1829 in science
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- Peter Gustav Lejeune Dirichlet publishes a memoir giving the Dirichlet conditions, showing for which functions the convergence of the Fourier series holds; introducing Dirichlet's test for the convergence of series; the Dirichlet function as an example that not any function is integrable; and, in the proof of the theorem for the Fourier series, the Dirichlet kernel and Dirichlet integral. He also introduces a general modern concept for a function.
- Nikolai Ivanovich Lobachevsky publishes his work on hyperbolic non-Euclidean geometry.
- S. D. Poisson publishes Sur l'attraction des sphéroides.
- Jules Desnoyers names the Quaternary period.
- Engis 2, part of the skull of a young child and other bones, recognised in 1936 as the first known Neanderthal fossil, is found in the Awirs cave near Engis in the United Kingdom of the Netherlands (modern-day Belgium) by Philippe-Charles Schmerling.
- May – Cyrill Demian patents a version of the accordion in Vienna.
- June 30 – Henry Robinson Palmer files a British patent application for corrugated iron for use in buildings.
- July 23 – In the United States, William Burt obtains the first patent for a form of typewriter, the typographer.
- October 6–14 – The Rainhill Trials, a steam locomotive competition, are run in England and won by Stephenson's Rocket.
- December 19 – Charles Wheatstone patents the concertina in Britain.
- Louis Braille publishes the first description of his method of embossed printing that allows the visually impaired to read.
- Chalmers University of Technology founded in Gothenburg, Sweden.
- Technical University of Denmark (originally named 'College of Advanced Technology') founded in Copenhagen, Denmark.
- University of Stuttgart founded in Stuttgart, Germany.
- Ecole Centrale Paris (originally named 'École Centrale des Arts et Manufactures') founded in Paris, France.
- February 2
- March 23 – N. R. Pogson (died 1891 in science), English-born astronomer.
- April 28 – Charles Bourseul (died 1912), Belgian-born telegraph engineer.
- April 30 – Ferdinand von Hochstetter (died 1884), German-born geologist.
- August 13 (O.S. August 1) – Ivan Sechenov (died 1905), "the father of Russian physiology".
- August 23 – Moritz Cantor (died 1920), German historian of mathematics.
- August 24 - Emanuella Carlbeck (died 1901), Swedish pioneer in the education of students with intellectual disability.
- September 7 – August Kekulé (died 1896), German chemist.
- September 30
- October 15 - Asaph Hall (died 1907), American astronomer.
- November 4 - Hanna Hammarström (died 1909), Swedish inventor.
- March 1 – Thomas Earnshaw (born 1749), English watchmaker.
- April 6 – Niels Henrik Abel (born 1802), Norwegian mathematician.
- May 10 – Thomas Young (born 1773), English physicist.
- May 29 – Humphry Davy (born 1778), English chemist.
- June 29 – James Smithson (born 1764), English mineralogist, chemist and benefactor.
- November 14 – Louis Nicolas Vauquelin (born 1763), French chemist.
- October 10 – Maria Elizabetha Jacson (born 1755), English botanist.
- December 28 – Jean-Baptiste Lamarck (born 1744), French naturalist.
- undated - Huang Lü, Chinese scientist.
- Bressoud, David M. (2007). A radical approach to real analysis (2nd ed.). [Washington, D.C.]: Mathematical Association of America. pp. 218–227. ISBN 978-0-88385-747-2.
- Elstrodt, Jürgen (2007). "The Life and Work of Gustav Lejeune Dirichlet (1805–1859)" (PDF). Clay Mathematics Proceedings. 7. Retrieved 2011-10-20. CS1 maint: discouraged parameter (link)
- Crilly, Tony (2007). 50 Mathematical Ideas you really need to know. London: Quercus. pp. 108–111. ISBN 978-1-84724-008-8.
- Radomski, Teresa (2005). "Manuel García (1805–1906): a bicentenary reflection" (PDF). Australian Voice. 11: 25–41. Retrieved 2012-02-07. CS1 maint: discouraged parameter (link)
- Schmerling, Philippe-Charles (1833). Recherches sur les ossements fossiles découverts dans les cavernes de la Province de Liège. Liège: P.-J. Collardin. S. 1–66.
- Thomson, Nick (2011). Corrugated Iron Buildings. Oxford: Shire Publications. pp. 7–8. ISBN 978-0-7478-0783-4.
- U.S. Patent 5581X.
- Procédé pour écrire les Paroles, la Musique et le Plain-chant au moyen de points, à l'usage des Aveugles et disposés pour eux. Paris.
- "Copley Medal | British scientific award". Encyclopedia Britannica. Retrieved 22 July 2020. CS1 maint: discouraged parameter (link)