{{Short description|none}} <!-- "none" is preferred when the title is sufficiently descriptive; see [[WP:SDNONE]] -->
{{Use dmy dates|date=August 2026}}
{{Distinguished men of science of Great Britain 1806-7|align=right|size=400px}}
The '''19th century in science''' saw the birth of science as a profession; the term scientist was coined in 1833 by [[William Whewell]],<ref>{{cite encyclopedia
| access-date=3 March 2008
| url=http://www.science.uva.nl/~seop/entries/whewell/
| title=William Whewell| encyclopedia=Stanford Encyclopedia of Philosophy
| publisher=The Metaphysics Research Lab, Stanford University| date=2000-12-23
| last1=Snyder
| first1=Laura J.
}}</ref> which soon replaced the older term of (natural) philosopher.

Among the most influential ideas of the 19th century were those of [[Charles Darwin]] (alongside the independent research of [[Alfred Russel Wallace]]), who in 1859 published the book ''[[On the Origin of Species]]'', which introduced the idea of [[evolution]] by [[natural selection]]. Another important landmark in medicine and biology were the successful efforts to prove the [[germ theory of disease]]. Following this, [[Louis Pasteur]] made the first [[vaccine]] against [[rabies]], and also made many discoveries in the field of chemistry, including the [[optical isomerism|asymmetry of crystals]]. In chemistry, [[Dmitri Mendeleev]], following the [[atomic theory]] of [[John Dalton]], created the first [[periodic table]] of [[Chemical element|elements]]. In physics, the experiments, theories and discoveries of [[Michael Faraday]], [[Andre-Marie Ampere]], [[James Clerk Maxwell]], and their contemporaries led to the creation of [[electromagnetism]] as a new branch of science. [[Thermodynamics]] led to an understanding of heat and the notion of energy was defined.

The discovery of new types of radiation and the simultaneous revelation of the nature of atomic structure and matter are two additional highlights. In astronomy, the planet Neptune was discovered. In mathematics, the notion of complex numbers finally matured and led to a subsequent analytical theory; they also began the use of [[hypercomplex number]]s. [[Karl Weierstrass]] and others carried out the [[arithmetization of analysis]] for functions of [[Function of a real variable|real]] and [[complex variable]]s. It also saw rise to [[Non-Euclidean geometry|new progress in geometry]] beyond those classical theories of Euclid, after a period of nearly two thousand years. The mathematical science of logic likewise had revolutionary breakthroughs after a similarly long period of stagnation. But the most important step in science at this time were the ideas formulated by the creators of electrical science. Their work changed the face of physics and made possible for new technology to come about such as electric power, electrical telegraphy, the telephone, and radio.

==Mathematics==
Throughout the 19th century mathematics became increasingly abstract. [[Carl Friedrich Gauss]] (1777–1855) epitomizes this trend. He did revolutionary work on [[function (mathematics)|function]]s of [[complex variable]]s, in [[geometry]], and on the convergence of [[series (mathematics)|series]], leaving aside his many contributions to science. He also gave the first satisfactory proofs of the [[fundamental theorem of algebra]] and of the [[quadratic reciprocity law]].<ref>{{Cite journal|last=Brown|first=Ezra|date=April 1981|title=The First Proof of the Quadratic Reciprocity Law, Revisited|journal=The American Mathematical Monthly|volume=88|issue=4|pages=257–264|doi=10.2307/2320549|jstor=2320549}}</ref> His 1801 volume ''[[Disquisitiones Arithmeticae]]'' laid the foundations of modern number theory.<ref>{{Cite book|url=https://books.google.com/books?id=lYXuBwAAQBAJ|title=Mathematical Expeditions: Chronicles by the Explorers|last1=Laubenbacher|first1=Reinhard|last2=Pengelley|first2=David|publisher=Springer Science & Business Media|year=1999|isbn=9781461205234|location=New York|pages=167|language=en}}</ref>

[[Image:noneuclid.svg|right|thumb|400px|Behavior of lines with a common perpendicular in each of the three types of geometry]]
This century saw the development of the two forms of [[non-Euclidean geometry]], where the [[parallel postulate]] of [[Euclidean geometry]] no longer holds.
The Russian mathematician [[Nikolai Ivanovich Lobachevsky]] and his rival, the Hungarian mathematician [[János Bolyai]], independently defined and studied [[hyperbolic geometry]], where uniqueness of parallels no longer holds.<ref>{{Cite journal|last1=Cannon|first1=James W.|last2=Floyd|first2=William J.|last3=Kenyon|first3=Richard|last4=Walter|last5=Parry|first5=R.|date=1997|title=Hyperbolic geometry|journal=Flavors of Geometry|publisher=MSRI Publications|volume=51|pages=59–115|doi=10.1017/9781009701853.003 |isbn=978-1-009-70185-3 }}</ref> In this geometry the sum of angles in a triangle add up to less than 180°. [[Elliptic geometry]] was developed later in the 19th century by the German mathematician [[Bernhard Riemann]]; here no parallel can be found and the angles in a triangle add up to more than 180°.<ref>{{Cite journal|last=Rudnev|first=S.V.|date=1988|title=Application of elliptic Reimannian geometry to problems of crystallography|journal=Computers & Mathematics with Applications|language=en|volume=16|issue=5–8|pages=597–616|doi=10.1016/0898-1221(88)90249-0|issn=0898-1221|doi-access=free}}</ref> Riemann also developed [[Riemannian geometry]], which unifies and vastly generalizes the three types of geometry.<ref>{{Cite web|url=http://www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf|title=An Introduction to Riemannian Geometry|last=Gudmundsson|first=Sigmundur|date=27 September 2018|publisher=[[Lund University]]|access-date=10 December 2018}}</ref>

The 19th century saw the beginning of a great deal of [[abstract algebra]]. [[Hermann Grassmann]] in Germany gave a first version of [[vector space]]s,<ref>{{Cite journal|last=Fearnley-Sander|first=Desmond|date=1979|title=Hermann Grassmann and the Creation of Linear Algebra|journal=American Mathematical Monthly|volume=86|issue=10|pages=809–817|doi=10.1080/00029890.1979.11994921}}</ref> [[William Rowan Hamilton]] in Ireland developed [[noncommutative algebra]].<ref>{{Cite journal|last=Spearman|first=T. D|date=1993|title=William Rowan Hamilton, 1805-1865|journal=Proceedings of the Royal Irish Academy, Section A|volume=95A|pages=1–12|jstor=20490182}}</ref> The British mathematician [[George Boole]] devised an algebra that soon evolved into what is now called [[Boolean algebra]], in which the only numbers were 0 and 1. Boolean algebra is the starting point of [[mathematical logic]] and has important applications in [[computer science]].<ref>{{Cite journal|url=https://www.maa.org/press/periodicals/convergence/origins-of-boolean-algebra-in-the-logic-of-classes-george-boole-john-venn-and-c-s-peirce|title=Origins of Boolean Algebra in the Logic of Classes: George Boole, John Venn and C. S. Peirce|last=Heine Barnett|first=Janet|date=July 2013|website=Mathematical Association of America|language=en|doi=10.4169/loci003997|doi-broken-date=18 January 2026|access-date=2018-12-09|url-access=subscription|archive-date=16 March 2024|archive-url=https://web.archive.org/web/20240316192647/https://maa.org/press/periodicals/convergence/origins-of-boolean-algebra-in-the-logic-of-classes-george-boole-john-venn-and-c-s-peirce|url-status=dead}}</ref>

[[Augustin-Louis Cauchy]], [[Bernhard Riemann]], and [[Karl Weierstrass]] reformulated the calculus in a more rigorous fashion.<ref>{{Cite book|chapter-url=https://books.google.com/books?id=2hDvzITtfdAC|title=Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences|last=Grattan-Guinness|first=I.|publisher=Johns Hopkins University Press|year=1994|isbn=9780801873966|location=Baltimore and London|pages=419|language=en|chapter=Three traditions in complex analysis: Cauchy, Riemann and Weierstrass}}</ref>

Also, for the first time, the limits of mathematics were explored. [[Niels Henrik Abel]], a Norwegian, and [[Évariste Galois]], a Frenchman, proved that there is no general algebraic method for solving polynomial equations of degree greater than four ([[Abel–Ruffini theorem]]).<ref>{{Cite journal|last=Edixhoven|first=Bas|date=4 November 2013|title=Galois theory and the Abel-Ruffini theorem|url=http://pub.math.leidenuniv.nl/~edixhovensj/talks/2013/indonesia/yogya/workshop.pdf|journal=Gadjah Mada University Lecture}}</ref> Other 19th-century mathematicians utilized this in their proofs that straightedge and compass alone are not sufficient to [[trisect an arbitrary angle]], to construct the side of a cube twice the volume of a given cube, nor to construct a square equal in area to a given circle. Mathematicians had vainly attempted to solve all of these problems since the time of the ancient Greeks. On the other hand, the limitation of three [[dimension]]s in geometry was surpassed in the 19th century through considerations of [[parameter space]] and [[hypercomplex number]]s.

In the later 19th century, [[Georg Cantor]] established the first foundations of [[set theory]], which enabled the rigorous treatment of the notion of infinity and has become the common language of nearly all mathematics.<ref>{{Cite journal|last=Srivastava|first=S.M.|date=November 2015|title=How did Cantor discover set theory and topology?|url=https://www.ias.ac.in/article/fulltext/reso/019/11/0977-0999|journal=Resonance: Journal of Science Education|volume=19|issue=11|pages=977–999|doi=10.1007/s12045-014-0117-8|s2cid=119608038|url-access=subscription}}</ref> Cantor's set theory, and the rise of [[mathematical logic]] in the hands of [[Peano]], [[L. E. J. Brouwer]], [[David Hilbert]], [[Bertrand Russell]], and [[A.N. Whitehead]], initiated a long running debate on the [[foundations of mathematics]].

The 19th century saw the founding of a number of national mathematical societies: the [[London Mathematical Society]] in 1865,<ref>{{Cite web|url=https://www.lms.ac.uk/about/history|title=History {{!}} London Mathematical Society|website=lms.ac.uk|access-date=2018-12-09}}</ref> the [[Société Mathématique de France]] in 1872,<ref>{{Cite book|url=https://books.google.com/books?id=AUwuAQAAIAAJ|title=La France mathématique: la Société mathématique de France (1872-1914)|last=Gispert-Chambaz|first=Hélène|date=1991|publisher=Sociét́ française d'histoire des sciences et des techniques|isbn=9782856290125|language=fr}}</ref> the [[Edinburgh Mathematical Society]] in 1883,<ref>{{Cite web|url=https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/information|title=Proceedings of the Edinburgh Mathematical Society|website=Cambridge Core|language=en|access-date=2018-12-09}}</ref> the [[Circolo Matematico di Palermo]] in 1884,<ref>{{Cite book|url=https://books.google.com/books?id=eMRlDwAAQBAJ|title=Giovanni Battista Guccia: Pioneer of International Cooperation in Mathematics|last1=Bongiorno|first1=Benedetto|last2=Curbera|first2=Guillermo P.|publisher=Springer|year=2018|isbn=9783319786674|pages=95|language=en}}</ref> and the [[American Mathematical Society]] in 1888.<ref>{{Cite journal|last=Archibald|first=Raymond Clare|date=1939|title=History of the American Mathematical Society, 1888–1938|url=https://projecteuclid.org/euclid.bams/1183501056|journal=Bulletin of the American Mathematical Society|language=EN|volume=45|issue=1|pages=31–46|issn=1936-881X|doi=10.1090/s0002-9904-1939-06908-5|doi-access=free}}</ref> The first international, special-interest society, the [[Quaternion Society]], was formed in 1899, in the context of a [[hyperbolic quaternion#Historical review|vector controversy]].<ref>{{Cite web|url=http://www-history.mcs.st-andrews.ac.uk/Societies/Quaternion.html|title=Quaternion Association|website=www-history.mcs.st-andrews.ac.uk|access-date=2018-12-09}}</ref>

==Physics==
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|upright|left|[[Michael Faraday]]<br/>(1791–1867)]]

In 1800, [[Alessandro Volta]] invented the electric battery (known as the [[voltaic pile]]) and thus improved the way electric currents could also be studied.<ref>{{Cite web|url=https://www.aps.org/publications/apsnews/200603/history.cfm|title=This Month in Physics History: March 20, 1800: Volta describes the Electric Battery|website=aps.org|language=en|access-date=2018-12-09}}</ref> A year later, [[Thomas Young (scientist)|Thomas Young]] demonstrated the wave nature of light—which received strong experimental support from the work of [[Augustin-Jean Fresnel]]—and the principle of interference.<ref>{{Cite web|url=https://www.bbvaopenmind.com/en/thomas-young-and-the-wave-nature-of-light/|title=Thomas Young and the Wave Nature of Light|last=Beléndez|first=Augusto|date=2015-06-13|website=OpenMind|language=en-US|access-date=2018-12-09}}</ref> In 1813, [[Peter Ewart]] supported the idea of the conservation of energy in his paper ''On the measure of moving force''.<ref>{{Cite book|url=https://archive.org/details/annalsphilosoph12thomgoog|title=Annals of Philosophy, Or, Magazine of Chemistry, Mineralogy, Mechanics, Natural History, Agriculture, and the Arts|last=Thomson|first=Thomas|publisher=Robert Baldwin|year=1818|pages=445|language=en}}</ref> In 1820, [[Hans Christian Ørsted]] found that a current-carrying conductor gives rise to a magnetic force surrounding it, and within a week after Ørsted's discovery reached France, [[André-Marie Ampère]] discovered that two parallel electric currents will exert forces on each other.<ref>{{Cite journal|last1=Blondel|first1=Christine|last2=Benseghira|first2=Abdelmadjid|date=18 April 2017|title=The key role of Oersted's and Ampère's 1820 electromagnetic experiments in the construction of the concept of electric current|journal=American Journal of Physics|volume=85|issue=5|pages=369–380|doi=10.1119/1.4973423|bibcode=2017AmJPh..85..369B}}</ref> In 1821, [[William Rowan Hamilton|William Hamilton]] began his analysis of Hamilton's characteristic function.<ref>{{Cite book|url=https://archive.org/details/in.ernet.dli.2015.213327|title=Geometrical Optics: An Introduction to Hamilton's Method|last=Synge|first=J. L.|date=1937-01-02|publisher=Cambridge University Press|isbn=9780521065900|language=en|bibcode=1937geop.book.....S}}</ref> In 1821, [[Michael Faraday]] built an electricity-powered motor,<ref>{{Cite web|url=http://www.rigb.org/our-history/iconic-objects/iconic-objects-list/faradays-motor|title=Michael Faraday's electric magnetic rotation apparatus (motor)|website=rigb.org|language=en|access-date=2018-12-09}}</ref> while [[Georg Ohm]] stated his law of electrical resistance in 1826, expressing the relationship between voltage, current, and resistance in an electric circuit.<ref>{{Cite journal|last=Gupta|first=Madhu|date=1980|title=Georg Simon Ohm and Ohm's Law|url=https://www.researchgate.net/publication/3052303|journal=IEEE Transactions on Education|volume=23|issue=3|pages=156–162|doi=10.1109/TE.1980.4321401|bibcode=1980ITEdu..23..156G|s2cid=32495985}}</ref> A year later, botanist [[Robert Brown (Scottish botanist from Montrose)|Robert Brown]] discovered [[Brownian motion]]: pollen grains in water undergoing movement resulting from their bombardment by the fast-moving atoms or molecules in the liquid.<ref>{{Cite web|url=http://web2.uwindsor.ca/courses/physics/high_schools/2005/Brownian_motion/discovery.html|title=The Discovery of Brownian Motion|website=web2.uwindsor.ca|access-date=2018-12-09}}</ref> In 1829, [[Gaspard-Gustave Coriolis|Gaspard Coriolis]] introduced the terms of [[Work (physics)|work]] (force times distance) and [[kinetic energy]] with the meanings they have today.<ref name=":0">{{Cite journal|last=Persson|first=Anders|date=July 1998|title=How Do We Understand the Coriolis Force?|journal=Bulletin of the American Meteorological Society|volume=79|issue=7|pages=1373–1385|doi=10.1175/1520-0477(1998)079<1373:HDWUTC>2.0.CO;2|bibcode=1998BAMS...79.1373P|doi-access=free}}</ref>

In 1831, Faraday (and independently [[Joseph Henry]]) discovered the reverse effect, the production of an electric potential or current through magnetism&nbsp;– known as [[Faraday's law of induction|electromagnetic induction]]; these two discoveries are the basis of the electric motor and the electric generator, respectively.<ref>{{Cite web|url=https://www.livescience.com/53509-faradays-law-induction.html|title=What Is Faraday's Law of Induction?|last=Lucas|first=Jim|website=Live Science|access-date=2018-12-09}}</ref> In 1834, [[Carl Gustav Jakob Jacobi|Carl Jacobi]] discovered his uniformly rotating self-gravitating ellipsoids (the [[Jacobi ellipsoid]]).<ref>{{Cite book|url=https://books.google.com/books?id=px_vBwAAQBAJ|title=Joseph Liouville 1809–1882: Master of Pure and Applied Mathematics|last=Lützen|first=Jesper|publisher=Springer Science & Business Media|year=1990|isbn=9781461209898|pages=479|language=en}}</ref> In 1834, [[John Scott Russell|John Russell]] observed a nondecaying solitary water wave ([[soliton]]) in the [[Union Canal (Scotland)|Union Canal]] near [[Edinburgh]] and used a water tank to study the dependence of solitary water wave velocities on wave amplitude and water depth.<ref>{{Cite web|url=http://www.ma.hw.ac.uk/solitons/press.html|title=Recreating the Soliton on the Scott Russell Aqueduct|website=ma.hw.ac.uk|access-date=2018-12-09|archive-date=29 April 2022|archive-url=https://web.archive.org/web/20220429202747/http://www.ma.hw.ac.uk/solitons/press.html|url-status=dead}}</ref> In 1835, William Hamilton stated [[Hamiltonian mechanics|Hamilton's canonical equations of motion]].<ref>{{Cite book|url=https://books.google.com/books?id=Bmcpsgp-Ml4C|title=A Cultural History of Physics|last=Simonyi|first=Károly|publisher=CRC Press|year=2012|isbn=9781568813295|pages=316|language=en}}</ref> In the same year, [[Gaspard-Gustave Coriolis|Gaspard Coriolis]] examined theoretically the mechanical efficiency of waterwheels, and deduced the [[Coriolis effect]].<ref name=":0" /> In 1841, [[Julius Robert von Mayer]], an amateur scientist, wrote a paper on the conservation of energy but his lack of academic training led to its rejection.<ref>{{Cite journal|last1=Moore|first1=Carl E.|last2=von Smolinski|first2=Alfred|last3=Claus|first3=Albert|last4=Graham|first4=Daniel J.|last5=Jaselskis|first5=Bruno|date=2014|title=On the First Law of Thermodynamics and the Contribution of Julius Robert Mayer: New Translation and Consideration of a Rejected Manuscript|url=http://acshist.scs.illinois.edu/bulletin_open_access/v39-2/v39-2%20p122-130.pdf|journal=[[Bulletin for the History of Chemistry]]|volume=39|issue=2|pages=122–130 |doi=10.70359/bhc2014v039p122 }}</ref> In 1842, [[Christian Doppler]] proposed the [[Doppler effect]]. In 1847, [[Hermann von Helmholtz]] formally stated the law of conservation of energy.<ref>{{Cite web|url=http://www-groups.dcs.st-and.ac.uk/history/Biographies/Helmholtz.html|title=Hermann von Helmholtz biography|website=www-groups.dcs.st-and.ac.uk|access-date=2018-12-10}}</ref> In 1851, [[Léon Foucault]] showed the Earth's rotation with a huge [[pendulum]] ([[Foucault pendulum]]).<ref>{{Cite web|url=https://www.aps.org/publications/apsnews/200702/history.cfm|title=This Month in Physics History: February 3, 1851: Léon Foucault demonstrates that Earth rotates|date=February 2007|website=aps.org|language=en|access-date=2018-12-10}}</ref>

There were important advances in [[continuum mechanics]] in the first half of the century, namely formulation of [[elastic modulus|laws of elasticity]] for solids and discovery of [[Navier–Stokes equations]] for fluids.

===Laws of thermodynamics===
{{further|History of thermodynamics}}
[[File:Baron Kelvin 1906.jpg|thumb|200px|right|{{nowrap|[[William Thomson, 1st Baron Kelvin|William Thomson (Lord Kelvin)]]<br/>(1824–1907)}}]]
In the 19th century, the connection between heat and mechanical energy was established quantitatively by [[Julius Robert von Mayer]] and [[James Prescott Joule]], who measured the mechanical equivalent of heat in the 1840s.<ref>{{Cite journal|last=Kipnis|first=Nahum|date=October 2014|title=Thermodynamics and Mechanical Equivalent of Heat|url=https://www.researchgate.net/publication/272039175|journal=Science & Education|volume=23|issue=10|pages=2007–2044|doi=10.1007/s11191-014-9698-6|bibcode=2014Sc&Ed..23.2007K|s2cid=123317474}}</ref> In 1849, Joule published results from his series of experiments (including the paddlewheel experiment) which show that heat is a form of energy, a fact that was accepted in the 1850s. The relation between heat and energy was important for the development of steam engines, and in 1824 the experimental and theoretical work of [[Nicolas Léonard Sadi Carnot|Sadi Carnot]] was published.<ref>{{Cite web|url=https://www.aps.org/publications/apsnews/200906/physicshistory.cfm|title=This Month in Physics History: June 12, 1824: Sadi Carnot publishes treatise on heat engines|date=June 2009|website=aps.org|access-date=2018-12-10}}</ref> Carnot captured some of the ideas of thermodynamics in his discussion of the efficiency of an idealized engine. Sadi Carnot's work provided a basis for the formulation of the [[first law of thermodynamics]]—a restatement of the [[law of conservation of energy]]—which was stated around 1850 by [[William Thomson, 1st Baron Kelvin|William Thomson]], later known as Lord Kelvin, and [[Rudolf Clausius]]. Lord Kelvin, who had extended the concept of absolute zero from gases to all substances in 1848, drew upon the engineering theory of [[Lazare Carnot]], Sadi Carnot, and [[Émile Clapeyron]]–as well as the experimentation of James Prescott Joule on the interchangeability of mechanical, chemical, thermal, and electrical forms of work—to formulate the first law.<ref>{{Cite book|chapter-url=https://books.google.com/books?id=dw_vAAAAMAAJ|title=A New Kind of Science|last=Wolfram|first=Stephen|publisher=Wolfram Media|year=2002|pages=1019|language=en|chapter=Irreversibility and the Second Law of Thermodynamics|isbn=9781579550080}}</ref>

Kelvin and Clausius also stated the [[second law of thermodynamics]], which was originally formulated in terms of the fact that heat does not spontaneously flow from a colder body to a hotter. Other formulations followed quickly (for example, the second law was expounded in Thomson and [[Peter Guthrie Tait]]'s influential work ''Treatise on Natural Philosophy'') and Kelvin in particular understood some of the law's general implications.<ref>{{Cite web|url=https://www.brighthubengineering.com/thermodynamics/4456-different-statements-of-second-law-of-thermodynamics/|title=Different Statements of Second Law of Thermodynamics, Kelvin-Planck statement of second law of thermodynamics and Clausius statement of second law of thermodynamics.|last=Khemani|first=Haresh|date=2008-08-14|website=Bright Hub Engineering|language=en-US|access-date=2018-12-10}}</ref> The second Law was the idea that gases consist of molecules in motion had been discussed in some detail by [[Daniel Bernoulli]] in 1738, but had fallen out of favor, and was revived by Clausius in 1857. In 1850, [[Hippolyte Fizeau]] and [[Léon Foucault]] measured the [[speed of light]] in water and find that it is slower than in air, in support of the wave model of light.<ref>{{Cite web|url=http://www.thestargarden.co.uk/Speed-of-light.html|title=Measuring the Speed of Light|date=2017-10-26|website=The Star Garden|language=en|access-date=2018-12-10}}</ref> In 1852, Joule and Thomson demonstrated that a rapidly expanding gas cools, later named the [[Joule–Thomson effect]] or Joule–Kelvin effect.<ref>{{Cite web|url=https://neutrium.net/fluid_flow/joule-thomson-cooling/|title=Joule-Thomson Effect|date=14 September 2015|website=Neutrium|access-date=2018-12-10}}</ref> [[Hermann von Helmholtz]] puts forward the idea of the [[heat death of the universe]] in 1854,<ref>{{Cite web|url=https://www.brighthub.com/education/homework-tips/articles/37457.aspx|title=What is Heat Death. Definition and Origin of the Term Heat Death|last=Cooper|first=Dr Crystal|date=2009-05-31|website=Bright Hub|language=en-US|access-date=2018-12-10}}</ref> the same year that Clausius established the importance of ''dQ/T'' ([[Clausius's theorem]]) (though he did not yet name the quantity).<ref>{{Cite journal|last1=Cerruti|first1=Luigi|last2=Ghibaudi|first2=Elena|last3=Pellegrino|first3=Emilio|last4=Pellegrino|first4=Emilio Marco|last5=Ghibaudi|first5=Elena|last6=Cerruti|first6=Luigi|date=25 June 2015|title=Clausius' Disgregation: A Conceptual Relic that Sheds Light on the Second Law|journal=Entropy|language=en|volume=17|issue=7|pages=4500–4518|doi=10.3390/e17074500|bibcode=2015Entrp..17.4500P|doi-access=free|hdl=2318/1522382|hdl-access=free}}</ref>

===James Clerk Maxwell===
[[File:James Clerk Maxwell big.jpg|thumb|180px|left|[[James Clerk Maxwell]]<br/>(1831–1879)]]
In 1859, [[James Clerk Maxwell]] discovered the [[Maxwell–Boltzmann distribution|distribution law of molecular velocities]]. Maxwell showed that electric and magnetic fields are propagated outward from their source at a speed equal to that of light and that light is one of several kinds of electromagnetic radiation, differing only in frequency and wavelength from the others. In 1859, Maxwell worked out the mathematics of the distribution of velocities of the molecules of a gas.<ref>{{Cite web|url=https://nationalmaglab.org/education/magnet-academy/history-of-electricity-magnetism/pioneers/james-clerk-maxwell|title=James Clerk Maxwell – MagLab|website=nationalmaglab.org|language=en-GB|access-date=2018-12-10}}</ref> The wave theory of light was widely accepted by the time of Maxwell's work on the electromagnetic field, and afterward the study of light and that of electricity and magnetism were closely related. In 1864 James Maxwell published his papers on a dynamical theory of the electromagnetic field, and stated that light is an electromagnetic phenomenon in the 1873 publication of Maxwell's ''[[A Treatise on Electricity and Magnetism|Treatise on Electricity and Magnetism]]''. This work drew upon theoretical work by German theoreticians such as [[Carl Friedrich Gauss]] and [[Wilhelm Eduard Weber|Wilhelm Weber]]. The encapsulation of heat in particulate motion, and the addition of electromagnetic forces to Newtonian dynamics established an enormously robust theoretical underpinning to physical observations.<ref>{{Cite book|url=https://global.oup.com/academic/product/a-treatise-on-electricity-and-magnetism-9780198503736?cc=ro&lang=en&#|title=A Treatise on Electricity and Magnetism: Volume 1|last=Maxwell|first=James Clerk|publisher=Oxford University Press|year=1998|isbn=9780198503736|series=Oxford Classic Texts in the Physical Sciences|location=Oxford, New York}}</ref>

The prediction that light represented a transmission of energy in wave form through a "[[Luminiferous aether|luminiferous ether]]", and the seeming confirmation of that prediction with Helmholtz student [[Heinrich Hertz]]'s 1888 detection of [[electromagnetic radiation]], was a major triumph for physical theory and raised the possibility that even more fundamental theories based on the field could soon be developed. Experimental confirmation of Maxwell's theory was provided by Hertz, who generated and detected electric waves in 1886 and verified their properties, at the same time foreshadowing their application in radio, television, and other devices.<ref>{{Cite web|url=https://www.aaas.org/heinrich-hertz-and-electromagnetic-radiation|title=Heinrich Hertz and electromagnetic radiation|website=American Association for the Advancement of Science|language=en|access-date=2018-12-10}}</ref> In 1887, Heinrich Hertz discovered the [[photoelectric effect]].<ref>{{Cite journal|last=Wofford|first=Thomas|date=2008|title=Hertz, Einstein, and the photoelectric effect|journal=Physics Today|volume=61, 5, 10|issue=5|pages=10|doi=10.1063/1.2930718|bibcode=2008PhT....61e..10W|doi-access=free}}</ref> Research on the electromagnetic waves began soon after, with many scientists and inventors conducting experiments on their properties. In the mid to late 1890s [[Guglielmo Marconi]] developed a [[radio wave]] based [[wireless telegraphy]] system<ref>{{Cite book|url=https://books.google.com/books?id=hX1jPbJVSu4C&dq=invention+of+radio&pg=PA193|title=Groundbreaking Scientific Experiments, Inventions, and Discoveries of the 19th Century|last=Windelspecht|first=Michael|publisher=Greenwood Publishing Group|year=2003|isbn=9780313319693|location=Westport, CN|pages=193|language=en}}</ref> (see [[invention of radio]]).

The atomic theory of matter had been proposed again in the early 19th century by the chemist John Dalton and became one of the hypotheses of the kinetic-molecular theory of gases developed by Clausius and James Clerk Maxwell to explain the laws of thermodynamics. The kinetic theory in turn led to the statistical mechanics of [[Ludwig Boltzmann]] (1844–1906) and [[Josiah Willard Gibbs]] (1839–1903), which held that energy (including heat) was a measure of the speed of particles. Interrelating the statistical likelihood of certain states of organization of these particles with the energy of those states, Clausius reinterpreted the dissipation of energy to be the statistical tendency of molecular configurations to pass toward increasingly likely, increasingly disorganized states (coining the term "[[entropy]]" to describe the disorganization of a state).<ref>{{Cite web|url=https://www.asme.org/engineering-topics/articles/heat-transfer/rudolf-julius-emanuel-clausius|title=Rudolf Julius Emanuel Clausius|last=Crawford|first=Mark|date=April 2012|website=American Society of Mechanical Engineers (ASME)|access-date=10 December 2018}}</ref> The statistical versus absolute interpretations of the second law of thermodynamics set up a dispute that would last for several decades (producing arguments such as "[[Maxwell's demon]]"), and that would not be held to be definitively resolved until the behavior of atoms was firmly established in the early 20th century.<ref>{{Cite journal|last=Bennett|first=Charles H.|date=1987-11-01|title=Demons, Engines and the Second Law|url=https://ecee.colorado.edu/~ecen5555/SourceMaterial/DemonsEnginesAndSecondLaw87.pdf|journal=Scientific American|volume=257|issue=5|pages=108–116|doi=10.1038/scientificamerican1187-108|issn=0036-8733|bibcode=1987SciAm.257e.108B|access-date=10 December 2018|archive-date=3 December 2020|archive-url=https://web.archive.org/web/20201203173214/https://ecee.colorado.edu/~ecen5555/SourceMaterial/DemonsEnginesAndSecondLaw87.pdf|url-status=dead}}</ref> In 1902, [[James Jeans]] found the length scale required for gravitational perturbations to grow in a static nearly homogeneous medium.

==Chemistry==
{{Expand section|date=May 2023}}

=== First synthesis of an organic compound ===
''see more about this in [[Wöhler synthesis]]''

In 1828, [[Friedrich Wöhler]] synthesized urea from certain inorganic compounds. He synthesized urea by slowly evaporating a water solution of ammonium cyanate, which he had prepared by adding silver cyanate to ammonium chloride. It has been previously believed that the substances produced by plants and animals (by generally all living beings or organisms) can not be produced in lab and can only be produced by "life force". This synthesis of urea changed that concept, which led to many discoveries later.<ref>
{{cite journal |journal=Mayo Clinic Proceedings |title=Early German Physician First To Synthesize Urea 
|url=https://www.mayoclinicproceedings.org/article/S0025-6196(12)60740-X/pdf 
|first1=Marc A. |last1=Shampo, Ph.D. |first2=Robert A.  |last2=Kyle, M.D
|volume=60 |date=Oct 1985 |issue=10 
|page=662 
|doi=10.1016/S0025-6196(12)60740-X 
|pmid=3897732 
|access-date=27 August 2024}}</ref>

=== Dalton's Atomic theory ===
[[File:John Dalton by Charles Turner.jpg|thumb|230x230px|John Dalton was an English chemist, physicist and meteorologist. He is best known for introducing the atomic theory into chemistry.]]In 19th century, [[John Dalton]] proposed the idea of atoms as small indivisible particles which together can form compounds. Although the concept of the atom dates back to the ideas of Democritus, John Dalton formulated the first modern description of it as the fundamental building block of chemical structures. Dalton developed the law of multiple proportions (first presented in 1803) by studying and expanding upon the works of Antoine Lavoisier and Joseph Proust.

The main points of Dalton's atomic theory, as it eventually developed, are:

# Elements are made of extremely small particles called [[atom]]s.
# Atoms of a given element are identical in size, mass and other properties; atoms of different elements differ in size, mass and other properties.
# Atoms cannot be subdivided, created or destroyed.
# Atoms of different elements combine in simple whole-number ratios to form [[chemical compounds]].
# In [[chemical reactions]], atoms are combined, separated or rearranged.

=== Periodic Table ===
''see more about this in detail'' ''in [[History of the periodic table]],''
[[File:Mendelejevs periodiska system 1871.png|thumb|283x283px|Mendeleev's periodic table]]
In 1869, Russian chemist Dmitri Mendeleev created the framework that became the modern periodic table, leaving gaps for elements that were yet to be discovered. While arranging the elements according to their atomic weight, if he found that they did not fit into the group he would rearrange them. Mendeleev predicted the properties of some undiscovered elements and gave them names such as "eka-aluminium" for an element with properties similar to aluminium. Later eka-aluminium was discovered as gallium. Some discrepancies remained; the position of certain elements, such as iodine and tellurium, could not be explained.

==Engineering and technology==

[[File:Thomas Edison, 1878.jpg|thumb|[[Thomas Edison]] was an American inventor and businessman whose companies developed many devices that greatly influenced life around the world, including the [[phonograph]], a [[Movie camera|motion picture camera]], and a long-lasting, practical electric [[light bulb]].]]
[[File:Erster Benzin-Omnibus der Welt.jpg|thumb|First motor bus in history: the [[Karl Benz|Benz]] Omnibus, built in 1895 for the Netphener bus company]]
* 1804: First [[steam locomotive]] begins operation.
* 1825: [[Erie Canal]] opened connecting the [[Great Lakes]] to the Atlantic Ocean.
* 1825: First isolation of aluminium.
* 1825: The [[Stockton and Darlington Railway]], the first public railway in the world, is opened.
* 1826: [[Samuel Morey]] patents the [[internal combustion engine]].
* 1829: First [[electric motor]] built.
* 1837: [[Telegraphy]] patented.
* 1841: The word "[[dinosaur]]" is coined by [[Richard Owen]]
* 1844: First publicly funded [[telegraph]] line in the world—between Baltimore and Washington—sends demonstration message on 24 May, ushering in the age of the telegraph. This message read "What hath God wrought?" (Bible, Numbers 23:23)
* 1849: The [[safety pin]] and the [[gas mask]] are invented.
* 1855: [[Bessemer process]] enables steel to be mass-produced.
* 1856: World's first [[oil refinery]] in Romania
* 1858: Invention of the [[phonautograph]], the first true device for [[recorded sound|recording sound]].
* 1863: First section of the [[London Underground]] opens.
* 1866: Successful [[transatlantic telegraph cable]] follows an earlier attempt in 1858.
* 1867: [[Alfred Nobel]] invents [[dynamite]].
* 1869: [[First transcontinental railroad]] completed in United States on 10 May.
* 1870: [[Rasmus Malling-Hansen]]'s invention the [[Hansen Writing Ball]] becomes the first commercially sold [[typewriter]].
* 1873: [[Jeans|Blue jeans]] and [[barbed wire]] are invented.
* 1877: [[Thomas Edison]] invents the [[phonograph]]
* 1878: First commercial [[telephone exchange]] in [[New Haven, Connecticut]].
* 1879: [[Thomas Edison]] tests his first [[light bulb]].
* 1881: First electrical [[power plant]] and [[Electricity distribution|grid]] in [[Godalming]], Britain.
* 1884: Sir [[Hiram Maxim]] invents the first self-powered Machine gun.
* 1885: [[Singer Manufacturing Company|Singer]] begins production of the '[[Singer Model 27 and 127|Vibrating Shuttle]]'. which would become the most popular model of [[sewing machine]].
* 1886: [[Karl Benz]] sells the first commercial [[automobile]].
* 1888: [[Galileo Ferraris]] and [[Nikola Tesla]] both introduce the idea of a rotating magnetic field [[induction motor]].
* 1890: The [[cardboard box]] is invented.
* 1892: [[John Froelich]] develops and constructs the first gasoline/petrol-powered [[tractor]].
* 1894: [[Karl Elsener (inventor)|Karl Elsener]] invents the [[Swiss Army knife]].
* 1894: First [[gramophone record]].
* 1895: [[Wilhelm Röntgen]] identifies [[x-rays]].
* 1896: [[Guglielmo Marconi]] applies for patent for the first radio wave base communication system.

==Biology and medicine==
{{see also|History of paleontology}}

In 1859, [[Charles Darwin]] published the book ''[[The Origin of Species]]'', which introduced the idea of [[evolution]] by [[natural selection]].<br>
[[Oscar Hertwig]] publishes his findings in reproductive and developmental biology. In 1875 he published his first work, being the first to correctly describe animal [[Conception (biology)|conception]]. In his later work in 1885, he described that the nucleus contained nuclein (now called [[nucleic acid]]) and that these nuclein were responsible for the transmission of hereditary characteristics.

===Medicine===
* 1804: [[Morphine]] first isolated.
* 1842: [[Anaesthesia]] used for the first time.
* 1855: [[Cocaine]] is isolated by [[Friedrich Gaedcke]].
* 1885: [[Louis Pasteur]] creates the first successful [[vaccine]] against rabies for a young boy who had been bitten 14 times by a rabid dog.
* 1889: [[Aspirin]] patented.

==Social sciences==
In 1871, [[William Stanley Jevons]] and [[Carl Menger]], working independently, solved [[Adam Smith]]'s [[paradox of value]] with the insight that people valued each additional unit of a good less than the previous unit. In 1874, [[Léon Walras]] independently came to a similar insight. Menger's student [[Friedrich von Wieser]] coined the term "[[marginal utility]]" to describe the new theory. Modern microeconomics is built on the insights of the Marginal Revolution.

===Economics===
* 1871: [[Marginalism]] introduced in economic theory.
* 1821: Comparative advantage in business was introduced by David Ricardo.
* 1824: The patronage of infant industries was explained by Friedrich List.
* 1828: The economic cooperative theory was stated by Charles Fourier.
* 1874: The law of general equilibrium was stated by Leon Walras from the Lausanne school.

==People==
<gallery widths="120" heights="140" perrow="7">
File:Carl Friedrich Gauss 1840 by Jensen.jpg|[[Carl Friedrich Gauss]]
File:Charles Robert Darwin by John Collier cropped.jpg|[[Charles Darwin]]
File:Kramskoy Mendeleev 01.jpg|[[Dmitri Mendeleev]]
File:Louis Pasteur.jpg|[[Louis Pasteur]], 1878
File:Mariecurie.jpg|[[Marie Curie]], c. 1898
</gallery>

The list of important 19th-century scientists includes:
{{colbegin}}
*[[Amedeo Avogadro]], physicist
*[[Johann Jakob Balmer]], mathematician, physicist
*[[Henri Becquerel]], physicist
*[[Alexander Graham Bell]], inventor
*[[Ludwig Boltzmann]], physicist
*[[János Bolyai]], mathematician
*[[Louis Braille]], inventor of [[braille]]
*[[Robert Bunsen]], chemist
*[[Marie Curie]], physicist, chemist
*[[Pierre Curie]], physicist
*[[Gottlieb Daimler]], engineer, industrial designer and industrialist
*[[Charles Darwin]], biologist
*[[Christian Doppler]], physicist, mathematician
*[[Thomas Edison]], inventor
*[[Michael Faraday]], scientist
*[[Léon Foucault]], physicist
*[[Gottlob Frege]], mathematician, logician and philosopher
*[[Sigmund Freud]], the father of psychoanalysis
*[[Carl Friedrich Gauss]], mathematician, physicist, astronomer
*[[Francis Galton]], English [[Victorian era|Victorian]] [[polymath]]
*[[Willard Gibbs|Josiah Willard Gibbs]], physicist
*[[Ernst Haeckel]], biologist
*[[William Rowan Hamilton]], physicist and mathematician
*[[Oliver Heaviside]], electrical engineer, physical mathematician
*[[Heinrich Hertz]], physicist
*[[Alexander von Humboldt]], naturalist, explorer
*[[Robert Koch]], physician, bacteriologist
*[[Justus von Liebig]], chemist
*[[Nikolai Lobachevsky]], mathematician
*[[James Clerk Maxwell]], physicist
*[[Wilhelm Maybach]], car-engine and automobile designer and industrialist
*[[Ilya Mechnikov]], biologist
*[[Gregor Mendel]], biologist
*[[Dmitri Mendeleev]], chemist
*[[Samuel Morey]], inventor
*[[Alfred Nobel]], chemist, engineer, inventor
*[[Louis Pasteur]], microbiologist and chemist
*[[Ivan Pavlov]], physiologist
*[[Santiago Ramón y Cajal]], biologist
*[[Franz Reuleaux]] mechanical engineer
*[[Bernhard Riemann]], mathematician
*[[William Emerson Ritter]], biologist
*[[Vladimir Shukhov]], inventor
*[[William Thomson, 1st Baron Kelvin|William Thomson]], Lord Kelvin, physicist
*[[Thomas Young (scientist)|Thomas Young]]<!--(1773-1829)-->, English [[polymath]].
{{colend}}

==References==
{{reflist}}

{{19th century}}

[[Category:19th century in science| ]]