Carl Wolfgang Benjamin Goldschmidt
Carl Wolfgang Benjamin Goldschmidt (1807–February 15, 1851) was a German astronomer, mathematician, and physicist of Jewish descent who was a professor of astronomy at the University of Göttingen. He is also known as Benjamin Goldschmidt, C. W. B. Goldschmidt, Carl Goldschmidt, and Karl Goldschmidt.
A student of Carl Friedrich Gauss and an assistant to Gauss at the university observatory, Goldschmidt frequently collaborated with Gauss on various mathematical and scientific works. Goldschmidt was in turn a professor of Gauss's protegé Bernhard Riemann. Data gathered by Gauss and Goldschmidt on the growth of the logarithmic integral compared to the distribution of prime numbers was cited by Riemann in "On the Number of Primes Less Than a Given Magnitude", Riemann's seminal paper on the prime-counting function.
In 1831, Goldschmidt wrote a mathematical treatise in Latin, "Determinatio superficiei minimae rotatione curvae data duo puncta jungentis circa datum axem ortae" ("Determination of the surface-minimal rotation curve given two joined points about a given axis of origin"). The paper dealt with the problem in the calculus of variations of determining the minimal surface of revolution, the surface of revolution of the planar curve between two given points which minimizes surface area. Solutions to the problem exist which are not continuous; such discontinuous solutions are known as Goldschmidt solutions in honor of Goldschmidt's discovery of them.
In 1834, Goldschmidt co-authored, in German, the textbook Lehrbuch der analytischen Optik (Textbook of Analytical Optics) with J. C. Eduard Schmidt. Together with Gauss and Wilhelm Eduard Weber, Goldschmidt published in 1840 Atlas des Erdmagnetismus: nach den Elementen der Theorie entworfen (Atlas of Geomagnetism: According to the Elements of the Theory of Design), a series of magnetic maps. In 1845, Goldschmidt published, also in German, a book on electromagnetism, Untersuchungen über die magnetische Declination in Göttingen (Studies of the Magnetic Declination in Göttingen).
- Nahin, Paul J. (2011). When Least Is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible. Princeton University Press. p. 272. "[...] obituary notice that appeared in the 1851 volume of the American Journal of Science (pp. 443–4). There it is reported that Carl Wolfgang Benjamin Goldschmidt was a professor of astronomy at the University of Göttingen [...] and served as an assistant to the great Gauss at the observatory there. [...] He had long suffered from the consequences of an enlargement of the heart; and on the morning of Feb. 15, he was found in his bed, sleeping the sleep that knows no waking."
- Dunnington, G. Waldo (2004). Carl Friedrich Gauss: Titan of Science. Mathematical Association of America. p. 226. "On February 15, 1851, Gauss' assistant Benjamin Goldschmidt died very suddenly at the age of forty-four. He had been observing the night before and had shown some visitors the Pleiades through the telescope. He was found dead in bed early the next morning."
- Kolmogorov, Andrei N.; Yushkevich, Adolf-Andrei P. (1996). Mathematics of the 19th Century: Vol. II: Geometry, Analytic Function Theory. Springer Publishing. p. 199. "Thus in the summer he [Bernhard Riemann] attended the lectures of Moritz Stern (1807–1894) on the numerical solution of equations and those of Karl Goldschmidt (1807–1851) on terrestrial magnetism [...]"
- Küssner, Martha (1982). "Carl Wolfgang Benjamin Goldschmidt und Moritz Abraham Stern, zwei Gaußschüler jüdischer Herkunft" [Carl Wolfgang Benjamin Goldschmidt and Moritz Abraham Stern, Two Gauss Students of Jewish Origin]. Mitteilungen der Gauß-Gesellschaft [Releases of the Gauss Society] (in German) (Göttingen) (19): 37–62.
- Lehrbuch der analytischen Optik (Google eBook). Google Books. Retrieved 2012-08-27.
- Nahin, Paul J. (2011). When Least Is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible. Princeton University Press. p. 266. "This discontinuous behavior is called the Goldschmidt solution, after the German mathematician C. W. B. Goldschmidt (1807–51) who discovered it (on paper) in 1831."
- Riemann, Bernhard (November 1859). "Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse" [On the Number of Primes Less Than a Given Magnitude]. Monatsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin (in German).
- Bibliographic Information: Determinatio superficiei minimae rotatione curvae data duo puncta jungentis circa datum axem ortae. Google Books. Retrieved 2012-08-27.
- Weisstein, Eric W.. "Minimal Surface of Revolution". Mathworld. Wolfram Research. Retrieved 2012-08-29.
- Weisstein, Eric W.. "Goldschmidt Solution". Mathworld. Wolfram Research. Retrieved 2012-08-29.
- "Book Details Page: Atlas Des Erdmagnetismus: Nach Den Elementen Der Theorie Entworfen". World Ebook Fair. Retrieved 2012-08-27.
- "Atlas Des Erdmagnetismus: Nach Den Elementen Der Theorie Entworfen". Alibris. Retrieved 2012-08-27.
- Bibliographic Information: Untersuchungen über die magnetische Declination in Göttingen. Google Books. Retrieved 2012-08-27.