in Crete, as well as retaining Tine and Cerigo in the Aegean, as well as Dalmatia.

The Peace of Breda ended the Second Anglo-Dutch War (but there would be two more). The English offered to return New Amsterdam (New York) to regain possession of the Indonesian islands of Banda, the Moluccas, and Ambon. The Netherlands refused and obtained complete control of the East Indies (nutmeg was grown on Run Island, in the Banda archipelago, and with Run the Dutch completed their monopoly on this precious spice), leaving New York to the English instead. The consequences of this agreement were enormous for future history: an English America rather than a Dutch one. Furthermore, the English, unable to gain access to Indonesia, turned to India and established it as a unitary state under their colonial rule. Nutmeg was considered extremely valuable at the time, not only for preserving and flavoring food, but also because it was thought to provide protection against the plague. Nutmeg’s distinctive odor is due to isoeugenol. Some plants, in fact, develop these compounds as natural pesticides. It is possible that isoeugenol kept fleas away.

London. John Locke is working on his major philosophical work: An Essay Concerning Human Understanding. It won’t be published until 1690, however. It consists of four books. He argues that our minds have no innate principles, whether speculative or practical: all our ideas derive from experience. He classifies ideas as simple and complex, confused and clear/distinct, sensational and reflective.

Isaac Newton invents (at the same time as Leibniz) the Infinitesimal Calculus: integration and derivation (differentiation)

Fermat dies after signing his last arrest warrant only three days earlier

Black Death (bubonic plague or Great Plague) in London: it was the worst epidemic of the century; sneezing was a warning sign and so people responded “God bless you” to a sneeze, as a sort of last rites.

Second Anglo-Dutch War. Under the command of Michiel De Ruyter, the Dutch inflict a severe defeat on the English in the Four Days’ Battle, the longest naval battle ever fought. He then attacks the English right in their refuge: the Thames Estuary. In a daring surprise attack, he cuts the Medway Chains and arrives where most of the English fleet is anchored: 15 ships are sunk, 3 burned, and one, the flagship Royal Charles of the entire English fleet, is captured and towed to Holland as a trophy. Its original stern coat of arms is still in the National Museum in Amsterdam. It is the Royal Navy’s worst defeat. De Ruyter is the son of a humble beer stevedore, and this too starkly represents the difference between the English aristocrats and the Dutch bourgeoisie.

The Royal Society’s Correspondence evolves into the Philosophical Transaction, the modern scientific journal. This marks the birth of the oldest English-language scientific periodical.

Ottoman disaster on the Raab River. Montecuccoli’s outnumbered cuirassiers and his deadly imperial field artillery manage to drive the Ottoman army back, once again on the road to Vienna. But the coalition assembled by Emperor Leopold, including the Rhineland States of the Holy Roman Empire, French volunteer knights, and other contingents, is disjointed and fractious, and only Montecuccoli’s skill prevents the worst.

Henry Lucas, a member of the British Parliament, with a royal warrant from King Charles, established a new chair of mathematics whose holder would be designated Lucasian Professor; the first holder would be Barrow, the second Newton, at the end of the 20th century. Hawking would occupy the same post.

This time, the Ottoman advance toward Vienna was halted by the stubborn defense of a small Habsburg fortress: Neuhausel (now Nove Zamky) on the Nitra River, which flows into the Danube. The siege dragged on for weeks, and by the time the city was taken, the season was too late to risk getting stuck in mud and snow. It was a story we’d seen before at Koszeg in 1532, Eger in 1552, Szigetvar in 1541 and 1566, and finally at Nove Zamky in 1663.

Shortly after Blaise Pascal’s death, a servant noticed a small bulge in the pocket of his jacket. He discovered a sewn lining containing sheets of paper and parchment with phrases dated November 23, 1654. Pascal described how, in a trance, God appeared to him, freeing him from corruption. He subsequently abandoned almost all his friends, calling them horrible bonds, along with all material possessions except the Bible, and wore an iron belt with nails protruding inward. He also renounced his mathematical and scientific studies.

Robert Boyle publishes “The Sceptical Chymist” which draws a clear and definitive distinction between chemistry and alchemy

England, General Monk restores Parliament