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Georg Friedrich Bernhard Riemann was a German mathematician who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis. His 1859 paper on the prime-counting function, containing the original statement of the Riemann hypothesis, is regarded as a foundational paper of analytic number theory. Through his pioneering contributions to differential geometry, Riemann laid the foundations of the mathematics of general relativity. He is considered by many to be one of the greatest mathematicians of all time.
Johann Peter Gustav Lejeune Dirichlet was a German mathematician. In number theory, he proved special cases of Fermat's last theorem and created analytic number theory. In analysis, he advanced the theory of Fourier series and was one of the first to give the modern formal definition of a function. In mathematical physics, he studied potential theory, boundary-value problems, and heat diffusion, and hydrodynamics.
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Julius Wilhelm Richard Dedekind was a German mathematician who made important contributions to number theory, abstract algebra, and the axiomatic foundations of arithmetic. His best known contribution is the definition of real numbers through the notion of Dedekind cut. He is also considered a pioneer in the development of modern set theory and of the philosophy of mathematics known as Logicism.
Jean-Baptiste Joseph Fourier was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and vibrations. The Fourier transform and Fourier's law of conduction are also named in his honour. Fourier is also generally credited with the discovery of the greenhouse effect.
References
- ↑ 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. Archived from the original (PDF) on 2021-05-22. Retrieved 2011-10-20.
- ↑ 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.
- ↑ 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.
- ↑ "Portfolio of Historic Concertina Patents".
- ↑ 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.