Editing Christiaan Huygens (section)

==Biography==
[[File:Adriaen Hanneman - Constantijn Huygens and his-five-children.png|thumb|upright=.9|[[Constantijn Huygens|Constantijn]] surrounded by his five children (Christiaan, top right). [[Mauritshuis]], [[The Hague]].]]
Christiaan Huygens was born into a rich and influential Dutch family in [[The Hague]] on 14 April 1629, the second son of [[Constantijn Huygens]].<ref>[[Stephen J. Edberg]] (14 December 2012) [http://www.encyclopedia.com/doc/1G2-3404703173.html Christiaan Huygens] {{Webarchive|url=https://web.archive.org/web/20210902210759/https://www.encyclopedia.com/people/science-and-technology/physics-biographies/christiaan-huygens|date=2 September 2021}}, ''Encyclopedia of World Biography''. 2004. Encyclopedia.com.</ref><ref name="opendoor">{{cite web |title=Christiaan Huygens (1629–1695) |url=http://www.saburchill.com/HOS/astronomy/016.html |url-status=live |archive-url=https://web.archive.org/web/20170613164310/http://saburchill.com/HOS/astronomy/016.html |archive-date=13 June 2017 |access-date=16 February 2013 |website=www.saburchill.com}}</ref> Christiaan was named after his paternal grandfather.<ref name="completedictionary">[[Henk J. M. Bos]] (14 December 2012) [http://www.encyclopedia.com/doc/1G2-2830902105.html Huygens, Christiaan (Also Huyghens, Christian)] {{Webarchive|url=https://web.archive.org/web/20210902210759/https://www.encyclopedia.com/people/science-and-technology/physics-biographies/christiaan-huygens |date=2 September 2021 }}, ''Complete Dictionary of Scientific Biography''. 2008. Encyclopedia.com.</ref><ref>R. Dugas and P. Costabel, "Chapter Two, The Birth of a new Science" in ''The Beginnings of Modern Science'', edited by Rene Taton, 1958,1964, Basic Books, Inc.</ref> His mother, [[Suzanna van Baerle]], died shortly after giving birth to Huygens's sister.<ref>''Strategic Affection? Gift Exchange in Seventeenth-Century Holland'', by Irma Thoen, p. 127</ref> The couple had five children: [[Constantijn Huygens Jr.|Constantijn]] (1628), Christiaan (1629), [[Lodewijck Huygens|Lodewijk]] (1631), Philips (1632) and Suzanna (1637).<ref name="father">{{Cite web |url=http://www.essentialvermeer.com/history/huygens.html |title=Constantijn Huygens, Lord of Zuilichem (1596–1687), by Adelheid Rech |access-date=16 February 2013 |archive-date=3 July 2017 |archive-url=https://web.archive.org/web/20170703211137/http://www.essentialvermeer.com/history/huygens.html |url-status=live }}</ref>

[[Constantijn Huygens]] was a diplomat and advisor to the [[House of Orange-Nassau|House of Orange]], in addition to being a poet and a musician. He [[Republic of Letters|corresponded widely]] with intellectuals across Europe, including [[Galileo Galilei]], [[Marin Mersenne]], and [[René Descartes]].<ref>''The Heirs of Archimedes: Science and the Art of War Through the Age of Enlightenment'', by Brett D. Steele, p. 20</ref> Christiaan was educated at home until the age of sixteen, and from a young age liked to play with miniatures of [[mill (grinding)|mills]] and other machines. He received a [[liberal education]] from his father, studying languages, [[music]], [[history]], [[geography]], [[mathematics]], [[logic]], and [[rhetoric]], alongside [[dancing]], [[fencing]] and [[horse riding]].<ref name="completedictionary" /><ref name="father" />

In 1644, Huygens had as his mathematical tutor [[Jan Jansz de Jonge Stampioen|Jan Jansz Stampioen]], who assigned the 15-year-old a demanding reading list on contemporary science.<ref>{{cite book|author=Jozef T. Devreese|title='Magic Is No Magic': The Wonderful World of Simon Stevin|url=https://books.google.com/books?id=f59h2ooQGmcC&pg=PA275|access-date=24 April 2013|date=31 October 2008|publisher=WIT Press|isbn=978-1-84564-391-1|pages=275–6|archive-date=16 June 2016|archive-url=https://web.archive.org/web/20160616194009/https://books.google.com/books?id=f59h2ooQGmcC&pg=PA275|url-status=live}}</ref> Descartes was later impressed by his skills in geometry, as was Mersenne, who christened him the "new [[Archimedes]]."<ref name=":0">{{Cite book |last=Dijksterhuis |first=F. J. |title=Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century. |publisher=Kluwer Academic Publishers |year=2005}}</ref><ref name="opendoor"/><ref name=":8">{{Cite book|last=Yoder|first=Joella G.|title=Unrolling Time: Christiaan Huygens and the Mathematization of Nature|publisher=Cambridge University Press|year=1989|isbn=978-0-521-52481-0|pages=174–175}}</ref>

===Student years===
At sixteen years of age, Constantijn sent Huygens to study law and mathematics at [[Leiden University]], where he enrolled from May 1645 to March 1647.<ref name="completedictionary"/> [[Frans van Schooten|Frans van Schooten Jr.]], professor at Leiden's Engineering School, became private tutor to Huygens and his elder brother, Constantijn Jr., replacing Stampioen on the advice of Descartes.<ref>{{cite book|author=H. N. Jahnke|title=A history of analysis|url=https://books.google.com/books?id=CVRZEXFVsZkC&pg=PA47|access-date=12 May 2013|date=2003|publisher=American Mathematical Soc.|isbn=978-0-8218-9050-9|page=47|archive-date=30 June 2014|archive-url=https://web.archive.org/web/20140630095949/http://books.google.com/books?id=CVRZEXFVsZkC&pg=PA47|url-status=live}}</ref><ref>{{cite book|author=Margret Schuchard|title=Bernhard Varenius: (1622–1650)|url=https://books.google.com/books?id=dmArFPaY5ZgC&pg=PA112|access-date=12 May 2013|date=2007|publisher=BRILL|isbn=978-90-04-16363-8|page=112|archive-date=30 June 2014|archive-url=https://web.archive.org/web/20140630095832/http://books.google.com/books?id=dmArFPaY5ZgC&pg=PA112|url-status=live}}</ref> Van Schooten brought Huygens's mathematical education up to date, particularly on the work of [[François Viète|Viète]], Descartes, and [[Pierre de Fermat|Fermat]].<ref name=":32">{{Cite journal |last=Paoloni |first=B. |date=2022 |title=L'art de l'analyse de Christiaan Huygens de l'Algebra à la Geometria |url=https://brill.com/view/journals/rds/143/3-4/article-p423_6.xml |journal=Revue de Synthèse |volume=143 |issue=3–4 |pages=423–455 |doi=10.1163/19552343-14234034 |s2cid=254908971 |issn=1955-2343}}</ref>

After two years, starting in March 1647, Huygens continued his studies at the newly founded [[Orange College of Breda|Orange College]], in [[Breda]], where his father was a [[curator]]. Constantijn Huygens was closely involved in the new College, which lasted only to 1669; the rector was [[André Rivet]].<ref>{{cite book|author=Andriesse|first=C. D.|url=https://books.google.com/books?id=6FTqA9fwxFMC&pg=PA80|title=Huygens: The Man Behind the Principle|publisher=Cambridge University Press|year=2005|isbn=978-0-521-85090-2|pages=80–82|access-date=|archive-url=https://web.archive.org/web/20160617112715/https://books.google.com/books?id=6FTqA9fwxFMC&pg=PA80|archive-date=17 June 2016|url-status=live}}</ref> Christiaan Huygens lived at the home of the jurist Johann Henryk Dauber while attending college, and had mathematics classes with the English lecturer [[John Pell (mathematician)|John Pell]]. His time in Breda ended around the time when his brother Lodewijk, who was enrolled at the school, duelled with another student.<ref name=":14" /><ref>{{Cite web |title=Christiaan Huygens – A family affair, by Bram Stoffele, pg 80. |url=http://www.proevenvanvroeger.nl/eindopdrachten/huygens/huygensfamily.pdf |url-status=live |archive-url=https://web.archive.org/web/20170812225640/http://proevenvanvroeger.nl/eindopdrachten/huygens/huygensfamily.pdf |archive-date=12 August 2017 |access-date=16 February 2013}}</ref> Huygens left Breda after completing his studies in August 1649 and had a stint as a diplomat on a mission with [[Henry, Duke of Nassau]].<ref name="completedictionary"/> After stays at [[County of Bentheim (district)|Bentheim]] and [[Flensburg]] in Germany, he visited [[Copenhagen]] and [[Helsingør]] in Denmark. Huygens hoped to cross the [[Øresund]] to see Descartes in [[Stockholm]] but was prevented due to Descartes' death in the interim.<ref name=":14" /><ref>{{Cite web |last=Stoffele |first=B. |date=2006 |title=Christiaan Huygens – A family affair - Proeven van Vroeger |url=https://www.yumpu.com/en/document/view/15920743/christiaan-huygens-a-family-affair-proeven-van-vroeger |access-date=2023-11-27 |website=Utrecht University |language=en}}</ref>

Although his father Constantijn had wished his son Christiaan to be a diplomat, circumstances kept him from becoming so. The [[First Stadtholderless Period]] that began in 1650 meant that the House of Orange was no longer in power, removing Constantijn's influence. Further, he realized that his son had no interest in such a career.<ref name="Dictionary, p. 469">Bunge et al. (2003), ''Dictionary of Seventeenth and Eighteenth-Century Dutch Philosophers,'' p. 469.</ref>

===Early correspondence===
[[File:KettingHyugens.jpg|thumb|upright=.9|Picture of a hanging chain ([[catenary]]) in a manuscript of Huygens]]
Huygens generally wrote in French or Latin.<ref>{{cite book|author=Lynn Thorndike|title=History of Magic & Experimental Science 1923|url=https://books.google.com/books?id=Sr923sVWH_QC&pg=PA622|access-date=11 May 2013|date=1 March 2003|publisher=Kessinger Publishing|isbn=978-0-7661-4316-6|page=622|archive-date=13 October 2013|archive-url=https://web.archive.org/web/20131013023137/http://books.google.com/books?id=Sr923sVWH_QC&pg=PA622|url-status=live}}</ref> In 1646, while still a college student at Leiden, he began a correspondence with his father's friend, [[Marin Mersenne]], who died soon afterwards in 1648.<ref name="completedictionary"/> Mersenne wrote to Constantijn on his son's talent for mathematics, and flatteringly compared him to Archimedes on 3 January 1647.<ref name=":10" />

The letters show Huygens's early interest in mathematics. In October 1646 there is the [[suspension bridge]] and the demonstration that a [[Catenary|hanging chain]] is not a [[parabola]], as Galileo thought.<ref>{{cite book|author=Leonhard Euler|editor=[[Clifford Truesdell]]|title=The Rational Mechanics of Flexible or Elastic Bodies 1638–1788: Introduction to Vol. X and XI|url=https://books.google.com/books?id=gxrzm6y10EwC&pg=PA44|access-date=10 May 2013|date=1 January 1980|publisher=Springer|isbn=978-3-7643-1441-5|pages=44–6|author-link=Leonhard Euler|archive-date=13 October 2013|archive-url=https://web.archive.org/web/20131013023135/http://books.google.com/books?id=gxrzm6y10EwC&pg=PA44|url-status=live}}</ref> Huygens would later label that curve the ''catenaria'' ([[catenary]]) in 1690 while corresponding with [[Gottfried Wilhelm Leibniz|Gottfried Leibniz]].<ref name=":16">{{Cite journal|last=Bukowski|first=J.|date=2008|title=Christiaan Huygens and the Problem of the Hanging Chain|url=https://doi.org/10.1080/07468342.2008.11922269|journal=The College Mathematics Journal|volume=39|issue=1|pages=2–11|doi=10.1080/07468342.2008.11922269|s2cid=118886615}}</ref>

In the next two years (1647–48), Huygens's letters to Mersenne covered various topics, including a mathematical proof of the [[Free fall|law of free fall]], the claim by [[Grégoire de Saint-Vincent]] of [[squaring the circle|circle quadrature]], which Huygens showed to be wrong, the rectification of the ellipse, projectiles, and the [[vibrating string]].<ref>{{cite book|author=Andriesse|first=C. D.|url=https://books.google.com/books?id=6FTqA9fwxFMC&pg=PA78|title=Huygens: The Man Behind the Principle|publisher=Cambridge University Press|year=2005|isbn=978-0-521-85090-2|pages=78–79|archive-url=https://web.archive.org/web/20131013023116/http://books.google.com/books?id=6FTqA9fwxFMC&pg=PA78|archive-date=13 October 2013|url-status=live}}</ref> Some of Mersenne's concerns at the time, such as the [[cycloid]] (he sent Huygens [[Evangelista Torricelli|Torricelli]]'s treatise on the curve), the [[Center of percussion|centre of oscillation]], and the [[gravitational constant]], were matters Huygens only took seriously later in the 17th century.<ref name=":7" /> Mersenne had also written on musical theory. Huygens preferred [[meantone temperament]]; he innovated in [[31 equal temperament]] (which was not itself a new idea but known to [[Francisco de Salinas]]), using logarithms to investigate it further and show its close relation to the meantone system.<ref name="Cohen1984">{{cite book|author=H.F. Cohen|title=Quantifying Music: The Science of Music at the First Stage of Scientific Revolution 1580–1650|url=https://books.google.com/books?id=itKDhDRaik8C&pg=PA217|access-date=11 May 2013|date=31 May 1984|publisher=Springer|isbn=978-90-277-1637-8|pages=217–9|archive-date=13 October 2013|archive-url=https://web.archive.org/web/20131013023051/http://books.google.com/books?id=itKDhDRaik8C&pg=PA217|url-status=live}}</ref>

In 1654, Huygens returned to his father's house in The Hague and was able to devote himself entirely to research.<ref name="completedictionary" /> The family had another house, not far away at [[Hofwijck]], and he spent time there during the summer. Despite being very active, his scholarly life did not allow him to escape bouts of depression.<ref name=":9">{{cite book|author=H. J. M. Bos|url=https://books.google.com/books?id=lSGvPI6LHvwC&pg=PA64|title=Lectures in the History of Mathematics|publisher=American Mathematical Soc.|year=1993|isbn=978-0-8218-9675-4|pages=64–65|archive-url=https://web.archive.org/web/20160616195750/https://books.google.com/books?id=lSGvPI6LHvwC&pg=PA64|archive-date=16 June 2016|url-status=live}}</ref>

Subsequently, Huygens developed a broad range of correspondents, though with some difficulty after 1648 due to the five-year ''[[Fronde]]'' in France. Visiting Paris in 1655, Huygens called on [[Ismael Boulliau]] to introduce himself, who took him to see [[Claude Mylon]].<ref>{{cite book|author=C. D. Andriesse|title=Huygens: The Man Behind the Principle|url=https://books.google.com/books?id=6FTqA9fwxFMC&pg=PA134|access-date=10 May 2013|date=25 August 2005|publisher=Cambridge University Press|isbn=978-0-521-85090-2|page=134|archive-date=16 June 2016|archive-url=https://web.archive.org/web/20160616202240/https://books.google.com/books?id=6FTqA9fwxFMC&pg=PA134|url-status=live}}</ref> The Parisian group of savants that had gathered around Mersenne held together into the 1650s, and Mylon, who had assumed the secretarial role, took some trouble to keep Huygens in touch.<ref>{{cite book|author=Thomas Hobbes|title=The Correspondence: 1660–1679|url=https://books.google.com/books?id=GYF_mBtgIVwC&pg=PA868|access-date=10 May 2013|date=1997|publisher=Oxford University Press|isbn=978-0-19-823748-8|page=868|archive-date=16 June 2016|archive-url=https://web.archive.org/web/20160616202651/https://books.google.com/books?id=GYF_mBtgIVwC&pg=PA868|url-status=live}}</ref> Through [[Pierre de Carcavi]] Huygens corresponded in 1656 with Pierre de Fermat, whom he admired greatly. The experience was bittersweet and somewhat puzzling since it became clear that Fermat had dropped out of the research mainstream, and his priority claims could probably not be made good in some cases. Besides, Huygens was looking by then to [[Applied mathematics|apply mathematics]] to physics, while Fermat's concerns ran to purer topics.<ref>{{cite book|author=Michael S. Mahoney|title=The Mathematical Career of Pierre de Fermat: 1601–1665|url=https://books.google.com/books?id=My19IcewAnoC&pg=PA67|access-date=10 May 2013|date=1994|publisher=Princeton University Press|isbn=978-0-691-03666-3|pages=67–8|archive-date=16 June 2016|archive-url=https://web.archive.org/web/20160616213214/https://books.google.com/books?id=My19IcewAnoC&pg=PA67|url-status=live}}</ref>

===Scientific debut===
[[File:Christiaan Huygens by Jaques Clerion.jpg|thumb|upright=.9|Christiaan Huygens, relief by [[Jean-Jacques Clérion]] (c. 1670)]]
Like some of his contemporaries, Huygens was often slow to commit his results and discoveries to print, preferring to disseminate his work through letters instead.<ref name=":12" /> In his early days, his mentor Frans van Schooten provided technical feedback and was cautious for the sake of his reputation.<ref>{{cite book|author=C. D. Andriesse|title=Huygens: The Man Behind the Principle|url=https://books.google.com/books?id=6FTqA9fwxFMC&pg=PA126|access-date=10 May 2013|date=25 August 2005|publisher=Cambridge University Press|isbn=978-0-521-85090-2|page=126|archive-date=31 December 2013|archive-url=https://web.archive.org/web/20131231214115/http://books.google.com/books?id=6FTqA9fwxFMC&pg=PA126|url-status=live}}</ref>

Between 1651 and 1657, Huygens published a number of works that showed his talent for mathematics and his mastery of [[Euclidean geometry|classical]] and [[Analytic geometry|analytical geometry]], increasing his reach and reputation among mathematicians.<ref name=":10" /> Around the same time, Huygens began to question Descartes's laws of [[collision]], which were largely wrong, deriving the correct laws algebraically and later by way of geometry.<ref name=":13">{{Cite journal|last=Hyslop|first=S. J.|date=2014|title=Algebraic Collisions|url=https://doi.org/10.1007/s10699-012-9313-8|journal=Foundations of Science|language=en|volume=19|issue=1|pages=35–51|doi=10.1007/s10699-012-9313-8|s2cid=124709121|access-date=28 August 2021|archive-date=2 September 2021|archive-url=https://web.archive.org/web/20210902210801/https://link.springer.com/article/10.1007%2Fs10699-012-9313-8|url-status=live}}</ref> He showed that, for any system of bodies, the [[Center of mass|centre of gravity]] of the system remains the same in velocity and direction, which Huygens called the [[Conservation law|conservation of "quantity of movement"]]. While others at the time were studying impact, Huygens's theory of collisions was more general.<ref name=":14">{{Cite book |last=Aldersey-Williams |first=H. |url=https://books.google.com/books?id=7n7VDwAAQBAJ&q=In+the+case+of+two+bodies+which+meet%2C+the+quantity+obtained+by+taking+the+sum+of+their+masses+multiplied+by+the+squares+of+their+velocities+will+be+found+to+beequal+before+and+after+the+collision.%E2%80%99&pg=PP86 |title=Dutch Light: Christiaan Huygens and the Making of Science in Europe |date=2020 |publisher=Pan Macmillan |isbn=978-1-5098-9332-4 |pages= |language=en |access-date=28 August 2021 |archive-url=https://web.archive.org/web/20210828235517/https://books.google.com/books?id=7n7VDwAAQBAJ&pg=PP86&lpg=PP86&dq=In+the+case+of+two+bodies+which+meet,+the+quantity+obtained+by+taking+the+sum+of+their+masses+multiplied+by+the+squares+of+their+velocities+will+be+found+to+beequal+before+and+after+the+collision.%E2%80%99&source=bl&ots=98NF_u7tbn&sig=ACfU3U08HzNIaxw5RlsDedPFq0KsaPbisw&hl=en&sa=X&ved=2ahUKEwi-ioTf8NTyAhU3RjABHQnyAXcQ6AF6BAgCEAM#v=onepage&q=In%20the%20case%20of%20two%20bodies%20which%20meet,%20the%20quantity%20obtained%20by%20taking%20the%20sum%20of%20their%20masses%20multiplied%20by%20the%20squares%20of%20their%20velocities%20will%20be%20found%20to%20beequal%20before%20and%20after%20the%20collision.%E2%80%99&f=false |archive-date=28 August 2021 |url-status=live}}</ref> These results became the main reference point and the focus for further debates through correspondence and in a short article in ''[[Journal des sçavans|Journal des Sçavans]]'' but would remain unknown to a larger audience until the publication of ''De Motu Corporum ex Percussione'' (''Concerning the motion of colliding bodies'') in 1703.<ref>{{Cite book |last=Meli |first=Domenico Bertoloni |url=https://books.google.com/books?id=I6QreZN02joC |title=Thinking with Objects: The Transformation of Mechanics in the Seventeenth Century |publisher=JHU Press |year=2006 |isbn=978-0-8018-8426-9 |pages=227–240 |language=en}}</ref><ref name=":13" />

In addition to his mathematical and mechanical works, Huygens made important scientific discoveries: he was the first to identify [[Titan (moon)|Titan]] as one of [[Saturn|Saturn's]] moons in 1655, invented the pendulum clock in 1657, and explained Saturn's strange appearance as due to a [[Rings of Saturn|ring]] in 1659; all these discoveries brought him fame across Europe.<ref name="completedictionary" /> On 3 May 1661, Huygens, together with astronomer [[Thomas Streete]] and Richard Reeve, observed the planet [[Mercury (planet)|Mercury]] transit over the Sun using Reeve's telescope in London.<ref>Peter Louwman, Christiaan Huygens and his telescopes, Proceedings of the International Conference, 13 – 17 April 2004, ESTEC, Noordwijk, Netherlands, ESA, sp 1278, Paris 2004</ref> Streete then debated the published record of [[Hevelius]], a controversy mediated by [[Henry Oldenburg]].<ref>{{cite book|author=Adrian Johns|title=The Nature of the Book: Print and Knowledge in the Making|url=https://books.google.com/books?id=ERpBdEUdhz8C&pg=PA437|access-date=23 April 2013|date=15 May 2009|publisher=University of Chicago Press|isbn=978-0-226-40123-2|pages=437–8|archive-date=17 June 2016|archive-url=https://web.archive.org/web/20160617101026/https://books.google.com/books?id=ERpBdEUdhz8C&pg=PA437|url-status=live}}</ref> Huygens passed to Hevelius a manuscript of [[Jeremiah Horrocks]] on the [[transit of Venus, 1639|transit of Venus in 1639]], printed for the first time in 1662.<ref>{{cite book|title=Venus Seen on the Sun: The First Observation of a Transit of Venus by Jeremiah Horrocks|url=https://books.google.com/books?id=KlA6UCyOboUC&pg=PR19|access-date=23 April 2013|date=2 March 2012|publisher=BRILL|isbn=978-90-04-22193-2|page=xix|archive-date=16 June 2016|archive-url=https://web.archive.org/web/20160616202523/https://books.google.com/books?id=KlA6UCyOboUC&pg=PR19|url-status=live}}</ref>

In that same year, [[Sir Robert Moray]] sent Huygens [[John Graunt]]'s [[life table]], and shortly after Huygens and his brother Lodewijk dabbled on [[life expectancy]].<ref name=":12" /><ref>{{cite book |author=Anders Hald |url=https://books.google.com/books?id=pOQy6-qnVx8C&pg=PA106 |title=A History of Probability and Statistics and Their Applications before 1750 |date=25 February 2005 |publisher=John Wiley & Sons |isbn=978-0-471-72517-6 |page=106 |access-date=11 May 2013 |archive-url=https://web.archive.org/web/20160617035707/https://books.google.com/books?id=pOQy6-qnVx8C&pg=PA106 |archive-date=17 June 2016 |url-status=live}}</ref> Huygens eventually created the first graph of a continuous distribution function under the assumption of a uniform [[Mortality rate|death rate]], and used it to solve problems in [[Annuity|joint annuities]].<ref>Hacking, I. (2006). ''The emergence of probability'' (p. 135). Cambridge University Press.</ref> Contemporaneously, Huygens, who played the [[harpsichord]], took an interest in [[Simon Stevin|Simon Stevin's]] theories on music; however, he showed very little concern to publish his theories on [[consonance]], some of which were lost for centuries.<ref>{{cite book|author=Jozef T. Devreese|title='Magic Is No Magic': The Wonderful World of Simon Stevin|url=https://books.google.com/books?id=f59h2ooQGmcC&pg=PA277|access-date=11 May 2013|date=2008|publisher=WIT Press|isbn=978-1-84564-391-1|page=277|archive-date=16 June 2016|archive-url=https://web.archive.org/web/20160616213542/https://books.google.com/books?id=f59h2ooQGmcC&pg=PA277|url-status=live}}</ref><ref>{{cite book|author=Fokko Jan Dijksterhuis|title=Lenses And Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century|url=https://books.google.com/books?id=KDBXCvx0-0oC&pg=PA98|access-date=11 May 2013|date=1 October 2005|publisher=Springer|isbn=978-1-4020-2698-0|page=98|archive-date=16 June 2016|archive-url=https://web.archive.org/web/20160616221604/https://books.google.com/books?id=KDBXCvx0-0oC&pg=PA98|url-status=live}}</ref> For his contributions to science, the [[Royal Society]] of London elected Huygens a Fellow in 1663, making him its first foreign member when he was just 34 years old.<ref>{{Cite journal |last=Kemeny |first=Maximilian Alexander |date=2016-03-31 |title="A Certain Correspondence": The Unification of Motion from Galileo to Huygens |url=https://ses.library.usyd.edu.au/handle/2123/15733 |journal=The University of Sydney |language=en |pages=80}}</ref><ref>{{cite book|author=Gerrit A. Lindeboom|title=Boerhaave and Great Britain: Three Lectures on Boerhaave with Particular Reference to His Relations with Great Britain|url=https://books.google.com/books?id=yOIUAAAAIAAJ&pg=PP15|access-date=11 May 2013|date=1974|publisher=Brill Archive|isbn=978-90-04-03843-1|page=15|archive-date=17 June 2016|archive-url=https://web.archive.org/web/20160617113611/https://books.google.com/books?id=yOIUAAAAIAAJ&pg=PP15|url-status=live}}</ref>

===France===
[[File:Christiaan-huygens2.jpg|thumb|upright=.9|Huygens, right of centre, from ''{{lang|fr|L'établissement de l'Académie des Sciences et fondation de l'observatoire}}, 1666'' by [[Henri Testelin]] (c. 1675)]]
The [[Montmor Academy]], started in the mid-1650s, was the form the old Mersenne circle took after his death.<ref>{{cite book|author=David J. Sturdy|title=Science and Social Status: The Members of the "Académie Des Sciences", 1666–1750|url=https://books.google.com/books?id=xLsNxkRXiNAC&pg=PA17|access-date=11 May 2013|date=1995|publisher=Boydell & Brewer|isbn=978-0-85115-395-7|page=17|archive-date=16 June 2016|archive-url=https://web.archive.org/web/20160616211016/https://books.google.com/books?id=xLsNxkRXiNAC&pg=PA17|url-status=live}}</ref> Huygens took part in its debates and supported those favouring experimental demonstration as a check on amateurish attitudes.<ref>{{cite book|title=The anatomy of a scientific institution: the Paris Academy of Sciences, 1666–1803|url=https://books.google.com/books?id=_G-MCYFN7R4C&pg=PA7|access-date=27 April 2013|date=1971|publisher=University of California Press|isbn=978-0-520-01818-1|page=7 note 12|archive-date=16 June 2016|archive-url=https://web.archive.org/web/20160616201537/https://books.google.com/books?id=_G-MCYFN7R4C&pg=PA7|url-status=live}}</ref> He visited Paris a third time in 1663; when the Montmor Academy closed down the next year, Huygens advocated for a more [[Baconian method|Baconian]] program in science. Two years later, in 1666, he moved to Paris on an invitation to fill a leadership position at [[Louis XIV|King Louis XIV]]'s new French [[French Academy of Sciences|Académie des sciences]].<ref>{{cite book|author=David J. Sturdy|title=Science and Social Status: The Members of the "Académie Des Sciences", 1666–1750|url=https://books.google.com/books?id=xLsNxkRXiNAC&pg=PA71|access-date=27 April 2013|date=1995|publisher=Boydell & Brewer|isbn=978-0-85115-395-7|pages=71–2|archive-date=17 June 2016|archive-url=https://web.archive.org/web/20160617112244/https://books.google.com/books?id=xLsNxkRXiNAC&pg=PA71|url-status=live}}</ref>

While at the Académie in Paris, Huygens had an important patron and correspondent in [[Jean-Baptiste Colbert]], First Minister to Louis XIV.<ref>{{cite book|author=Jacob Soll|title=The information master: Jean-Baptiste Colbert's secret state intelligence system|url=https://books.google.com/books?id=vVjru_uV_hoC&pg=PA99|access-date=27 April 2013|date=2009|publisher=University of Michigan Press|isbn=978-0-472-11690-4|page=99|archive-date=16 June 2016|archive-url=https://web.archive.org/web/20160616220714/https://books.google.com/books?id=vVjru_uV_hoC&pg=PA99|url-status=live}}</ref> His relationship with the French Académie was not always easy, and in 1670 Huygens, seriously ill, chose [[Francis Vernon]] to carry out a donation of his papers to the Royal Society in London should he die.<ref>A. E.  Bell, ''Christian Huygens'' (1950), pp. 65–6; [https://archive.org/stream/christianhuygens029504mbp#page/n79/mode/2up archive.org.]</ref> However, the aftermath of the [[Franco-Dutch War]] (1672–78), and particularly England's role in it, may have damaged his later relationship with the Royal Society.<ref>{{cite book|author=Jonathan I. Israel|title=Enlightenment Contested : Philosophy, Modernity, and the Emancipation of Man 1670–1752: Philosophy, Modernity, and the Emancipation of Man 1670–1752|url=https://books.google.com/books?id=7qAeKpIIxCsC&pg=PA210|access-date=11 May 2013|date=12 October 2006|publisher=OUP Oxford|isbn=978-0-19-927922-7|page=210|author-link=Jonathan I. Israel|archive-date=17 June 2016|archive-url=https://web.archive.org/web/20160617113007/https://books.google.com/books?id=7qAeKpIIxCsC&pg=PA210|url-status=live}}</ref> [[Robert Hooke]], as a Royal Society representative, lacked the finesse to handle the situation in 1673.<ref>{{cite book |author=Lisa Jardine |title=The Curious Life of Robert Hooke |date=2003 |publisher=HarperCollins |isbn=0-00-714944-1 |pages=180–3|author-link=Lisa Jardine }}</ref>

The physicist and inventor [[Denis Papin]] was an assistant to Huygens from 1671.<ref>{{cite book|author=Joseph Needham|title=Science and Civilisation in China: Military technology : the gunpowder epic|url=https://books.google.com/books?id=BZxSnd2Xyb0C&pg=PA556|access-date=22 April 2013|date=1974|publisher=Cambridge University Press|isbn=978-0-521-30358-3|page=556|author-link=Joseph Needham|archive-date=16 June 2016|archive-url=https://web.archive.org/web/20160616221807/https://books.google.com/books?id=BZxSnd2Xyb0C&pg=PA556|url-status=live}}</ref> One of their projects, which did not bear fruit directly, was the [[gunpowder engine]], a precursor of the [[internal combustion engine]] that used [[gunpowder]] as its fuel.<ref>{{Cite book |url=https://books.google.com/books?id=6zYTD5kUyZkC&pg=PA2 |title=Internal Combustion Engines |date=1988 |publisher=Academic Press |isbn=978-0-12-059790-1 |editor-last=Arcoumanis |editor-first=Constantine |series=Combustion Treatise |location= |pages=2}}</ref><ref>{{cite book|author=Joseph Needham|title=Military Technology: The Gunpowder Epic|url=https://books.google.com/books?id=hNcZJ35dIyUC&pg=PR31|access-date=22 April 2013|date=1986|publisher=Cambridge University Press|isbn=978-0-521-30358-3|page=xxxi|author-link=Joseph Needham|archive-date=16 June 2016|archive-url=https://web.archive.org/web/20160616211010/https://books.google.com/books?id=hNcZJ35dIyUC&pg=PR31|url-status=live}}</ref> Huygens made further astronomical observations at the Académie using the [[Paris Observatory|observatory]] recently completed in 1672. He introduced [[Nicolaas Hartsoeker]] to French scientists such as [[Nicolas Malebranche]] and [[Giovanni Cassini]] in 1678.<ref name=":14" /><ref>{{Cite journal|last=Abou-Nemeh|first=S. C.|date=2013|title=The Natural Philosopher and the Microscope: Nicolas Hartsoeker Unravels Nature's "Admirable Œconomy"|url=https://doi.org/10.1177/007327531305100101|journal=History of Science|language=en|volume=51|issue=1|pages=1–32|doi=10.1177/007327531305100101|s2cid=141248558|issn=0073-2753}}</ref>

The young diplomat Leibniz met Huygens while visiting Paris in 1672 on a vain mission to meet the French Foreign Minister [[Arnauld de Pomponne]]. Leibniz was working on a [[Stepped reckoner|calculating machine]] at the time and, after a short visit to London in early 1673, he was tutored in mathematics by Huygens until 1676.<ref name="Leibniz1996">{{cite book|author=Gottfried Wilhelm Freiherr von Leibniz|title=Leibniz: New Essays on Human Understanding|url=https://books.google.com/books?id=vD6nSUSbL7IC&pg=RA1-PR82|access-date=23 April 2013|date=7 November 1996|publisher=Cambridge University Press|isbn=978-0-521-57660-4|page=lxxxiii|archive-date=16 June 2016|archive-url=https://web.archive.org/web/20160616191719/https://books.google.com/books?id=vD6nSUSbL7IC&pg=RA1-PR82|url-status=live}}</ref> An extensive correspondence ensued over the years, in which Huygens showed at first reluctance to accept the advantages of Leibniz's [[infinitesimal calculus]].<ref>{{cite book|author=Marcelo Dascal|title=The practice of reason|url=https://books.google.com/books?id=4XhKkK9Ms70C&pg=PA45|access-date=23 April 2013|date=2010|publisher=John Benjamins Publishing|isbn=978-90-272-1887-2|page=45|archive-date=17 June 2016|archive-url=https://web.archive.org/web/20160617035625/https://books.google.com/books?id=4XhKkK9Ms70C&pg=PA45|url-status=live}}</ref>

===Final years===
[[File:Hofwijck (3).JPG|thumb|222px|[[Hofwijck]], Huygens's summer home; now a museum]]
Huygens moved back to The Hague in 1681 after suffering another bout of serious depressive illness. In 1684, he published ''Astroscopia Compendiaria'' on his new tubeless [[aerial telescope]]. He attempted to return to France in 1685 but the [[revocation of the Edict of Nantes]] precluded this move. His father died in 1687, and he inherited Hofwijck, which he made his home the following year.<ref name="Dictionary, p. 469"/>

On his third visit to England, Huygens met Newton in person on 12 June 1689. They spoke about [[Iceland spar]], and subsequently corresponded about resisted motion.<ref>{{cite book |author=Alfred Rupert Hall |title=Isaac Newton: Adventurer in thought |date=1996 |publisher=Cambridge University Press |page=[https://archive.org/details/isaacnewtonadven0000hall/page/232 232] |url=https://archive.org/details/isaacnewtonadven0000hall/page/232 |url-access=registration |author-link=Alfred Rupert Hall |isbn=9780631179023}}</ref>

Huygens returned to mathematical topics in his last years and observed the acoustical phenomenon now known as [[flanging]] in 1693.<ref>{{cite book|author=Curtis ROADS|title=The computer music tutorial|url=https://books.google.com/books?id=nZ-TetwzVcIC&pg=PA437|access-date=11 May 2013|date=1996|publisher=MIT Press|isbn=978-0-262-68082-0|page=437|archive-date=17 June 2016|archive-url=https://web.archive.org/web/20160617113110/https://books.google.com/books?id=nZ-TetwzVcIC&pg=PA437|url-status=live}}</ref> Two years later, on 8 July 1695, Huygens died in The Hague and was buried, like his father before him, in an unmarked grave at the [[Grote Kerk, The Hague|Grote Kerk]].<ref>{{cite web |url=http://www.grotekerkdenhaag.nl/ |title=GroteKerkDenHaag.nl |language=nl |publisher=GroteKerkDenHaag.nl |access-date=13 June 2010 |archive-url=https://web.archive.org/web/20170720102056/http://www.grotekerkdenhaag.nl/ |archive-date=20 July 2017 |url-status=dead }}</ref>

Huygens never married.<ref>{{Cite web|title=Christiaan Huygens|url=https://biography.yourdictionary.com/christiaan-huygens|access-date=2022-02-16|website=biography.yourdictionary.com|language=en}}</ref>